TECHNICAL FIELD
The present invention relates to a method for automatically
equalizing a sound system.

BACKGROUND
In the past, the normal practice has been to acoustically
optimize dedicated systems such as motor vehicles by hand. Although there have been
major efforts in the past to automate this manual process, these methods, for example
the Cooper/Bauk method have, however, shown weaknesses in practice. In small, highly
reflective areas, such as the interior of a car there were generally no improvements
in the acoustics. In most cases, the results are even worse.

Up to now, major efforts were devoted to analysis and correction
of these inadequacies. Methods for equalization of acoustic poles and nulls (= CAP
method) occurring jointly at different listening locations are worthy of mention,
or those intended to achieve equalization with the aid of a large number of sensors
in the area with the assistance, for example of the MELMS (=Multiple Error Least
Mean Square) algorithm. Spatial filters or smoothing methods such as complex smoothing
according to John N. Mourjopoulos, or else centroid methods have led only to a limited
extent to the aim of achieving good acoustics in a poor acoustic environment. However,
the fact that it is possible to achieve a good acoustic result even with simple
means has been proven by the work by professional acousticians.

Actually, there is already one method which allows any
acoustics to be modelled in virtually any area. However, wave-field synthesis requires
very extensive resources such as computation power, memories, loudspeakers, amplifier
channels, etc. This technique is thus not suitable at the moment for motor vehicle
applications, for cost and feasibility reasons.

SUMMARY
It is an object of the present invention to provide an
automated method for equalizing a sound system, e.g., in a passenger compartment
of a motor vehicle, which replaces the previously used, complex process of manual
equalizing by means of experienced acousticians and reliably provides frequency
responses of the level and of the phase of the reproduced sound signal at the predetermined
seating positions in the vehicle interior which, as most accurately, match the profile
of predetermined target functions. Said sound system includes at least two groups
of loudspeakers supplied with electrical sound signals to be converted into acoustical
sound signals,

The method according to the present invention for automatically
adjusting such sound system to a target sound comprises the steps of: individually
supplying each group with the respective electrical sound signal; individually assessing
the deviation of the acoustical sound signal from the target sound for each group
of loudspeakers; and adjusting at least two groups of loudspeakers to a minimum
deviation from the target sound by equalizing the respective electrical sound signals
supplied to said groups of loudspeakers.

Accordingly, an automatic, e.g., iterative method for equalizing
the magnitude and phase of the transfer function of all of the individual loudspeakers
of a sound system, e.g., in a motor vehicle is disclosed which determines all of
the necessary parameters for equalizing without any manual actions and thus, e.g.,
provides appropriate filtering in a digital signal processing system.

The advantageous effect of the invention results from the
completely automatic matching of the transfer function of the sound system to a
predetermined target function, in which case the number and frequency range of the
loudspeakers which are used for the sound system may be variable.

Further advantages may result if an automatic algorithm
approaches the predetermined target function, by considering each individual loudspeaker
of a pair of loudspeakers which form a stereo pair in the sound system individually,
and by optimizing each individual loudspeaker with regard to equalizing its transfer
function.

Even further advantages can also be obtained if not only
the equalizing of the loudspeakers in the sound system is carried out by means of
the automatic algorithm, but also the crossover filters for all of the loudspeakers
in the sound system are modelled and implemented in a digital signal signal processing
system.

Even further advantages can likewise result if the automatic
algorithm optimizes the equalizing not only for one seat position, for example that
of the driver, but allows all of the seat positions in a motor vehicle, and thus
listener positions, to be included in the equalizing process with selectable weighting.

BRIEF DESCRIPTION OF THE DRAWINGS
The invention can be better understood with reference to
the following drawings and description. The components in the figures are not necessarily
to scale, instead emphasis being placed upon illustrating the principles of the
invention. Moreover, in the figures, like reference numerals designate corresponding
parts. In the drawings:

- Figure 1
- shows the Blauert direction-determining bands;
- Figure 2
- shows curves of equal volume for the planar sound field;
- Figure 3
- shows a transfer function of a broadband loud-speaker and the method for automatically
finding the crossover frequencies;
- Figure 4
- shows transfer function and the level function of a woofer loudspeaker pair
or of an individual sub-woofer of a loudspeaker, and the method for automatically
finding the crossover frequencies;
- Figure 5
- shows transfer functions and level functions for the method for automatically
finding the cross-over frequencies of a sub-woofer loudspeaker while at the same
time using a woofer loudspeaker pair;
- Figure 6
- shows magnitude frequency responses of all the loudspeakers and the resultant
overall magnitude frequency response of a sound system including crossover filters
after pre-equalizing has been carried out with and without sub-woofer loud-speakers;
- Figure 7
- shows overall magnitude frequency responses of the sound system before and after
equalizing the overall magnitude frequency response;
- Figure 8
- shows a measurement arrangement in a motor vehicle for determination of the
binaural transfer functions for mono signals and stereo signals;
- Figure 9
- shows the spectral weighting function for the measurement at different positions;
- Figure 10
- shows the sound pressure levels in the lower frequency range at four listening
positions over frequency;
- Figure 11
- shows the sound pressure distribution of a standing wave in a vehicle interior;
- Figure 12
- shows phase shift of one channel at certain frequency related to a reference
channel;
- Figure 13
- shows a three-dimensional diagram of phase equalization function with no phase
limiting;
- Figure 14
- shows an equalization phase frequency response for a certain position with respect
to a reference signal in the example of figure 13;
- Figure 15
- shows a three-dimensional diagram of phase equalization function with phase
limiting;
- Figure 16
- shows the equalization phase frequency response for a certain position with
respect to a reference signal in the example of figure 15;
- Figure 17
- shows a modelled equalizing phase frequency response for a certain position
with respect to the reference signal;
- Figure 18
- shows the transfer functions of the sums of all speakers at different positions
before phase equalization;
- Figure 19
- shows the transfer functions of the sums of all speakers at different positions
after phase equalization;
- Figure 20
- shows the transfer functions of the sums of all speakers at different positions
after phase equalization and phase shift limiting;
- Figure 21
- shows the transfer functions of the sums of all speakers at different positions
after phase equalization and phase shift limiting;
- Figure 22
- shows the transfer functions of the sums of all speakers at different positions
after phase equalization;
- Figure 23
- the global amplitude equalization function for the bass management;
- Figure 24
- shows the transfer functions of the sums of all speakers at different positions
after phase and global amplitude equalization; and
- Figure 25
- shows signal flow diagram of a system for executing a method according to the
present invention.

DETAILED DESCRIPTION
The following example describes the procedure and the investigations
in order to create an algorithm which is also referred to in the following text
as AutoEQ, for automatically adjusting, e.g., of equalizing filters in accordance
with the present invention. Two procedures are investigated which are disclosed
in detail further below, together with a sequential method and a method taking account
of the maximum interval between a measured level profile and a predetermined target
function. The results obtained are used to derive a method, which is then used for
automatic equalizing, that is to say without any manual influence on the parameters
involved. The major tonal sensitivities to be taken into account in this case which
comprise psycho-acoustic parameters of human perception of sounds, are the location
capability, the tonality and the staging.

In this case, the location capability, which is also referred
to as localization, denotes the perceived location of a hearing event, as a result,
for example from the superimposition of stereo signals. The tonality results from
the time arrangement and the harmony of sounds and the ratio of the background noise
to the useful signal that is presented, for example, stereophonic audio signals.
Staging is used to refer to the effect of perception of the point of origin of a
complex hearing event that is composed of individual hearing events, such as that
which results from an orchestra, in which case individual hearing events, for example
instruments, always have their own location capability.

In principle, the location capability of phantom sound
sources which are produced by stereophonic audio signals depends on a plurality
of parameters, the delay-time difference of arriving sound signals, the level difference
of arriving sound signals, the inter-aural level difference of an arriving sound
between the right and left ear (inter-aural intensity difference IID), the inter-aural
delay time difference of an arriving sound between the right and left ear (inter-aural
time difference ITD), the head related transfer function HRTF, and on specific frequency
bands in which levels have been raised, with the spatial directional localization
in terms of front, above and to the rear depending solely on the level of the sound
in these frequency bands without their being any delay-time difference or level
difference in the sound signals at the same time in the latter case.

The major parameters for spatial-acoustic perception are
the inter-aural time difference ITD, the inter-aural intensity difference IID and
the head related transfer function HRTF. The ITD results from delay-time differences
between the right and left ear in response to a sound signal arriving from the side,
and may assume orders of magnitude of up to 0.7 milliseconds. If the speed of sound
is 343 m/s, this corresponds to a difference of about 24 centimetres in the path
length of an acoustic signal, and thus to the anatomical characteristics of a human
listener. In this case, the hearing evaluates the psycho-acoustic effect of the
law of arrival of the first wavefront. At the same time it is evident for a sound
signal which arrives at the head at the side, that the sound pressure which is applied
to the ear which is spatially further away is less (IID) owing to sound attenuation.

It is also known that the auricle of the human ear is shaped
such that it represents a transfer function for received audio signals into the
auditory system. The auricles thus have a characteristic frequency response and
phase response for a given sound signal incidence angle. This characteristic transfer
function is convolved with the sound which is entering the auditory system and contributes
considerably to the spatial hearing capability. In addition, a sound which reaches
the human ear is also changed by further influences. These changes are caused by
the environment of the ear, that is to say the anatomy of the body.

The sound which reaches the human ear has already been
changed on its path to the ear not only by the general spatial acoustics but also
by shadowing of the head or reflections on the shoulders or on the body. The characteristic
transfer function which takes account of all of these influences is in this case
referred to as the head related transfer function (HRTF) and describes the frequency
dependency of the sound transmission. HRTFs thus describe the physical features
which the auditory system uses for localization and perception of acoustic sound
sources. In this case, there is also a relationship with the horizontal and vertical
angles of the incident sound.

In the simplest embodiment of a stereo presentation, correlated
signals are offered via two physically separated loudspeakers, forming a so-called
phantom sound source between the two loudspeakers. The expression phantom sound
source is used because a hearing event is perceived where there are no loudspeakers
as a result of the superimposition and addition of two or more sound signals produced
by different loudspeakers. When two correlated signals at the same level are reproduced
by two loudspeakers in a stereo arrangement, then the sound source (phantom sound
source) is located as being on the loudspeaker base, that is to say in the centre.
This also applies in principle to the presentation of audio signals via sound systems
using a large number of loudspeakers, as are normally used nowadays both in domestic
stereo systems and in motor vehicle applications.

A phantom sound source can move between the loudspeakers
as a result of delay-time and/or level differences between the two loudspeaker signals.
Level differences of between 15 and 20 dB and delay-time differences of between
0.7 and 1 ms, up to a maximum of 2 ms are required to shift the phantom sound source
to the extreme on one side, depending on the signal.

The asymmetric seat position (driver, front-seat passenger,
front and rear row or rows of seats) for loudspeaker configuration in a vehicle
leads to sounds arriving neither with the same phase nor with the same delay time
with respect to the position of a single listener. This primarily changes the spatial
sensitivity, although the tonality and localization are also adversely affected.
The staging propagates on both sides unequally in front of the listener. Although
delay-time correction with respect to an individual listener position would be possible,
this is not desirable since this would automatically lead to matching specifically
for one individual seat, with a disadvantageous effect on the remaining seats in
the motor vehicle.

As already mentioned above, the spatial directional localization
also depends on the level of the sound in specific frequency bands, without there
being any delay-time difference or level difference between the sound signals at
the same time (for example a mono signal arriving from the front). By way of example,
investigations have in this case shown that, for a mid-frequency of 1 kHz and above
10 kHz (narrowband test signal), test subjects locate a signal that is offered as
being behind them, while an identical sound event with a mid-frequency of 8 kHz
is localized as being above. If a signal contains frequencies of around 400 Hz or
4 kHz, then this enhances the impression that the sound has come from in front,
and thus the presence of a signal. These different frequency ranges, which are shown
in Figure 1, are referred to as Blauert direction-determining bands (see
Jens Blauert, Räumliches Hören, [Spatial listening] S. Hirzel Verlag,
Stuttgart, 1974
) and the knowledge of the effect of these various frequency bands on the
spatial localization of a complex sound signal can be very helpful for filtering
or equalizing complex sound signals in order to produce desired hearing sensitivities,
since it is possible to determine in advance those frequency ranges in which, by
way of example, filtering and equalizing associated with it will best achieve the
greatest possible desired effect.

The influences of the various parameters, such as the level
in different frequency ranges, the level differences between loudspeakers and loudspeaker
groups, phase differences between the signals on arrival at the right and left ear,
have been investigated in the following text with respect to the effect on the localization
capability, tonality and staging, in order then to use the knowledge obtained to
derive a method for automatic equalizing of sound systems, for example in motor
vehicles.

During the investigations, it was found that the production
of stable tonal properties and good location (localization capability) can essentially
be achieved only by influencing the phase angle of the arriving sound signals and
not by equalizing of the amplitudes. In this case, the matching process was carried
out taking into account the Blauert direction-determining bands mentioned above
and taking account of individual loudspeaker groups in the sound system. According
to the invention, the procedure is in this case similar to the known procedure by
acousticians for adjustment of an optimum hearing environment. This procedure is
characterized in that groups of mutually associated loudspeakers are processed successively
in order to determine their contribution to a desired required frequency response
(sequential method).

The required frequency response, which is used as a reference
in this case and is also referred to in the following text as the target function
of the level and phase profile over the frequency, is determined during hearing
trials. In this case, a sound system with all of the individual loudspeakers is
simulated in laboratory conditions (low-echo room) as in the situation, for example
when producing sound in passenger compartments in motor vehicles. A significant
group of trial subjects is in this case offered various sound signals which comprise
music of different styles, such as classical, rock, pop, etc. The trial subjects
reproduce their subjective hearing impression (tonality, localization capability,
presence, staging, etc.) for different settings of the parameters of the sound system,
such as cut-off frequencies of the crossover filters of the loudspeakers, the level
profile in the various spectral ranges and thus loudspeaker groups (woofers, medium-tone
speakers, tweeters) or the phase angle of the sound signals arriving at the location
of the test subjects. This results in an idealized target function being determined
which is used as a reference for the equalizing of sound systems in motor vehicles,
and which is intended to be achieved as exactly as possible by these sound systems
in actual environmental conditions. In this case, it should be noted that complex
sound systems now allow hearing environments to be created which have desired individual
features and which thus, for example, can be associated by trained listeners with
specific manufacturers of sound systems and/or, for example, loudspeakers.

The loudspeaker groups which have been mentioned further
above and have been mentioned for the equalizing of a sound system in order to achieve
an optimum listening environment in this case, by way of example, comprise the groups
of sub-woofers, woofers, rear, side, front and centre, and the phases of these loudspeaker
groups, for example front left and front right, are matched by the equalizing process
such that signals from the respective loudspeaker groups arrive as far as possible
in the same phase as the left and right ear, thus making it possible to achieve
the best-possible location capability effect.

Typically, the process of adjustment of the tonality is
started once the phases of the individual, independent loudspeaker groups have been
matched. For this purpose, the individual loudspeaker groups are first of all equalized
separately with respect to the level, corresponding to the sum target function.
This results in all of the medium-high-tone loudspeaker pairs sounding similar.
Excessive levels in an individual loudspeaker group and/or in an individual spectral
range would reduce the so-called sweet spot, that is to say that spatial area in
which the listening experience is at its best in terms of the stated parameters,
since the localization is fixed on that loudspeaker group which actually produces
the highest level for the signal being reproduced at that time.

Once this process of equalizing the individual loudspeaker
pairs has been carried out, the levels of these individual groups are then matched
to one another. This is done in a simple form by changing the maxima of the measured
sound levels of the individual broadband loudspeaker groups to a common level value.
This can be done by reducing the levels of specific loudspeaker groups, increasing
the levels of specific loudspeaker groups or by a mixture of these techniques. In
each case, care is taken to ensure that none of the loudspeaker groups is overdriven
by raising the level, which could result in undesirable effects, such as non-linear
distortion, while excessive reduction in the level would no longer ensure adequate
transmission of all of the frequency components associated with this loudspeaker
group.

The levels for matching of the bass channels, which are
likewise predistorted in the previous equalizing process, are in this case determined
using a somewhat modified method, to be precise by relating the sum function of
all of the loudspeaker groups for the medium-tone range to a target function. In
the broadband case, the levels of the bass channels are dealt with differently during
the matching process.

In a further method step, the level, averaged over the
frequency range of the respective loudspeaker group, of this loudspeaker group can
also be used as a measure for the extent to which the individual loudspeaker groups
must be matched to one another, that is to say must be changed to a common, medium
level value. In this case, care is taken, as mentioned above, to ensure that this
matching process does not lead to undesirable effects such as excessively high or
excessively low sound levels from the individual loudspeaker groups.

Furthermore, sound levels can be assessed before the matching
process, using the so-called A-assessed level. As can be seen from Figure 2, the
sensitivity of the human ear depends on the frequency. Tones at very low frequencies
and tones at very high frequencies are in this case perceived as being quieter than
medium-frequency tones.

The expressions volume and loudness that are used in this
context relate to the same sensitivity variable and differ only in their units.
They take account of the frequency-dependent sensitivity of the human ear. The psycho-acoustic
variable loudness indicates how loud a sound event at a specific level, with a specific
spectral composition and for a specific duration is perceived to be subjectively.
The loudness is doubled when a sound is perceived as being twice as loud and thus
allows comparison of different sound events with respect to the perceived volume.
The unit for assessment and measurement of loudness is in this case the sone. A
sone is defined as the perceived volume of a sound event of 40 phons, that is to
say the perceived volume of a sound event which is perceived as being equally loud
to a sinusoidal tone at the frequency of 1 kHz with a sound pressure level of 40
dB.

At medium and high volume levels, an increase in the volume
by 10 phon leads to the loudness being doubled. At low volume levels, even minor
volume increases lead to the perceived loudness being doubled. The volume as perceived
by people in this case depends on the sound pressure level, the frequency spectrum
and the behaviour of the sound over time and is likewise used for modelling of masking
effects. By way of example, standardized measurement methods for loudness measurement
also exist according to DIN 45631 and ISO 532 B.

Figure 2 illustrates curves of equal volume. In this case
the frequency is plotted logarithmically on the abscissa, and the level L of the
offered narrowband sounds is plotted along the ordinate. For various level volumes
L_{N} whose unit is the phon, and associated loudnesses N whose unit is
the sone, it can be seen that tones or noises with the same sound pressure level
L are perceived as being quieter at low and high frequencies than at medium frequencies.
The illustration in Figure 2 has been taken from
E. Zwicker and R. Feldtkeller, Das Ohr als Nachrichtenempfänger [The
ear as an information receiver], S. Hirzel Verlag, Stuttgart, 1967
.

This knowledge about the frequency dependency of volume
sensitivity can be taken into account according to the invention by subjecting the
frequencies contained in the sound to the A-assessment as mentioned above, before
matching of the various loudspeaker groups. The A-assessment is a frequency-dependent
correction of measured sound levels, by means of which the physiological hearing
capability of the human ear is simulated, with the level values which result from
this assessment being stated using dB(A) as the units. As generally known, highs
and lows are reduced and medium-levels are (slightly) increased by the A-assessment.

A considerably different matching process is obtained,
however, by further subdividing the frequency range into subgroups rather than making
use of the relatively coarse subdivision of the offered frequency band, as is initially
carried out by means of the individual loudspeaker groups. This prevents any level
peaks in closely bounded frequency ranges in a loudspeaker group resulting in a
corresponding reduction of all of the frequency ranges represented by this loudspeaker
group. This subdivision can, in this case, be carried out in fractions of thirds
for example, or in regions which are oriented to the characteristics of the human
hearing. This subdivision will be described in more detail further below.

Since the addition of the level profiles of the individual,
equalized frequency ranges or loudspeaker groups does not necessarily correspond
to the profile of the desired required frequency response, the sum function itself
which is obtained from the addition of the individual, equalized ranges and groups
is equalized in a further process step. According to the invention, the procedure
is in this case once again similar to the known procedure by acousticians for adjustment
of an optimum hearing environment, that is to say the sequential processing of loudspeaker
groups.

During this process, the group with the greatest influence
on the profile of the sum level is first of all changed such that this results in
a profile that is as close as possible to the required frequency response. This
change to the loudspeaker group with the greatest influence is carried out within
previously defined limits, which once again ensure that none of the loudspeaker
groups is overdriven by raising the level, which could result in undesirable effects
such as non-linear distortion, while excessively reducing the level could mean that
adequate transmission of all frequency components associated with this loudspeaker
group was no longer ensured.

If the aim of approximating the profile of the required
frequency response as exactly as possible with the loudspeaker group which makes
the greatest contribution to the change in the sum level is not achieved in the
frequency range under consideration in this case, that group which makes the next
greater contribution to changing the sum level is then varied. According to the
invention, this procedure is continued until either the required frequency response
is adequately approximated, or the predetermined limits, as defined in advance,
for the permissible level change in the corresponding group are reached.

The investigations carried out have also shown that staging
and spatial sensitivity can be influenced by the change in the sequence of processing
of the groups, with desirably good staging being achieved in particular when the
volumes of the various loudspeaker groups are changed with respect to one another.
If, by way of example, front-seat passengers were to be given the hearing impression
that the staging is perceived further in front, the rear and/or the side loudspeakers
would have to be reduced and/or the front loudspeakers or the centre loudspeaker
would have to have their or its levels raised.

If, in contrast, the perceived location of the staging
is initially too far upwards or downwards, or else too far forwards or backwards,
the desired effect can be achieved, that is to say the perceived location of the
staging can be optimized as desired, by appropriate moderate level changes in the
area of the Blauert direction-determining bands (see Figure 1). However, it is obvious
that even in the case of moderate level changes in the area of the Blauert direction-determining
bands, or if individual loudspeaker groups are raised or lowered in order to optimize
the staging, a subsequent change in the sum level which has already been matched
to the required frequency response and thus a renewed, possibly undesirable, discrepancy
from the required frequency response, can result.

In order to keep this undesirable effect, the subsequent
changing of the sum level which has already been matched to the required frequency
response, as a result of the optimization of the staging as small as possible, the
sequential processing is defined in advance in a specific manner, according to the
invention. In this case, the procedure according to the invention comprises definition
of the sequence of processing of the individual loudspeaker groups for adjustment
of the equalizing, in advance, in such a way that this empirically ensures that
the discrepancy from the approximation that has already been achieved to the required
frequency response is minimized.

If, by way of example, one wished to move the perceived
location of the staging further forwards, which is normally a situation that occurs
frequently, it is recommended that the equalizing be carried out in the following
sequence of loudspeaker groups: sub-woofer, woofer, rear, side, centre and front.
Variations in this fixed predetermined sequence can in this case be defined depending
on the situation with regard to the current acoustic environment and the preference
for a specific acoustic configuration. For example, from experience, it is possible
in this case to interchange the rear and side as well as the centre and front loudspeakers
in the sequence with the desired staging still being produced in this case as well,
but allowing variations in the overall impression of the acoustic environment. This
allows good staging to be achieved by skilful choice, defined in advance, of the
sequence of processing of the loudspeaker groups during the procedure per se, without
excessively changing the sum level which has already been matched to the required
frequency response.

In general, the aim is to carry out an equalizing process
which is as independent as possible of position, for acoustic presentation in motor
vehicles. This means that the aim of the equalizing process should not only result
in a sweet spot as such but should also cover the region of optimum presentation,
covering as large a spatial area as possible, while providing spatial areas of optimum
presentation that are as large as possible at the respective positions of the driver
and front-seat passenger as well as in the rear row or rows of seats. If one observes
the manual work by acousticians with the same aim in the measurement and equalizing
of sound systems for passenger compartments in motor vehicles, then it is evident
that these acousticians set the filters for equalizing of each loudspeaker group
to be left/right-balanced. This is understandable, because both the arrangement
of the loudspeakers of a sound system per se and the interior of the passenger compartment
of a motor vehicle, with the exception of the steering wheel and dashboard, are
normally designed to be strictly left/right symmetrical. This procedure is also
adopted in the method according to the invention for automatic equalizing according
to the present invention.

In order to determine the results achieved by the respective
equalizing process by recording of the impulse responses of the regulated sound
system, two B & K (Brüel & Kjaer, Denmark) S" microphones without any
separating disc and separated by 150 mm, were introduced, during the course of the
investigations, at the four seat positions for the driver, front-seat passenger,
rear left and rear right, which corresponds to the normal measurement method for
investigation of the transfer functions in sound systems.

A further aspect of the optimization of the acoustic presentation
via a sound system is the setting of the crossover filters, also referred to as
frequency filters, for the individual loudspeakers. In principle, these crossover
filters must be adjusted as a first step before carrying out any equalizing process
on the entire sound system. During the course of the investigations carried out,
it was in this case found that it was relatively complicated to develop a suitable
algorithm with acceptable computation complexity for automatic adjustment of the
crossover filters and, initially, these crossover filters were therefore not adjusted
automatically during the course of the further investigations so that, initially,
they were adjusted manually (a method for automatic adjustment of crossover filters
is described further below). Manual adjustment such as this can be carried out quickly
and effectively if, as in the present case, the physical data for the loudspeakers
and their installation state are known. FIR filters (finite impulse response filters)
or IIR filters (infinite impulse response filters) can also be used as an embodiment
for the crossover filters.

FIR filters are characterized in that they have an extremely
linear frequency response in the transmission range, a very high cut-off attenuation,
linear phase and constant group delay time, have a finite impulse response and operate
in discrete time steps, which are normally governed by the sampling frequency of
an analogue signal. An Nth order FIR filter is in this case described by the following
differential equation:
$$\mathrm{y}\left(\mathrm{n}\right)\mathrm{=}{\mathrm{b}}_{\mathrm{0}}\mathrm{*}\mathrm{x}\left(\mathrm{n}\right)\mathrm{+}{\mathrm{b}}_{\mathrm{1}}\mathrm{*}\mathrm{x}\left(\mathrm{n},\mathrm{-},\mathrm{1}\right)\mathrm{*}{\mathrm{b}}_{\mathrm{2}}\mathrm{*}\mathrm{x}\left(\mathrm{n},\mathrm{-},\mathrm{2}\right)\mathrm{+}\mathrm{\dots}\mathrm{+}{\mathrm{b}}_{\mathrm{N}}\mathrm{*}\mathrm{x}\left(\mathrm{n},\mathrm{-},\mathrm{N}\right)\mathrm{=}{\displaystyle \mathrm{\sum}_{\mathrm{i}\mathrm{=}\mathrm{0}}^{\mathrm{N}}}{\mathrm{b}}_{\mathrm{i}}\mathrm{*}\mathrm{x}\left[\mathrm{n},\mathrm{-},\mathrm{i}\right]$$

where y(n) is the initial value of the time n and is calculated from the sum, weighted
with the filter coefficients b_{i}, of the N most recently sampled input
values x(n-N) to x(n). In this case, the desired transfer function and thus the
filtering of the signal are achieved by the definition of the filter coefficients
b_{i}.

In contrast to FIR filters, IIR filters also use already
calculated initial values in the calculation (recursive filters) and they are characterized
in that they have an infinite impulse response, no initial oscillations, no level
drop and a very high cut-off attenuation. The disadvantage in comparison to FIR
filters is that IIR filters do not have a linear phase response, as is often highly
desirable in acoustic applications. Since the calculated values in the case of IIR
filters become very small after a finite time, however, the calculation can in practice
be terminated after a finite number of sample values n, and the computation power
complexity is considerably less than that required for FIR filters. The calculation
rule for an IIR filter is:
$$\mathrm{y}\left(\mathrm{n}\right)\mathrm{=}{\displaystyle \mathrm{\sum}_{\mathrm{i}\mathrm{=}\mathrm{0}}^{\mathrm{N}}}{\mathrm{b}}_{\mathrm{i}}\mathrm{*}\mathrm{x}\left(\mathrm{n},\mathrm{-},\mathrm{i}\right)-{\displaystyle \mathrm{\sum}_{\mathrm{i}\mathrm{=}\mathrm{0}}^{\mathrm{N}}}{\mathrm{a}}_{\mathrm{i}}\mathrm{*}\mathrm{y}\left(\mathrm{n},\mathrm{-},\mathrm{i}\right)$$

where y(n) is the initial value of the time n and is calculated from the sum, weighted
with the filter coefficients b_{i}, of the sampled input values x(n) added
to the sum, weighted with the filter coefficients a_{i} of the initial values
y(n). In this case, the desired transfer function is once again achieved by the
definition of the filter coefficients a_{i} and b_{i}.

In contrast to FIR filters, IIR filters may in this case
be unstable, but have a higher selectivity for the same implementation complexity.
In practice, the filter chosen is that which best satisfies the required conditions
taking into account the requirements and computation complexity associated with
them.

In the present case, it is thus preferred that crossover
filters in the form of IIR filters be used. The use of FIR filters is advantageous
because of the linear profile of the phase in the case of FIR filters, but would
lead to an undesirably high level of computation complexity during use owing to
the low filter cut-off frequencies required. IIR filters were thus used as the basis
for the crossover filters in the following text, in which case these crossover filters
are adjusted before carrying out the automatic equalizing process according to the
invention (AutoEQ) with their parameters first of all being transferred to the subsequent
AutoEQ algorithm so that the phase distortion in the transmitted signals caused
by these IIR filters can be taken into account in the calculation of the equalizing
filters for phase matching, as described further above, for the location capability,
and, if necessary, can be compensated for appropriately.

The channel gains of the individual loudspeaker groups
should likewise also be set before the start of an automatic equalizing process.
This may be done manually or automatically. The step-by-step procedure for automatic
matching in one preferred embodiment is described, by way of example, as follows:

- 1. Automatic matching of the maximum values of the magnitudes of the frequency
responses of all the broadband loudspeaker groups to the highest value, so that
the quieter loudspeaker groups down to the quietest loudspeaker group are raised
to the maximum value of the magnitude of the frequency response of the loudest loudspeaker
pair.
- 2. Automatic matching of the averaged levels of the broadband loudspeaker groups,
which have already been equalized automatically and individually in advance, to
a target function.
- 3. Formation of the sum of the magnitudes of the frequency responses of the
broadband loudspeakers whose levels have in the meantime been matched.
- 4. Setting of the channel gains of the woofer loudspeakers to the maximum value
or to the mean level of the sum of the magnitudes of the frequency responses of
the broadband loudspeakers.
- 5. Formation of the new sum of the magnitudes of the frequency responses of
the broadband loudspeakers including the woofer loudspeakers.
- 6. Setting of the channel gain of the sub-woofer loudspeaker to the new maximum
value or to the mean level of the new sum of the magnitudes of the frequency responses
of the broadband loudspeakers, including the woofer loudspeakers from 5.

Furthermore, the maximum values of the levels and/or the
mean values of the levels can optionally also be assessed for the method steps 1
to 6 as described above, before matching with the A-assessed level. As described
further above, the A-assessment represents a frequency-dependent correction of measured
sound levels which simulates the physiological hearing capability of the human ear.

In contrast to the use of crossover filters, FIR filters,
whose advantages have already been described further above, are used in the implementation
of the filters as determined for the automatic equalizing (AutoEQ algorithm) in
the amplifier of a sound system. Since, depending on the embodiment and in particular
when they have a wide bandwidth, these FIR filters can result in stringent requirements
for the computation power of a digital signal processor on which they are carried
out, the psycho-acoustic characteristics of the human hearing are made use of again
in this case, as well. According to the invention this is achieved in that the filtering
is carried out by means of FIR filters via a filter bank, with the bandwidth of
the filters increasing as the frequency increases, in a manner which corresponds
to the frequency-dependent, integrating characteristic of the human hearing.

The modelling of the psycho-acoustic hearing sensitivities
is in this case based on fundamental characteristics of the human hearing, in particular
of the inner ear. The human inner ear is incorporated in the so-called petrous bone,
and is filled with incompressible lymph fluid. In this case, the inner ear is in
the form of a worm (cochlea) with about 2.5 turns. The cochlea in turn comprises
channels which run parallel, with the upper and lower channel being separated by
the basilar lamina. The cortical organ with the hearing sense cells is located on
this lamina. When the basilar lamina is caused to oscillate by sound stimuli, so-called
moving waves are formed during this process, that is to say there are no oscillation
antinodes or nodes. This results in an effect which governs the hearing process,
the so-called frequency/location transformation on the basilar lamina, which can
be used to explain psycho-acoustic concealment effects and the pronounced frequency
selectivity of the hearing.

In this case, the human hearing comprises different sound
stimuli which fall in limited frequency ranges. These frequency bands are referred
to as critical frequency groups or else as the critical bandwidth CB. The frequency
group width has its basis in the fact that the human hearing combines sounds which
occur in specific frequency ranges, in terms of the psycho-acoustic hearing sensitivities
which result from these sounds, to form a common hearing sensitivity. Sound events
which are within a frequency group in this case produce different influences than
sounds which occur in different frequency groups. Two tones at the same level within
one frequency group are, for example, perceived as being quieter than if they were
in different frequency groups.

Since a test tone within a masker is audible when the energy
levels are the same and the masker falls in the frequency band which the frequency
of the test tone has as its mid-frequency, it is possible to determine the desired
bandwidth of the frequency groups. At low frequencies, the frequency groups have
a bandwidth of 100 Hz. At frequencies above 500 Hz, the frequency groups have a
bandwidth which corresponds to about 20% of the mid-frequency of the respective
frequency group (
Zwicker, E.; Fastl, H. Psycho-acoustics - Facts and Models, 2nd edition, Springer-Verlag,
Berlin/Heidelberg/New York, 1999
).

If all of the critical frequency groups are arranged in
a row over the entire hearing range then this results in a hearing-oriented non-linear
frequency scale which is referred to as tonality, with the Bark as the unit. This
represents a distorted scaling of the frequency axis, so that frequency groups have
the same width of precisely 1 Bark at each point. The non-linear relationship between
the frequency and tonality originates from the frequency/location transformation
on the basilar lamina. The tonality function has been stated by Zwicker (
Zwicker, E.; Fastl, H. Psycho-acoustics - Facts and Models, 2nd edition, Springer-Verlag,
Berlin/Heidelberg/New York, 1999
) on the basis of monitoring threshold and loudness investigations, in
tabular form. As can be seen, 24 frequency groups can actually be arranged in a
row in the audibility frequency range from 0 to 16 kHz, so that the associated tonality
range is 0 to 24 Bark.

Transferred to the application in a sound system amplifier
according to the invention, this means that a filter bank is preferably formed from
individual FIR filters whose bandwidth is in each case 1 Bark or less. Although
FIR filters are used for automatic equalizing as investigations progress and in
order to produce embodiments, possible alternatives exist which, for example, comprise
rapid convolution, the PFDFC algorithm (Partition Frequency Domain Fast Convolution
Algorithm), WFIR filters, GAL filters or WGAL filters.

For automatic equalizing of the levels and/or amplitudes
of the sound system, two different methods were investigated, which are referred
to in the following text as "MaxMag" and "Sequential". "MaxMag" in this case searches
in the manner described further above in all of the available independent loudspeaker
groups to find that which, in terms of its maximum or average level, is furthest
away from the target function of the frequency profile and thus provides the greatest
contribution to approximation to the target function by raising or lowering the
level. If the maximum possible level change of the selected loudspeaker group, which
is restricted to the region of predefined limit values, is in this case found not
to be adequate for complete approximation to the target function, the value which
is set for the selected loudspeaker group within the permissible limit values is
that which allows the greatest possible approximation to the target function and,
following this, the loudspeaker group which is selected and whose level is changed
is that which now has the greatest level difference from the target function from
the group of loudspeaker groups whose levels have not yet been matched. This method
is continued until either the target function is reached with sufficient accuracy
or the dynamic limits of the overall system, that is to say the permissible reductions
or increases (limit values) by equalizers are exhausted within the respective loudspeaker
groups.

In contrast, as has been described in detail above, the
sequential method processes the existing loudspeaker groups successively in a previously
defined sequence, in which case the user can produce the described influence on
the mapping of the staging by the previous definition of the sequence. In this case
the automatic algorithm also attempts to achieve the best approximation to the target
function just by the equalizing of the first loudspeaker group within the permissible
limits (dynamic range).

To further improve this method, it was modified in such
a way that each group no longer reaches its maximum dynamic limits at each frequency
location but may now only act at the restricted dynamic range. The algorithm uses
the ratio of the signal vectors of the relevant group to the existing sum signal
vector at this frequency location as a weighting parameter. This avoids the first
groups provided for processing being excessively (over a broad bandwidth) attenuated.
With the introduction of the self-scaling target function, which is oriented on
the minimum of the sum function and then scales the target function such that the
minimum value of the sum transfer function in a predetermined frequency range is
located exactly by the maximum permissible increase below the target function, this
indicated the strengths and weaknesses of the two versions "MaxMag" and "Sequential".

However, this procedure can lead to the level profile of
the first loudspeaker group, which is modified by equalizing using the described
"sequential" method, being raised or lowered more than proportionally over a broad
bandwidth while, in contrast, the other loudspeaker groups which are processed using
the "sequential" method, are not subject to any changes, or only to minor changes,
since the target function has already been largely approximated by the equalizing
of the first loudspeaker group. One possibly disadvantageous effect in this case
is that the first loudspeaker in the defined sequence may experience a major increase
or attenuation as the result of this procedure, with the following loudspeaker groups
remaining largely unchanged, so that the frequency range which is represented by
the first loudspeaker group is more than proportionally amplified or attenuated,
which could lead to a considerable discrepancy from the desired sound impression.

The "sequential" method was thus subsequently modified
such that a single loudspeaker group may now no longer be raised or lowered within
its theoretical maximum available dynamic range, but only within a dynamic range
which is less than this. This reduced dynamic range is calculated from the original
maximum dynamic range by weighting this original maximum dynamic range with a factor
which is obtained from the ratio of the overall level of the relevant loudspeaker
group to the totaled overall level from all of the loudspeaker groups in this frequency
range in the relevant loudspeaker group, so that this factor is always less than
unity and results in a restriction to the maximum dynamic range which can be regulated
out for the relevant loudspeaker group. This reliably avoids the level profiles
of the first loudspeaker groups that are processed in the sequence previously determined
being undesirably strongly raised or lowered in the course of the automatic equalizing
process.

In order to take account of this restriction to the maximum
control range (dynamic range) of the loudspeaker groups, a modification has also
been introduced in the target function to be achieved, in order always to ensure
reliable approximation to the target function of the desired level and phase profile
despite the reduced control range of the loudspeaker groups. In this case, the target
function to be achieved is raised or lowered over its entire level profile (parallel
shifting of the level profile without changing the frequency response, also referred
to in the following text as scaling), such that, in predetermined frequency ranges,
the interval between this target function and the sum function of the level profile
of all the loudspeaker groups to be considered and to be adjusted by the automatic
equalizing process is not greater than the maximum increase or decrease as determined
using the above method in the level profile of the individual loudspeaker groups.

The specified frequency ranges in which the level profiles
of the target function and sum function of all the loudspeaker groups are compared,
may, for example be oriented to the transmission bandwidths of the loudspeaker groups
being used, but preferably to the Bark scale, as explained further above, that is
to say in the region of frequency-group wide frequency ranges or partial ranges,
thus once again taking account of the physiological hearing capability of the human
hearing in this case in particular tone level perception and volume sensitivity
(loudness).

The results of the loudspeaker settings achieved by the
two "sequential" and "MaxMag" methods on the basis of the embodiment described above
were obtained by hearing trials with suitable subjects, that is to say subjects
with experience in the assessment of sound environments produced by sound systems.
In this case, these trials were carried out in order to assess the major parameters
of the hearing impression, such as location capability, tonality and staging for
in each case four seat positions in the passenger compartment of a motor vehicle.
These seat positions comprise the driver, front-seat passenger, rear left and rear
right.

For the method based on the "MaxMag" method, these hearing
trials showed the tonality of the sound impression was found to be highly positive
both on the front seats and on the rear seats. One disadvantage in the assessment
of the use of the "MaxMag" method was that a deterioration in the localization and
localization clarity and hence also of the staging, was perceived at all of the
seat positions.

Because the process based on the "MaxMag" method for equalizing
of the individual loudspeaker groups first of all places the major emphasis on that
loudspeaker group whose variation (raising or lowering) approximates the sum function
over all the loudspeaker groups with the greatest contribution to a predetermined
target function, an automated process can result in an unsuitable processing sequence
of the loudspeaker groups. For example, it is possible for a situation to occur
in which the automated algorithm for equalizing first of all identifies, in the
case of the loudspeaker group for the front loudspeakers, the greatest contribution
for the desired approximation to the target function, and correspondingly strongly
raises or lowers its level profile.

As is known from the descriptions provided further above,
however, the front loudspeakers in particular contribute a major proportion to,
for example, good staging and, furthermore, this relates to their transmission quality,
they are relatively unproblematic in comparison to other loudspeaker groups in the
sound system by virtue of the installation location and the loudspeaker quality
which can thus be used. In a situation such as this, further loudspeaker groups
which may have disturbing spectrum components that have an adverse effect on the
location capability will no longer be included in the automatic equalizing process,
resulting in the parameters becoming worse, in the manner which has been mentioned.

For the process based on the "sequential" method, the hearing
trials resulted in very good channel separation and localization clarity for the
offered audio signals in all seat positions. Although very good tonality was also
achieved, at the front seat positions using the "sequential" method, this tonality
at the rear seat position became considerably worse as a result of the variation
of the loudspeaker groups dealt with first according to the method, with the degree
of this deterioration increasing in proportion to the respective maximum permissible
raising or lowering in the respective loudspeaker groups. This means that the process
based on the "sequential" method, despite the already introduced reduction in the
maximum decrease or increase in the individual loudspeaker groups, in particular
in the first loudspeaker groups in the predetermined sequence of processing, still
results in an automatic algorithm producing excessive variation.

In the embodiments of the automatic equalizing process
investigated so far, neither of the two methods used always produce good results
in the hearing tests carried out, although the "sequential" method appeared overall
to be advantageous in comparison to the "MaxMag" method. Further modifications to
the described methods are investigated in the following text in order to achieve
both good localization and good tonality in an automated process, and to achieve
both of these at both the front and rear seat positions in the passenger compartment
of a motor vehicle.

The further investigations have shown that, when using
the "sequential" method, an even greater restriction to the permissible reduction
in the level of the loudspeaker groups, in particular of the first loudspeaker groups
in the respective specified sequence, made it possible to achieve a result which
was satisfactory for all seat positions even for tonality as the hearing sensitivity.
This was not satisfactory at the rear seat positions with the previous embodiment
for automatic equalizing. As mentioned further above, the target function to be
achieved is raised or lowered over its entire level profile (scaling, parallel shifting
of the level profile without variation of the frequency response), such that the
interval between this target function and the sum function of the level profile
of all the loudspeaker groups to be considered and to be adjusted by the automatic
equalizing process is no greater in predetermined frequency ranges than the maximum
permissible increase or decrease in the level profile of the individual loudspeaker
groups in the respective frequency range.

This means that the target function to be approximated
by the equalizing process is aligned by virtue of this scaling in its absolute position
at the minimum level of the sum function of the level profile of all the loudspeaker
groups to be considered, which generally leads to a reduction, which in some cases
is considerable, in this target function to be approximated, since the sum function
of the level profile of all the loudspeaker groups to be considered normally has
a highly fluctuating profile with pronounced maxima, and, in particular, minima.
It is thus desirable to vary the sum function of the level profile of all the loudspeaker
groups to be considered in a previous processing step such that these pronounced
maxima and in particular minima, no longer occur and, as a consequence of this,
the matching or scaling of the absolute position of the target function to this
sum function results in far less reduction in the original specified target function.

This is achieved in the following text by matching, which
is referred to as "pre-equalizing" of the levels of the individual loudspeaker groups
(not the sum function) to the target function of the level profile, with this pre-equalizing
process being coordinated with the equalizing of the phases as already described
further above and as carried out even before the equalizing, in which the phases
are matched by equalizing such that signals from the respective loudspeaker groups
arrive as far as possible in phase at the left ear and at the right ear. This previous
pre-equalizing of the individual loud speaker groups also results in the sum function
that results from the level profiles of the individual loudspeaker groups being
approximated at this stage to the target function to such an extent that the problem
described above of major reduction in the target function as a consequence of pronounced
minima in the sum function no longer occurs.

The equalizing values which are determined in the course
of the pre-equalizing process may in this case be used as initial values for the
subsequent, final equalizing by means of the "sequential" method. However, before
the addition of the level profile over all of the loudspeaker groups, the levels
of the loudspeaker groups as approximated to the target function in a first step
by means of the pre-equalizing process must, however, be matched to one another
within their frequency ranges which are bounded by the respectively associated crossover
filters. This matching process is necessary because the efficiency of the various
loudspeaker groups may be different, and it is desirable for each loudspeaker group
to produce volume sensitivity that is identical as possible, which, when the volume
sensitivity is the same for the sound components of the various loudspeaker groups,
can lead to these loudspeaker groups being operated at considerably different electrical
voltage levels in order to produce these sound components.

The level difference between the groups is also amplified
by the pre-equalizing process, because the dynamic range of the equalizer is designed
such that major reductions, but only slight increases, are permitted. If the frequency
response of a group differs to a major extent from the target function, a considerable
level reduction must therefore be expected. Major level increases are therefore
not permissible, because they will be perceived as disturbing, particularly in conjunction
with high filter Q factors.

As it has been possible to verify in appropriate hearing
trials and measurements, the desired result of the described method is obtained
in that, once the equalizing steps have been carried out, the transmission response
of all the loudspeaker groups is maintained over a broad bandwidth and the loudspeaker
groups each in their own right make a contribution to the overall sound impression,
which leads to good tonality and the largest possible sweet spot at all four passenger
locations under consideration.

Furthermore, the resultant sum transfer function, that
is to say the addition of the level profiles over all of the loudspeaker groups,
is approximated by the step of pre-equalizing in its own right to the target function
of the desired level frequency response to such an extent that this target function
need no longer be reduced to such a major extent in the scaling process with respect
to the sum function minima, which are in consequence less pronounced.

As described above, this is once again a precondition for
the use according to the invention of one of the two methods already described ("sequential"
and "MaxMag") for automatic equalizing of the sum of the level profiles of all the
loudspeaker groups in the sound system, in order, in the end, also to obtain a balanced
sound impression at all seat positions.

So far, the equalizing of the loudspeakers has always been
carried out in groups of more than one loudspeaker. However, more extensive investigations
have shown that equalizing of each individual loudspeaker in all the loudspeaker
groups (forming groups of only one loudspeaker each) on the basis of the magnitude
and phase made it possible to achieve even better results, although this process
resulted in the previously achieved strict symmetry of the sound field now no longer
being obtained. In this case, the advantages of individual equalizing of all the
individual loudspeakers was evident not only at one location in the passenger compartment
of the motor vehicle, for example the driver's seat position, but also at the other
seat positions.

One precondition for this is that the results of the transfer
functions recorded binaurally at different seating positions using the described
measurement method are included with appropriate weighting in the definition of
the equalizing filters. As expected, it was possible to achieve the best results
by equal weighting of the binaurally measured transfer functions. This equated consideration
of the spatial transfer functions of the left and right hemisphere leads to quasi-balanced
acoustics in the vehicle interior even though the equalizing filters are now set
on a loudspeaker-specific basis.

This equalizing process on an individual loudspeaker basis
increases the number of filters to be considered individually by virtually 50%,
since a dedicated equalizing filter and thus a dedicated filter coefficient set
are now also required in each case in the algorithm for automatic equalizing, per
loudspeaker, for the loudspeaker groups which are arranged symmetrically with respect
to the longitudinal axis of the vehicle interior and whose transfer function as
in the past in each case was equalized by means of a common equalizing filter. The
additional complexity which results from this and the consequently more stringent
requirements for the computation power of the digital signal processor for provision
of the equalizing filters, appear in the opinion of the inventors to be justified,
however, since the results of the hearing tests in some cases resulted in considerable
and significant improvements in the perceived hearing impression.

The two-stage procedure described so far, with pre-equalizing
followed by equalizing of the sum function of the transfer function of all the loudspeakers,
was retained, with both pre-equalizing and equalizing now being carried out on a
loudspeaker-specific basis, by virtue of the described advantages. In contrast to
the previous sequence of the processing steps, the matching of the channel gain
was, however, no longer carried out subsequently but after the pre-equalizing has
been carried out. In this case, both the matching of the channel gains and the adjustment
of the crossover filters are carried out directly as before, for each loudspeaker
group.

This means that the transfer functions of the individual
loudspeakers of a symmetrically arranged pair of stereo loudspeakers in each case
have the same channel gain and the same crossover filter applied to them. This stipulation
has been made since, in the course of the investigations, situations occurred in
which, when using loudspeaker-specific channel gains, particularly in the case of
woofer loudspeakers, major differences in some cases occurred in the individual
channel gains, which shifted the sound impression in an unnatural and undesirable
manner in space. Problems of the same type would also occur if the crossover filters
were designed on a loudspeaker-specific basis. A loudspeaker-specific crossover
filter would admittedly make it possible for each loudspeaker in a loudspeaker group,
normally a loudspeaker pair, to be operated with maximum efficiency in its frequency
range, but loudspeaker environments or installation conditions which are not the
same can result in situations in which the transmission range of one loudspeaker
in a loudspeaker group differs to a major extent from that of another loudspeaker
in the same loudspeaker group. If the crossover filters in a situation such as this
were designed on a loudspeaker-specific basis, this could likewise lead to undesirable
spatial shifts in the resultant sound impression.

After carrying out the crossover filtering, the loudspeaker-specific
pre-equalizing both of the phase response and of the magnitude frequency response,
as well as the matching of the channel gain, fine matching of the sum transfer function
is now carried out, that is to say of the sum of the level profiles of all the loudspeakers
involved, to the target function. In contrast to the previous procedure, the process
based on the "MaxMag" method is in this case preferred to the process based on the
"sequential" method. Since the pre-equalizing process is now carried out on a loudspeaker-specific
basis, only a small number of narrowband frequency ranges of individual loudspeakers
now need to be modified by the filter algorithm in order to achieve the desired
approximations of the target function, and the broadband and major level changes
produced by the equalizing filters, which in the past when using the "MaxMag" method
have led to the undesirable results in terms of the location capability, no longer
occur. The results of the hearing trials confirm that, for using the loudspeaker-specific
pre-equalizing process, a good localization capability is now achieved even with
the process for automatic equalizing based on the "MaxMag" method, in which case
the tonality was also additionally improved by the previous loudspeaker-specific
pre-equalizing process.

In contrast, the use of the process based on the "sequential"
method in conjunction with loudspeaker-specific equalizing may now have considerable
disadvantages, which are evident in the form of major spatial shifting of the sound
impression. This is due to the fact that the first individual loudspeaker in the
processing chain in the sequence defined in the "sequential" method will in the
worst case have its transfer function in all of the relevant frequency ranges change,
normally by being reduced, by the equalizing filters to such a major extent that
the distance from the target function becomes minimal (as is the aim of this method).
If this aim has already been achieved adequately by the first individual loudspeaker,
all of the subsequent loudspeakers would no longer be processed any further by the
automatic algorithm, in particular and in addition not the partner in the balanced
loudspeaker pair with which the individual loudspeaker whose transfer function has
been changed is associated. This will result in a broadband and one-sided, for example,
reduction in the level profile in the frequency range of the relevant individual
loudspeaker, which would lead to undesirable spatial shifting of the location of
the perception of the sound events.

If required, this effect could be counteracted by in each
case still applying the process based on the "sequential" method to each of the
known loudspeaker groups jointly irrespective of the loudspeaker-specific pre-equalizing.
However, investigations have shown that the changed initial situation resulting
from the loudspeaker-specific pre-equalizing for the process of the equalizing based
on the "sequential" method leads to poorer results in comparison to the "sequential"
method with pre-equalizing being carried out in groups so that this method was no
longer considered any further subsequently in conjunction with loudspeaker-specific
pre-equalizing.

A renewed investigation of the influence of non-linear
smoothing showed that excessive smoothing (for example third averaging) led to a
"lifeless", "soft" or "washed-out" sound impression, while in contrast, no smoothing
or only excessively weak smoothing (for example third/12 averaging) resulted in
an excessively "hard", "piercing" sound impression. Therefore third/8 averaging
may be a good compromise.

As stated further above, the crossover filters were adjusted
manually in the course of the previous investigations, for simplicity reasons. In
the following, an approach is searched for in order to carry out this adjustment
process automatically as well, since the aim of the present invention is to develop
automatic equalizing, which is as comprehensive as possible and covers all aspects,
of a sound system in a motor vehicle, including the adjustment of the crossover
filters in the automatic equalizing process, as well.

The following disclosure relating to the automatic adjustment
of the crossover filters is based on the assumption that Butterworth filters of
a sufficient order are, in principle, sufficient for the desired delineation of
the respective frequency response of the relevant loudspeaker. The empirical values
of acousticians, maintained over many years, for the equalizing of sound systems
show that fourth-order filters are adequate both for high-pass and low-pass filters
in order to achieve the desired crossover filter quality. A higher-order filter
would result in advantages, for example by having a steeper edge gradient, however
the amount of computation time required for this purpose for implementation in digital
signal processors would rise in a corresponding manner at the same time. Fourth-order
Butterworth filters are therefore used in the following text.

The transfer function of the left rear loudspeaker, measured
binaurally using the described measurement method and averaged over the recordings
at the driver's seat and the front-seat passenger's seat, is shown in comparison
to the target function being used in the top left of Figure 3. As can be seen in
this case, it appears from this illustration to be difficult, particularly in the
lower frequency range, to define a lower cut-off frequency of the crossover high-pass
filter from the profile of the measured transfer function in comparison to the profile
of the target function. In contrast, a suitable upper cut-off frequency of a cross-over
low-pass filter can be determined quite easily in the present case.

The right-hand upper illustration in Figure 3 shows the
same transfer function for the left rear loudspeaker, measured binaurally using
the described measurement method and averaged over the recordings at the driver's
seat and front-seat passenger's seat in comparison to the target function used,
after carrying out the pre-equalizing process according to the invention. As can
be seen, the range boundaries of the transfer function of the investigated broadband
loudspeaker stand out in a significantly more pronounced manner and can be read
from the graph without any difficulties. In this case, personnel who are experienced
in this special field are assisted by practice in handling the representation and
the meaning of such transfer functions. However, in conjunction with carrying out
an automated equalizing process, this raises the question of how the definition
of the cut-off frequencies of a cross-over filter can be determined sufficiently
accurately and reliably with the aid of an algorithm.

The algorithm which has been developed for this purpose
is described in the following. In a first step, the difference is formed between
the target function and the transfer function of the respective loudspeaker as determined
after the pre-equalizing process. The result associated with the example under discussion
is shown in the illustration at the bottom left in Figure 3. This difference transfer
function, which is also referred to for short in the following text as the difference,
is then investigated in the next step, to determine the frequency of this difference
function at which it is within, above, or below a specific, predetermined limit
range. The threshold values defined in the illustrated example form a symmetrical
limit range with limits at, for example, +/-6 dB around the null point of the difference
function which results at all frequencies at which the transfer function as determined
after pre-equalizing at a level corresponding to the target function.

Since, as stated further above, the human hearing inter
alia has a frequency resolution related to the frequency, the difference transfer
function as calculated from the measured data and the target function was introduced
into a level difference function, which had been smoothed by averaging, before evaluation
of whether the limit range had been overshot or undershot. The mean value at the
respective frequency is in this case preferably calculated from empirical values
over a range with a width of 1/8 third octave band (in the following mentioned just
as "third"). This means that the frequency resolution of the smoothed level difference
function is high at low frequencies and decreases as the frequency increases. This
corresponds to the fundamental frequency-dependent behaviour of the human hearing
to whose characteristics the illustration of the level difference function in Figure
3 is thus matched.

The level difference spectrum is then smoothed once again
in a further processing step with the aid of a simple first-order IIR low-pass filter
in the direction from low to high frequencies and in the direction from high to
low frequencies in order to eliminate bias problems and smoothing-dependent frequency
shifts resulting from them. The level difference spectrum processed in this way
is now compared by the automatic algorithm with the range limits (in this case +/-6
dB), and this is used to form a value for the trend of the profile of the level
difference spectrum. In this case, the value "1" for this trend denotes that the
upper range limit has been exceeded at the respective frequency of the level difference
spectrum, while the value "-1" indicates that the lower range limit of the level
difference spectrum has been undershot at the respective frequency, and the value
"0" for the trend indicates level values of the level difference spectrum at the
respective frequency which are within the predetermined range limits. The result
in evaluations such as this can be seen in the illustration at the bottom right
in Figure 3, with the graph in red showing the described and calculated trend of
the level difference spectrum at the respective frequency.

Despite the described smoothing of the signal of the level
difference spectrum before evaluation of the trend, if the level difference spectra
are initially unknown in an automated method, that is to say when using an automatic
algorithm, it is possible for a situation to occur in which predetermined range
limits are exceeded within a relatively narrow spectral range when, for example,
the loudspeaker and/or the space into which sound is being emitted have/has a narrowband
resonance point, and the profile of the level difference spectrum then falls again
below the predetermined range limit (situations of the same type can also occur
when the predetermined range limits are undershot). In situations such as these,
the previously described method cannot determine clear cut-off frequencies for the
cross-over filters.

Thus, in a further processing step, the level values determined
by averaging using a filter in each case with a width of 1/8 third are thus investigated
for the frequency of successive overshoots and undershoots of the predetermined
range limits. Only when a specific minimum number (which can be predetermined in
the algorithm) of related overshoots and undershoots of the predetermined range
limits is overshot at successive frequency points is this interpreted by the algorithm
as reliable overshooting or undershooting of the predetermined range limits, and
thus as a frequency position of a cut-off frequency of the crossover filter. In
the present case, with range limits of +/-6 dB and with smoothing of the level profile
using filters with a width of 1/8 third, and a level spectrum resulting from this
with discrete level values separated by 1/8 third, this minimum number of associated
level values which overshoot or undershoot the range limits (+/-6 dB) is typically
about 5-10 level values.

Depending on whether the respective loudspeakers that are
being dealt with by the algorithm are loudspeakers designed to have a broadband
or narrowband transmission response, upper and lower frequency ranges are predetermined
within which the upper and lower cut-off frequency of the respective loudspeaker
type will move, from experience, or on the basis of the characteristic data for
that loudspeaker. In this way, the automatic algorithm can be designed to be very
robust and appropriate by the addition of parameters or parameter ranges known in
advance. In the case of the broadband loudspeakers that are used in the present
case, by way of example, a minimum, lower cut-off frequency of f_{gu} =
50 Hz can be assumed, while in the case of narrowband loudspeakers (woofers) used
in the low-tone range, an upper cut-off frequency of f_{go} = 500 Hz can
be assumed. If the largest found and related level overshoot or level undershoot
range is now located within the frequency range delineated in this way, the extreme
value of the level overshoot and/or level undershoot is now looked for within this
frequency range (maximum and minimum in the level profile).

If, in this case, this extreme value of the largest found
and related level overshoot or level undershoot range is in this case below a specific
cut-off frequency (for example about 1 kHz), and if this extreme value furthermore
also has a negative value (minimum), then the decision is made to use a high-pass
filter for the sought crossover filter. In order to find the cut-off frequency of
this high-pass filter, a search is now carried out, starting from the frequency
of the minimum, in the direction of higher frequencies within the level difference
function as determined after pre-equalizing for its first intersection with the
0 dB line. This frequency denotes the filter cut-off frequency of the crossover
high-pass filter.

If the extreme value of the largest found and related level
overshoot or level undershoot range is above a specific cut-off frequency (for example
about 10 kHz), and if this extreme value furthermore also has a negative value (minimum),
then the decision is made to use a low-pass filter for the sought crossover filter.
In order to find the cut-off frequency of this low-pass filter a search is now carried
out starting from the frequency of the minimum in the direction of lower frequencies
within the level difference function as determined after pre-equalizing, for its
first intersection with the 0 dB line. This frequency denotes the filter cut-off
frequency of the crossover low-pass filter.

If a plurality of extreme values exist, in which case at
least the two most pronounced must be of a negative nature, and if the first minimum
is below a specific cut-off frequency (for example about 1 kHz) and the other minimum
is above a specific cut-off frequency (for example about 10 kHz), then the decision
is made to use a bandpass filter for the sought crossover filter. In order to find
the cut-off frequencies of this bandpass filter, a search is now carried out starting
from the frequency of the minimum which is below the cut-off frequency of, for example,
about 1 kHz in the direction of higher frequencies within the level difference function
determined after the pre-equalizing, for its first intersection with the 0 dB line,
and from the other minimum from its frequency in the direction of lower frequencies,
for the first intersection with the 0 dB line. These frequencies then denote the
filter cut-off frequencies of the crossover bandpass filter as the result of the
automatic algorithm according to the invention. If applied to the example as illustrated
in Figure 3, this results in a crossover bandpass filter with a lower cut-off frequency
of f_{gu}= 125 Hz and an upper cut-off frequency of f_{go} = 7887
Hz.

The crossover filter cut-off frequencies for all of the
broadband loudspeakers in the medium and high-tone range of the sound system to
be regulated and to be equalized are determined and set in the manner described
above. The crossover filter cut-off frequencies of the narrowband low-tone loudspeakers
must be dealt with separately, in further steps, and are restricted here just to
logical range limits which, however, still need not represent final values. In general,
the lower range limit of the crossover filters for the low-tone loudspeakers remains
after the above processing at its lower cut-off value of f_{gu} = 10 Hz
while, in contrast, the upper range limit is generally governed by the lowermost
cut-off frequency of all of the broadband loudspeakers, provided that this is greater
than the lower cut-off frequency of the broadband loudspeakers (for example about
50 Hz). This prior stipulation is important for the described method because, once
all of the crossover filter cut-off frequencies have been set, the complete automatic
equalizing process (AutoEQ) is carried out once again in order to achieve a more
accurate approximation to the target function, with the crossover filters being
taken into account, in a second run. The final range limits of the crossover filters
for the low-tone loudspeakers can then be looked for as will be described in the
following text.

Once, as described above, the crossover filters of all
of the broadband loudspeakers have been defined and the cross-over filters of the
narrowband loudspeakers in the low-tone range have been preset to suitable values,
the search for better filter cut-off frequency values for the low-tone loudspeakers
can be started. This procedure is necessary because the frequency transition from
the narrowband loudspeakers for low-tone reproduction to the broadband loudspeakers
depends on the nature and number of the low-tone loudspeakers being used and thus
cannot easily be determined in a comparable manner.

In principle, a distinction is drawn between two typical
situations for adjustment of the crossover filter cut-off frequencies, with the
lower spectral range of the low frequencies being modelled by only one sub-woofer
or only one woofer stereo pair in the first situation and with the lower spectral
range of the low frequencies being modelled by a woofer stereo pair together with
a sub-woofer in the other situation. Irrespective of which of the two situations
is appropriate, the crossover filter cut-off frequencies of the woofers are in this
case always defined and determined in the same way and a distinction is just drawn
in the calculation of the crossover filter cut-off frequencies for the sub-woofer
between the two situations mentioned above. The crossover filter cut-off frequencies
of the sub-woofer are in this case calculated in the same way as that for the woofer
stereo pair in the situation in which only one subwoofer and no woofer stereo pair
is used. Only in the situation in which a woofer stereo pair is also present in
addition to the sub-woofer is the way in which the crossover filter cut-off frequencies
of the sub-woofer are calculated changed.

As shown in the illustration at the top left in Figure
4, particularly in the case of the transition from the woofer loudspeakers to the
broadband loudspeakers in the range from about 50 Hz to about 150 Hz, there is a
peak in the sum magnitude frequency response (blue curve in Figure 4, illustration
top left) with respect to the target function. In this case, it should be noted
that the sum magnitude frequency response was formed only from the level contributions
of the broadband loudspeakers and the level contributions of the woofer loudspeakers.
Any sub-woofer loudspeaker which may be present is in this case ignored at this
stage. In order to keep the peak in the sum magnitude frequency response within
the transitional range as small as possible, or in order to match this transitional
range to the target function as well as possible, as indicated by the boundary lines
in the illustrations in Figure 4, a search for a difference which is as balanced
as possible between the sum transfer function after pre-equalizing (blue curve Figure
4, illustration top left) and the target function (black curve in Figure 4, illustration
top left) carried out only in an upper and lower spectral range. The upper spectral
range within which a search is carried out for a minimum distance in this case results
from the upper filter cut-off frequency of the woofer loudspeakers, which has already
been determined prior to this, that is to say during the search for the crossover
filter cut-off frequencies of the broadband loudspeakers. In this case, the minimum
from the double upper filter cut-off frequency and the maximum permissible upper
filter cut-off frequency of the low-tone loudspeakers which, as stated above, was
defined to be f_{go} = 500 Hz, determines the upper limit of the upper spectral
range while half its value determines the associated lower limit of the upper spectral
range. The lower limit of the lower spectral range for the search for the cut-off
frequency results, in contrast to this, from the maximum of the minimum permissible
lower filter cut-off frequency of the low-tone loudspeakers which, as stated above,
was set to f_{gu} = 10 Hz, and from half of the lower filter cut-off frequency,
as already found. The upper limits of the lower spectral range for searching for
the cut-off frequency results from twice the value of the lower limit.

The decision as to whether the upper or the lower cut-off
frequency of the crossover filter for the woofer loudspeakers should be reduced
or increased is, however, not made directly from the profile of the difference between
the sum magnitude frequency response and the target function (distance) but from
the previously smoothed level profile, as is illustrated by way of example in the
illustration top right in Figure 4.

As mentioned further above, the procedure for determination
of the crossover filter cut-off frequencies for the relevant loudspeakers or loudspeaker
groups is identical in the situation in which the sound system either comprises
only a single sub-woofer loudspeaker, or a stereo pair formed from woofer loudspeakers.
The following text explains and describes the transfer functions and level profiles
of a single sub-woofer or of a woofer stereo pair, as well as the procedure for
determination of the associated crossover filter cut-off frequencies.

In this case, once again the filter cut-off frequency or
the filter cut-off frequencies of the sought crossover filter for the woofer loudspeakers
has or have its or their frequency varied within the permissible limits of the lower
or upper spectral range, respectively, for as long as it is possible in this way
to reduce the magnitude of the mean value, formed from the profile of the difference
between the sum magnitude frequency response and the target function (distance).
If the magnitude of the mean value of the distance of the upper spectral range is
in this case greater than that of the lower spectral range, depending on whether
the mean value of the distance of the upper spectral range is positive or negative,
the filter cut-off frequency of the upper crossover filter is reduced at most until
the filter cut-off frequency of the lower crossover filter is reached, or is increased
at most until the maximum permissible filter cut-off frequency of the low-tone loudspeakers
(about 500 Hz) is reached. If, in contrast to this, the magnitude of the mean value
of the distance in the upper spectral range is less than the mean value of the distance
in the lower spectral range then, depending on whether the mean value of the distance
of the lower spectral range is positive or negative, the filter cut-off frequency
of the lower crossover filter is reduced at most until the minimum permissible filter
cut-off frequency of the low-tone loudspeakers (about 10 Hz) of the lower crossover
filter is reached or is increased at most until the filter cut-off frequency of
the upper crossover filter is reached.

After the appropriate number of runs, this method leads
to crossover filters whose filter cut-off frequencies are set such that they have
reached either their minimum or their maximum permissible range limits, or are located
within the frequency range predetermined by these range limits and are set such
that the magnitude of the mean value of the distance between the lower range limits
of the lower spectral range and the upper range limits of the upper spectral range
is minimized. This is illustrated, once again by way of example, in the two lower
illustrations in Figure 4, with the left-hand illustration once again showing the
magnitude frequency responses of the transfer function and the right-hand illustration
showing the frequency responses of the level functions. As mentioned further above,
this method is used when the sound system either has only a single subwoofer loudspeaker
for low-tone reproduction or has only one stereo pair, formed from woofer loudspeakers.

The following text describes the procedure for determination
of the cut-off frequencies of the crossover filters for the situation in which the
sound system comprises not only the stereo pair as described above, formed from
woofer loudspeakers, but at the same time, in addition to this, a sub-woofer loudspeaker
as well. The method according to the invention is in this case dependent on the
filter cut-off frequencies of the crossover filters for the stereo pair that is
formed from woofer loudspeakers in this situation being calculated in advance and
being already available, since these are used as input variables for determination
of the filter cut-off frequencies of the crossover filter for the sub-woofer.

In order to set the filter cut-off frequencies of the crossover
filter for the sub-woofer loudspeaker, its upper cut-off frequency is first of all
set as a start value to the value of the upper cut-off frequency of the upper crossover
filter of the woofer loudspeakers, and the already previously determined lower filter
cut-off frequency is used to determine the new lower and upper range limits for
the permissible filter cut-off frequencies in the same way as that which has already
been described for the woofer loudspeakers.

This further restriction to the permissible frequency range
of the upper filter cut-off frequencies of the crossover filter for the sub-woofer
by means of the algorithm, which generally represents a reduction in the frequency
range in the direction of lower frequencies is necessary in order to prevent the
sub-woofer from reproducing excessively high frequencies. The major object of a
sub-woofer which is optionally used as a single loudspeaker in the sound system
is to reproduce a sound component in a frequency range in which the human hearing
cannot carry out any spatial location. The range of operation of a sub-woofer in
this case ideally covers the frequency range up to about 50 Hz, with this being
dependent on the respective installation situation and the characteristics of the
area into which sound is intended to be output, so that, in principle, it therefore
cannot be defined exactly in advance.

The filter cut-off frequencies of the crossover filters
for the sub-woofer loudspeaker are now found in a different way than would be the
case if the sub-woofer were to be the only loudspeaker responsible for reproduction
of the low frequencies of the sound system. In a first step, the sum magnitude frequency
responses are in each case determined for this purpose with and without inclusion
of the sub-woofer loudspeaker and the corresponding target functions are determined
for each of these two sum magnitude frequency responses, and the respectively associated
difference transfer functions are calculated. These are then once again averaged
using the described methods and are in each case changed to the appropriate level
function.

The top left illustration in Figure 5 in this case shows
the magnitude frequency responses of the target function, of the difference function
as well as of the sum function including the sub-woofer and the range limits derived
from this for the permissible upper and lower spectral range for the filter cut-off
frequencies of the crossover filters for the sub-woofer loudspeaker. The top right
illustration in Figure 5 in contrast shows the unaveraged and averaged level functions
of the differences, in each case with and without a sub-woofer. As can be seen from
this, the difference function is increased by inclusion of the sub-woofer loudspeaker,
that is to say the discrepancy is undesirably increased.

The filter cut-off frequencies of the crossover filters
for the sub-woofer loudspeaker must therefore be changed by the algorithm in order
once again to achieve a distance which is at least just as short from the target
function, as was the case without consideration of the sub-woofer. This iterative
method is continued until the system including the sub-woofer is at a distance from
the target function which is at most just as great as was the case previously for
the sound system without a sub-woofer. In this case, the difference between the
sound system without a sub-woofer loudspeaker, as previously determined in the processing
step, and the target function is used as a reference for this iteration.

The resultant magnitude frequency responses after successful
iteration are illustrated in the bottom left illustration of Figure 5, and the associated
level frequency responses are illustrated in the bottom right illustration in Figure
5. This shows how the difference functions with the sub-woofer included behave before
and after the iteration. After carrying out the iteration, the difference function,
particularly in the upper of the two permissible spectral ranges for the filter
cut-off frequencies of the crossover filters is considerably reduced, as desired,
from the state before processing of the iteration.

Furthermore, a considerably more uniform profile of the
difference function can now also be achieved overall than was previously the case
without use of the sub-woofer. The reduction in the upper filter cut-off frequency
of the crossover filter for the sub-woofer makes it possible to achieve a sum magnitude
frequency response, by carrying out the automatic algorithm, whose distance from
the target function is at the same time reduced and which furthermore has a more
uniform profile, thus leading to a considerable improvement in the transfer function
of the sound system in comparison to a sound system without use of a sub-woofer.

Once all of the cut-off frequencies of the crossover filters
have been determined using the method described above, the complete automatic algorithm
of the equalizing process is carried out once again, but with the previously determined
cut-off frequencies of the crossover filters remaining fixed, and not being modified
again in this repeated run. In this case, the impulse responses are determined using
the crossover filters defined in the meantime, first of all for all of the individual
loudspeakers in the sound system, as well as for all the loudspeakers jointly -
once with and once without a sub-woofer - before running through the algorithm for
automatic equalizing (AutoEQ) once again, that is to say once the phase equalizing
and loudspeaker-specific pre-equalizing have already been carried out. The associated
results are illustrated in Figure 6. In this case, Figure 6 shows the measured transfer
functions for the front left and front right individual loudspeakers (Front-Left
and FrontRight in Figure 6), for the left side and right side individual loudspeakers
(SideLeft and SideRight in Figure 6), for the rear left and rear right individual
loudspeakers (RearLeft and RearRight in Figure 6), for the woofer individual loudspeakers
on the left and right (WooferLeft and WooferRight in Figure 6), the centre loudspeaker
(Center in Figure 6), the sub-woofer loudspeaker (Sub in Figure 6), and for all
of the loudspeakers jointly without any sub-woofer loudspeaker (Broadband-Sum+Woofer
in Figure 6) and for all of the loudspeakers jointly including a sub-woofer loudspeaker
(Complete Sum), in this case all in comparison to the defined target function (Target
Function in Figure 6). In this case, the settings and values determined in the first
run through the AutoEQ algorithm are likewise used for the loudspeaker-specific
pre-equalizing filters and for the phase-equalizing filters.

In the next step, the process according to the "MaxMag"
method is used to form the optimized sum transfer function. The associated result
is shown in Figure 7, once again for the frequency range up to about 3 kHz which
governs the localization capability and the tonality.

As can be seen from Figure 7, the equalizing of the sum
function which is carried out in this run by the automatic algorithm using the "MaxMag"
method once again produces a better approximation to the target function in comparison
to the sum function shown in Figure 6. In this embodiment of the algorithm, only
the lowest spectral range of the transfer function under consideration up to about
30 Hz exhibits a somewhat poorer approximation to the target function, with discrepancies
up to about 3 dB. One major reason for this is the embodiment of the FIR filters
that are used for the equalizing, in this case the FIR filter for the sub-woofer
loudspeaker, which, in the present example, was limited to a maximum length of 4096
summation steps or sampling points in the calculation, irrespective of the frequency.

An increase in the number of summation steps for approximation
of the FIR filter while at the same time increasing the requirement for memory and
computation complexity in the digital signal processor in order to improve the approximation
to the target function at very low frequencies is possible at any time, and when
desired also for FIR filters at higher frequencies. Since the effect of limiting
the length of the FIR filters in the present case slightly affected only the frequency
range below 30 Hz, however, this maximum length of 4096 calculation steps was also
retained subsequently for all the FIR filters.

The following text describes the procedure for measurement
of the impulse responses of the sound system and the procedure for formation of
the sum functions of the transmission frequency responses and of the associated
level profiles as a function of the frequency. In this case, the left illustration
in Figure 8 shows the principle for the measurements of the binaural transfer functions
for the front left and front right positions in the passenger compartment, using
the example of the centre loudspeaker C, which in this case represents an example
of the presentation of mono signals. Furthermore, the left illustration in Figure
8 shows the two front left FL_Pos and front right FR_Pos measurement positions and,
associated with them, the positions simulated by the measurement microphones for
the left ear L and the right ear R in each case at these measurement points. In
this case, the transfer function from the centre loudspeaker C to the left ear position
L of the front left measurement position FL_Pos is annotated H_FL_Pos_CL, and the
transfer function from the centre loudspeaker C to the right ear position R of the
front left measurement position FL_Pos is annotated H_FL_Pos_CR, the transfer function
from the centre loudspeaker C to the left ear position L of the front right measurement
position FR_Pos is annotated H_FR_Pos_CL, and the transfer function from the centre
loudspeaker C to the right ear position R of the front right measurement position
FR_Pos is annotated H_FR_Pos_CR. As mentioned initially, the localization of mono
signals depends essentially on inter-aural level differences IID and inter-aural
delay-time differences ITD, which are formed by the transfer functions H_FL_Pos_CL
and H_FL_Pos_CR on the left front seat position, and by the transfer functions H_FR_Pos_CL
and H_FR_Pos_CR on the right front seat position, respectively.

In contrast, the right-hand illustration in Figure 8 shows
the principle of the measurements of the binaural transfer functions for the front
left and front right positions in the passenger compartment, using the example of
the front loudspeaker pair FL (front left loudspeaker) and FR (front right loudspeaker),
which in this case represent examples of the presentation of stereo signals. Furthermore,
the right-hand illustration in Figure 8 once again shows the two measurement positions,
front left FL_Pos and front right FR_Pos, as well as the associated positions which
are modelled by the measurement microphones respectively for the left ear L and
the right ear R at these measurement points. In this case, the transfer function
from the front left loudspeaker FL to the left ear position L at the front left
measurement position FL_Pos is annotated H_FL_Pos_FLL, the transfer function from
the front left loudspeaker FL to the right ear position R at the front left measurement
position FL_Pos is annotated H_FL_Pos_FLR, the transfer function from the front
left loudspeaker FL to the left ear position L of the front right measurement position
FR_Pos is annotated H_FR_Pos_FLL, the transfer function from the front left loudspeaker
FL to the right ear position R at the front right measurement position FR_Pos is
annotated H_FR_Pos_FLR, the transfer function from the front right loudspeaker FR
to the left ear position L at the front left measurement position FL_Pos is annotated
H_FL_Pos_FRL, the transfer function from the front right loudspeaker FR to the right
ear position R at the front left measurement position FL_Pos is annotated H_FL_Pos_FRR,
the transfer function from the front right loudspeaker FR to the left ear position
L of the front right measurement position FR_Pos is annotated H_FR_Pos_FRL, and
the transfer function from the front right loudspeaker FR to the right ear position
R at the front right measurement position FR_Pos is annotated H_FR_Pos_FRR. The
transfer functions for the further loudspeaker groups, which are arranged in pairs
and comprise the woofer, the loudspeakers arranged at the side and the rear loudspeakers,
are obtained in a corresponding manner. The addition of the sum transfer functions
and sum levels resulting from these transfer functions and the weightings of the
measurement points, for the complete sum transfer function of the sound system,
can easily be derived from the exemplary description of the situations for mono
signals and stereo signals shown in Figure 8, and will therefore not be described
in detail here.

As already mentioned further above, the respective binaural
transfer functions in the form of impulse responses of the sound system and of its
individual loudspeakers and loudspeaker groups are, however, measured not only at
the two front seat positions but also at the two rear positions, in the case of
a vehicle which has a second row of seats. The algorithm can be extended to, for
example, the seat positions in a third row of seats, for example as in minibuses
or vans, by appropriate distribution of the weighting of the components for the
seat positions at any time. However, the invention is not restricted to vehicle
interior but is also applicable with all kinds of rooms, for example living rooms,
concert halls, ball rooms, arenas, railway stations, airports, etc. as well as under
open air conditions.

For all of the embodiments, it can be stated in this case,
that the large number of measured transfer functions of a single loudspeaker must
be combined at the left and right ear positions at the respective seat positions
to form a common transfer function, in order to obtain a single representative transfer
function for each individual loudspeaker in the sound system, for processing in
the algorithm for automatic equalizing. In particular, the weighting with which
the transfer functions at the various seat positions are in each case included in
the addition process for the transfer function, can in this case be chosen differently
depending on the vehicle interior (vehicle type) and preference for individual seat
positions.

By way of example, the following text describes a procedure
which has been used in the course of the investigations relating to the present
invention, although the algorithm according to the invention is not restricted to
this procedure. As described further above, for the addition of the transfer functions
to form the overall transfer function of an individual loudspeaker, the respective
components at the various seat position are weighted, to be precise, both for the
magnitude frequency response and for the phase frequency response, at the various
seat positions. The annotations for a vehicle interior with two rows of seats are
in this case as follows:

- &agr; the weighting of the component of the magnitude frequency response at
the front left seat position,
- &bgr; the weighting of the component of the magnitude frequency response at
the front right seat position,
- &ggr; the weighting of the component of the magnitude frequency response at
the rear left seat position,
- &dgr; the weighting of the component of the magnitude frequency response at
the rear right seat position,
- &egr; the weighting of the component of the phase frequency response at the
front left seat position,
- &PHgr; the weighting of the component of the phase frequency response at the
front right seat position,
- ϕ the weighting of the component of the phase frequency response at the
rear left seat position,
- &eegr; the weighting of the component of the phase frequency response at the
rear right seat position.

In this case, &agr; = 0.5, &bgr; = 0.5, &ggr; = 0
and &dgr; = 0 are used for the weighting of the components of the magnitude frequency
response for the examples described in the following text and &egr; = 1.0, &PHgr;
= 0, ϕ = 0 and &eegr; = 0, are used for the weighting for the components
of the phase frequency response, that is to say that, in this example, only the
measurements of the two front positions are used with the same weighting (in each
case 0.5) for the calculation of the resultant magnitude frequency response, and
the measurements for the driver position (generally front left, as here) are used
on their own for determination of the resultant phase frequency response. The hearing
tests carried out showed that it was possible to achieve very good results at all
seat positions even with this very rough weighting, but in principle the automatic
algorithm is designed for any desired distribution of the weightings and, since
hearing tests with a statistically significant number of test subjects at all seat
positions are highly time-consuming, the improvements in the hearing impression
which can be achieved beyond this will be the subject matter of future investigations.
It should be noted that the sum of all the weightings of the transmission frequency
responses and of the phase frequency responses at the various seat positions in
each case results in the value unity, irrespective of the number of seat positions
to be measured.

The combination of all of the transfer functions for all
of the positions in the case of the centre loudspeaker C (mono signal) for the microphone
which in each case represents the left ear is accordingly:
$$\begin{array}{|l|}\hline \mathrm{H\_CL}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_CL}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_CL}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_CL}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_CL}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_CL},+,\varphi ,*,\mathrm{H\_FR\_Pos\_CL},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_CL},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_CL}\right)\\ \hline\end{array}$$
and for the microphone which in each case represents the right ear:
$$\begin{array}{|l|}\hline \mathrm{H\_CR}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_CR}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_CR}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_CR}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_CR}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_CR},+,\varphi ,*,\mathrm{H\_FR\_Pos\_CR},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_CR},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_CR}\right)\\ \hline\end{array}$$

The combined transfer functions determined in this way
for the left and right microphones over all seat positions, in this case four seat
positions, which correspond to the transfer functions added in a weighted form for
the left and right ears, that is to say H_CL and H_CR, are then transformed from
the frequency domain to the time domain using an inverse Fourier transform (IFFT)
in which case only its real part is of importance here:
$$\mathrm{h\_CL}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_CL}\right\}\right\}\phantom{\rule{1em}{0ex}}\mathrm{and\; h\_CR}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_CR}\right\}\right\}$$

In the next step, these real impulse responses are transformed
back from the time domain to the frequency domain using the Fourier transform (FFT),
and are then combined to form a transfer function of the H_C of the centre loudspeaker
C:
$$\mathrm{H\_CL}=\mathrm{FFT}\left\{\mathrm{h\_CL}\right\}\phantom{\rule{1em}{0ex}}\mathrm{and\; H\_CR}=\mathrm{FFT}\left\{\mathrm{h\_CR}\right\}\to \mathrm{H\_C}=\mathrm{H\_CL}+\mathrm{H\_CR}$$

Furthermore, in the case of the loudspeaker pair comprising
the front loudspeakers FL and FR (stereo signal), the combination of all the transfer
functions of all the positions for the microphone which represents the left ear
in each case and for the left front loudspeaker FL is:
$$\begin{array}{|l|}\hline \mathrm{H\_FLL}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_FLL}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_FLL}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_FLL}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_FLL}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_FLL},+,\varphi ,*,\mathrm{H\_FR\_Pos\_FLL},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_FLL},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_FLL}\right)\\ \hline\end{array}$$
and for the microphone which in each case represents the right ear and the left
front loudspeaker FL
$$\begin{array}{|l|}\hline \mathrm{H\_FLR}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_FLR}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_FLR}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_FLR}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_FLR}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_FLR},+,\varphi ,*,\mathrm{H\_FR\_Pos\_FLR},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_FLR},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_FLR}\right)\\ \hline\end{array}$$
and for the microphone which in each case represents the left ear, and the right
front loudspeaker FR
$$\begin{array}{|l|}\hline \mathrm{H\_FRL}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_FRL}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_FRL}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_FRL}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_FRL}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_FRL},+,\varphi ,*,\mathrm{H\_FR\_Pos\_FRL},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_FRL},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_FRL}\right)\\ \hline\end{array}$$
and for the microphone which in each case represents the right ear and the right
front loudspeaker FR
$$\begin{array}{|l|}\hline \mathrm{H\_FRR}=\mathrm{\&agr;}*\left|\mathrm{H\_FL\_Pos\_FRR}\right|+\mathrm{\&bgr;}*\left|\mathrm{H\_FR\_Pos\_FRR}\right|+\mathrm{\&ggr;}*\left|\mathrm{H\_RL\_Pos\_FRR}\right|+\mathrm{\&dgr;}*\left|\mathrm{H\_RR\_Pos\_FRR}\right|*\\ {}_{\mathrm{e}}\mathrm{j}*\angle \left(\mathrm{\&egr;},*,\mathrm{H\_FL\_Pos\_FRR},+,\varphi ,*,\mathrm{H\_FR\_Pos\_FRR},+,\mathrm{\&phgr;},*,\mathrm{H\_RL\_Pos\_FRR},+,\mathrm{\&eegr;},*,\mathrm{H\_RR\_Pos\_FRR}\right)\\ \hline\end{array}$$

The combined transfer functions determined in this way
for the left and right microphones are then transformed from the frequency domain
to the time domain using the inverse Fourier transform (IFFT) over all seat positions,
in this case four seat positions, which correspond to the transfer functions added
in a weighted form for the left and right ear for the respective FL and FR loudspeakers,
that is to say H_FLL, H_FLR, H_FRL and H_FRR, in which case, once again, only their
real part is of importance here:
$$\begin{array}{|c|}\hline \mathrm{h\_FLL}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_FLL}\right\}\right\}:\mathrm{h\_FLR}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_FLR}\right\}\right\};\\ \mathrm{h\_FRL}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_FRL}\right\}\right\}:\mathrm{h\_FRR}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_FRR}\right\}\right\}\\ \hline\end{array}$$

In the next step, these real impulse responses are once
again transformed from the time domain to the frequency domain using the Fourier
transform (FFT), and are then combined to form a respective transfer function H_FL
and H_FR for the left loudspeaker FL and for the right loudspeaker FR, respectively:
$$\mathrm{H\_FLL}=\mathrm{FFT}\left\{\mathrm{h\_FLL}\right\}\mathrm{und\; H\_FLR}=\mathrm{FFT}\left\{\mathrm{h\_FLR}\right\}\to \mathrm{H\_FL}=\mathrm{H\_FLL}+\mathrm{H\_FLR}$$
and
$$\mathrm{H\_FRL}=\mathrm{FFT}\left\{\mathrm{h\_FRL}\right\}\mathrm{und\; H\_FRR}=\mathrm{FFT}\left\{\mathrm{h\_FRR}\right\}\to \mathrm{H\_FR}=\mathrm{H\_FRL}+\mathrm{H\_FRR}\mathrm{.}$$

As the above formulae show, both phase components and magnitude
components of the transfer function for each seat position in the passenger compartment
of a motor vehicle can be included in the formation of the transfer functions which
result in the end, depending on the chosen weighting. In this case, a number of
different weightings have already been used in the investigations relating to this
invention application, and these have led to the following provisional discoveries.
Any such weighted superimposition of the phase frequency responses over more than
one seat position always resulted in a deterioration, in some cases a considerable
deterioration, in the received acoustics in the vehicle. Furthermore, this deterioration
was generally evident at every listening position, and was therefore not position-dependent.

For this reason, in the further investigations so far of
the phase frequency response, the resultant, loudspeaker-dependent transfer function
was made dependent exclusively on the measurements at the driver's position (generally
front left), to be precise by combination of the phase frequency responses of the
left and right microphones. None of the other phase frequency responses of the other
seat positions were included. This stipulation was made in order initially to restrict
the amount of effort associated with this, and in particular that relating to the
hearing tests with a significant number of test subjects. More detailed investigations
will have to be carried out relating to this in order to determine whether other
constellations (weightings) of the superimposition of the phase frequency responses
cannot be found which lead to a further improvement in the hearing impression. For
example, one approach would be to use a position in the centre of the passenger
compartment or else the position between the two front seats as the only point for
recording the impulse responses for calculation of the equalizing filters for the
phase response.

A different impression was gained in the formation of the
added magnitude frequency response. Because the AutoEQ algorithm is processed on
a loudspeaker-specific basis and no longer in pairs, attention must now be paid
to the symmetry between the left and right hemisphere in the formation of the resultant
magnitude frequency response, that is to say the weighting values of the left measurement
positions must correspond to those of the right measurement positions, in order
to maintain this symmetry.

In this case, although a uniform weighting for all of the
measurement positions would produce a good acoustic result, an even better result,
however, has been achieved by using only the two front measurement positions in
order to form the resultant magnitude frequency response. However, in this case
as well, it is possible to achieve an even better result by also including the measurements
of the rear positions, by means of suitable weighting in the formation of the resultant
magnitude frequency response (for example &agr; = 0.35, &bgr; = 0.35, &ggr;
= 0.15 and &dgr; = 0.15).

Once the measurements as described above have been combined
binaurally for each loudspeaker over all of the seat positions, the resultant transfer
functions of the individual loudspeakers are split into their real and imaginary
parts. For the present examples, this means, in the case of the mono signal from
the centre loudspeaker C:
$$\mathrm{ReC}=\mathrm{Re}\left\{\mathrm{H\_C}\right\}\mathrm{and\; ImC}=\mathrm{Im}\left\{\mathrm{H\_C}\right\}$$
and for the stereo signal from the loudspeakers FL and FR:
$$\mathrm{ReFL}=\mathrm{Re}\left\{\mathrm{H\_FL}\right\}\mathrm{and\; ImFL}=\mathrm{Im}\left\{\mathrm{H\_FL}\right\}$$
and
$$\mathrm{ReFR}=\mathrm{Re}\left\{\mathrm{H\_FR}\right\}\mathrm{and\; ImFR}=\mathrm{Im}\left\{\mathrm{H\_FR}\right\}$$

The respective phase frequency response of the respective
loudspeakers are then determined from the real and imaginary parts, and the real
and imaginary parts are then changed such that a desired phase shift of 0°
is always achieved, that is to say purely real signals are produced. For the example
of the mono signal (loudspeaker C), this means that the phase response of the signal
of the loudspeaker C becomes:
$$\mathrm{PhaseC}=-\mathrm{arc}\mathrm{tan}\left({\mathrm{ImC}}_{\mathrm{old}},/,{\mathrm{ReC}}_{\mathrm{old}}\right)$$
and accordingly
$$\mathrm{Re}{C}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{C}_{\mathit{Alt}}^{2}+\mathrm{Im}{C}_{\mathit{Alt}}^{2}}*\mathrm{cos}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{C}_{\mathit{Alt}}}{\mathrm{Re}{C}_{\mathit{Alt}}}\right),+,\mathit{PhaseC}\right)$$
$$\mathrm{Im}{C}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{C}_{\mathit{Alt}}^{2}+\mathrm{Im}{C}_{\mathit{Alt}}^{2}}*\mathrm{sin}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{C}_{\mathit{Alt}}}{\mathrm{Re}{C}_{\mathit{Alt}}}\right),+,\mathit{PhaseC}\right)$$
the new real and imaginary parts are obtained, which now have a phase shift of
0° over a broad bandwidth. A corresponding situation applies to the example
of the stereo signal:
$$\mathrm{PhaseFL}=-\mathrm{arc}\mathrm{tan}\left({\mathrm{ImFL}}_{\mathrm{old}},/,{\mathrm{ReFL}}_{\mathrm{old}}\right)$$
$$\mathrm{PhaseFR}=-\mathrm{arc}\mathrm{tan}\left({\mathrm{ImFR}}_{\mathrm{old}},/,{\mathrm{ReFR}}_{\mathrm{old}}\right)$$
and accordingly
$$\mathrm{Re}{\mathit{FL}}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{\mathit{FL}}_{\mathit{Alt}}^{2}+\mathrm{Im}{\mathit{FL}}_{\mathit{Alt}}^{2}}*\mathrm{cos}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{\mathit{FL}}_{\mathit{Alt}}}{\mathrm{Re}{\mathit{FL}}_{\mathit{Alt}}}\right),+,\mathit{PhaseFL}\right)$$
$$\mathrm{Im}{\mathit{FL}}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{\mathit{FL}}_{\mathit{Alt}}^{2}+\mathrm{Im}{\mathit{FL}}_{\mathit{Alt}}^{2}}*\mathrm{sin}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{\mathit{FL}}_{\mathit{Alt}}}{\mathrm{Re}{\mathit{FL}}_{\mathit{Alt}}}\right),+,\mathit{PhaseFL}\right)$$
$$\mathrm{Re}{\mathit{FR}}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{\mathit{FR}}_{\mathit{Alt}}^{2}+\mathrm{Im}{\mathit{FR}}_{\mathit{Alt}}^{2}}*\mathrm{cos}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{\mathit{FR}}_{\mathit{Alt}}}{\mathrm{Re}{\mathit{FR}}_{\mathit{Alt}}}\right),+,\mathit{PhaseFR}\right)$$
$$\mathrm{Im}{\mathit{FR}}_{\mathit{Neu}}=\sqrt{\mathrm{Re}{\mathit{FR}}_{\mathit{Alt}}^{2}+\mathrm{Im}{\mathit{FR}}_{\mathit{Alt}}^{2}}*\mathrm{sin}\left(\mathrm{arc},,\mathrm{tan},\left(\frac{\mathrm{Im}{\mathit{FR}}_{\mathit{Alt}}}{\mathrm{Re}{\mathit{FR}}_{\mathit{Alt}}}\right),+,\mathit{PhaseFR}\right)$$

Following these processing steps (equalizing of the phases)
of the automatic algorithm, which has been described in more detail above, for equalizing
of a sound system (AutoEQ) the pre-equalizing process is now carried out, as before,
whose basic procedure is summarized as follows:

- 1.) Smoothing of the magnitude frequency response (preferably non-linearly with
averaging over 1/8 third) of the respective loudspeaker.
- 2.) Scaling of the target function with respect to the already smooth, individual
magnitude frequency response. In this case, the scaling factor of the target function
is not calculated over a broad bandwidth, but is determined within a predetermined
frequency range which is predetermined by the lower limit of f
_{gu} = 10
Hz and the upper limit of f_{go} = 3 kHz and the respective limits for the
associated, already determined and adjusted crossover filters.
- 3.) Determination of the distance between the individual, smoothed magnitude
frequency response and the target function scaled onto it, before calculation of
the pre-equalizing.
- 4.) Calculation of the pre-equalizing, which corresponds to the inverse profile
of the difference between the scaled target function and the smoothed magnitude
frequency response. In this case, the profile of the target function is restricted
at the top and bottom ends corresponding to the maximum permissible increase and
decrease if some of the values should overshoot or undershoot these range limits.
- 5.) Renewed calculation of the distance as in 3.), after application, however,
of the pre-equalizing, as calculated in 4.), to the magnitude frequency response.
- 6.) Adoption of the filter coefficients of the pre-equalizing for those frequencies
in which the magnitude of the distance after application of pre-equalizing is less
than the distance as determined in 3.) before application of the pre-equalizing.
- 7.) Optional smoothing (preferably non-linearly with, for example, 1/8 third
filtering) of the magnitude frequency response determined by the pre-equalizing.
- 8.) Transformation of the spectral FIR filter coefficient sets from the pre-equalizing
to the time domain with the aid of the "frequency sampling" method, and optional
restriction of the length of the FIR filter coefficients in the time domain, with
subsequent transformation back to the spectral domain.
- 9.) Determination of the crossover filter cut-off frequencies of the broadband
loudspeakers and, optionally, initial allocation of the narrowband crossover filter
cut-off frequencies.
- 10.) Storage of the individual pre-equalizing filter coefficient sets and, as
previously determined, of the respective crossover filter cut-off frequencies.

Once the pre-equalizing filters have been calculated and
stored and, if desired, the filter cut-off frequencies of the crossover filters
as well as the individual values for the channel gain have been calculated and applied,
the sum transfer function is calculated on the basis of the real and imaginary parts
before the equalizing of the sum transfer function is then carried out using the
"MaxMag" method, as described in the following text:

- 1.) Smoothing of the sum magnitude frequency response (preferably non-linearly
with 1/8 third filtering).
- 2.) Scaling of the target function with respect to the already smoothed sum
magnitude frequency response. In this case, the scaling factor for the target function
is not calculated over the entire audio spectral range but is determined within
a predetermined frequency range, which is predetermined by the lower limit of f
_{gu}
= 10 Hz and the upper limit of f_{go} = 3 kHz, and the respective limits
for the associated, already determined and adjusted crossover filters.

The following calculation steps as a loop over the frequency
(0<f<=fs/2):

- 3.) Renewed calculation of the current sum transfer function based on the real
and imaginary parts at the frequency f.
- 4.) Determination of the current distance between the sum transfer function
and the target function at the point f.
- 5.) Resetting of the previous minimum distance, setting the distance to the
new distance as determined in 4.), and incrementation of the counter (loop over
frequency f).

Iteration:

- 6.) Calculation of all the filters for magnitude equalizing, based on the previously
determined filters of the pre-equalizing at the frequency f.
- 7.) Limiting of the filters for the magnitude equalizing to the permissible
raising and lowering range.
- 8.) Calculation of the individual magnitudes, and of the respective distances
to the target function at the frequency f.
- 9.) After exclusion of all those values from the equalizing which have already
reached the predetermined limits for raising or lowering, the search is carried
out for that magnitude value with the maximum magnitude and the maximum distance.
- 10.) The individual loudspeaker which has the greatest distance and which, when
its magnitude equalizing is changed at the point f, thus leads to the expectation
of the maximum reduction in the distance of the sum transfer function in the direction
of the target function, is then selected, and the associated function of the magnitude
equalizing is modified at the relevant frequency f so that this leads to the desired
reduction in the distance.
- 11.) The sum transfer function on the basis of the magnitude and phase is then
calculated once again using the current parameters for the magnitude equalizing
and then the calculation of the new difference between the previous distance and
the distance determined in the current iteration step takes place. If the difference
between the previous distance and the current distance is below a specific predetermined
threshold value in this case, the iteration is finished. In any case, the iteration
is terminated at the latest after carrying out a specific, predetermined number
of iterations (for example 20), in order to avoid endless loops.
- 12.) Finally, the newly calculated distance is set as the current distance,
and the process continues with the next iteration step.

Once the iteration of the equalizing of the sum transfer
function has been ended, the filters which have been modified in the course of the
iteration process are optionally smoothed again for the pre-equalizing (preferably
matched to the hearing, non-linearly, for example with 1/8 third filtering), are
then transformed to the time domain using the "frequency sampling" method, and finally
optionally have their length limited before being transformed back to the spectral
domain, in this way resulting in the final filters for the magnitude equalizing.
The FIR filters for the equalizing of the phases are in this case determined using
the following method.

The profile of the filters for the equalizing of the phases
is calculated individually for each loudspeaker to be:
$$\mathrm{PhaseEQ}=-\mathrm{arctan}\left(\mathrm{Im},/,\mathrm{Re}\right)$$

This profile is broken down again, after optional smoothing,
into its real and imaginary parts:
$$\mathrm{RePhaseEQ}=\mathrm{cos}\left(\mathrm{PhaseEQ}\right)\phantom{\rule{1em}{0ex}}\mathrm{and\; ImPhaseEQ}=\mathrm{sin}\left(\mathrm{PhaseEQ}\right)$$

The spectra are then extended symmetrically on their two
sideband spectrum, thus resulting in a real FIR filter being produced in the time
domain:
$$\mathrm{RePhaseEQ}=\left[\mathrm{RePhaseEQ\; RePhaseEQ},,\left(\mathrm{end},-,1,:,-,1,:,2\right)\right]$$
and
$$\mathrm{ImPhaseEQ}=\left[\mathrm{ImPhaseEQ},-,\mathrm{ImPhaseEQ},,\left(\mathrm{end},-,1,:,-,1,:,2\right)\right]$$

The (complex) transfer function is then calculated from
the real and imaginary parts:
$$\mathrm{H\; PhaseEQ}\mathrm{=}\mathrm{RePhaseEQ}\mathrm{+}\mathrm{j}\mathrm{*}\mathrm{ImPhaseEQ}\mathrm{.}$$

In order to obtain a causal all-pass FIR filter, the filter
has to be superimposed with a modelling delay, which ideally has half the FIR filter
length:
$$\mathrm{H\_PhaseEQ}=\mathrm{H\_PhaseEQ}*\mathrm{H\_Delay}$$

where H_Delay = FFT(Delay) and Delay=[1, 0, 0, ..., 0] and has a length which corresponds
to half the length of the FIR filter for the equalizing of the phases. The transfer
function which has been modified in this way is once again transformed to the time
domain, with its real part corresponding to the FIR filter coefficients of the filter
for the equalizing of the phases:
$$\mathrm{h\_PhaseEQ}=\mathrm{Re}\left\{\mathrm{IFFT},\left\{\mathrm{H\_PhaseEQ}\right\}\right\}\mathrm{.}$$

Convolution with the previously calculated filters for
the equalizing of the magnitude frequency response finally results in the non-linear,
loudspeaker-specific FIR filters for the equalizing, which are used both for the
equalizing of the phases and for the equalizing of the magnitude frequency response
of the sound system.

For a high symmetry and a high acoustical sound quality
for a given listening position, a position specific equalizing may be based only
on sound picked up in said position in view of only those loudspeaker positions
which are relevant for said listening position. Further, channel (group) specific
equalizing is applied in each position to the effect that only adjacent loudspeaker
positions are used for the equalization in order to maintain symmetry. Thus, there
are separate calculations for the front and rear positions. The front channels may
include, e.g., the front left and right channels (FL, FR) as well as the center
speaker. Those speakers are only relevant for the front left and front right listening
positions with respect to cross-over frequency, gain, amplitude, and phase. Accordingly,
the left and right speakers in the rear are only used for the rear listening positions.
However, all positions are influenced by the sound from the woover. Figure 9 shows
in a diagram an exemplary spectral weighting function for measurements at different
positions (FL_Pos+FR_Pos+RL_Pos+RR_Pos)/4 and (FL_Pos+FR_Pos)/2 over frequency.

As can be seen from figure 10, the sound levels may vary
depending on the particular position and frequency. Improvements addressing this
situation may be reached by a bass management system. Measurements showed that problems
especially with woofers and subwoofers arranged in the rear of a car occur in a
frequency range of 40Hz to 90Hz which corresponds to a wave length of one half of
the length of a vehicle interior indicating that this is because of a standing wave.
In particular, measurements of the unsigned amplitude over frequency showed that
the unsigned amplitude at the front seats are different from the ones at the rear
seats, i.e., at the rear seats a maximum and at the front seats a minimum may occur.
The difference between front and rear seats may be up to 10dB especially if the
subwoofer is arranged in the trunk of a car (see figure 11). Although a different
position, e.g., under the front seats, of the subwoofer may provide some improvement,
the bass management system according improves the sound even more, not only in view
of the front-rear mode but also the left-right mode. The bass management system
of the present invention creates the same or at least a similar sound pressure at
different locations by, i.a., adapting the phase over frequency for one or more
of the low frequency loudspeakers. If this successfully took place, it is no problem
to adapt the amplitude over frequency to the target function, since all loudspeakers
only have to be weighted with an overall amplitude equalizing function to get amplitude
over frequency being equal to the target function at all positions.

However, it is difficult to adapt the phases such that
the sound levels at different positions are almost the same. A major problem is
to find an appropriate cost function to be minimized subsequently. For example,
the level over frequency of one position or the average level over frequency of
all positions may be taken as a reference wherein subsequently the distance of each
individual position to the reference is determined. The individual distances are
added leading to a first cost function which stands for the overall distance from
the reference mentioned above. To minimize the first cost function, it is investigated
what phase shift has what influence to the cost function.

A very simple approach is to choose a first group of loudspeakers
(which may be only one loudspeaker) or a first channel serving as the reference
to which a second group of loudspeakers (which also may be only one loudspeaker)
or a second channel is adapted in terms of phase such that the cost function is
minimized. Investigating the influence of the phase shift (0° to 360°)
of the second channel to the cost function at an individual frequency, a cost function
over phase is derived which shows the dependency of the distance from the phase.
Determining the minimum of this cost function leads to the phase shift that has
to be applied to the respective group or channel in order to reach a maximum reduction
of the cost function and, accordingly, a maximum equalization of the sound levels
of all positions.

However, the steps described above may result in an undesired
overall reduction of the sound level. To overcome this problem, another condition
is introduced which effects not only the same sound level at each position but also
the maximum overall sound level possible. This is achieved by taking the reciprocal
function of the mean position sound level for scaling the above-mentioned distance
wherein the scaling is adjustable by means of a weighting function.

As shown in figure 12, with a 0° phase shift at 7o
Hz there is a huge difference between the front positions and the rear positions.
Introducing an additional phase shift, the level at each position decreases further,
however, the levels are equalized. The behaviour of such so-called inner distance,
i.e., the cost function for a maximum adaptation of all listening positions, has
its minimum at a phase shift of about 180°. The curve depicted as MagMean represents
the average level of all positions. Inverting and weighting the MagMean function
by, e.g., a factor 0.65, and adding the inner distance weighted by a complementary
factor 0.35 (= 1-0.65) leads to a new inner distance InnerDistanceNew which finally
is the cost function to be minimized. Figure 12 illustrates how the cost function
is changed by changing the mean sound pressure level. In the example of figure 12
the optimum phase shift is not changed since the original cost function and the
modified cost function have their overall minimum at the same position. By the modification
described above, beside a good amplitude equalization at all positions and a maximum
level also a more even phase equalization can be achieved.

However, the above measures may lead to a very discontinuous
phase behaviour which requires a very long FIR filter length. The problem behind
can better be seen from a three-dimensional illustration like the one shown in figure
13 where the cost functions of figure 12 are arranged side by side resulting in
a "mountain"-like three-dimensional structure representing the cost function of
one loudspeaker (or one group of loudspeakers) as inner distance (InnerDistance
[db]) over phase [degree] and frequency [Hz]. Figure 14 illustrates the corresponding
equalizing phase-frequency response for the front right loudspeaker with respect
to the reference signal.

In order to reach an even more straight, more continuous
curve in said "mountains", and in particular to achieve a very continuous phase
behaviour, the phase shift per frequency change (e.g., 1Hz) may be restricted to
a certain maximum phase shift, e.g., ±10°. For each such restricted phase
shift range the local minimum is determined for each frequency (e.g., 1 Hz steps)
which then is used as a new phase value in the phase equalization process. The results
can be seen from the three-dimensional illustration in figure 13 where the maximum
phase shift per frequency change is restricted to ±10° per frequency step.
Figure 16 illustrates the corresponding equalizing phase-frequency response for
the front right loudspeaker with respect to the reference signal.

As already mentioned, the restriction of the maximum phase
shift per frequency change leads to a flat phase response such that already existing
FIR filters as, for example, the one used for the other equalizing purposes, are
applicable. Such FIR filter may comprise only 4096 taps at a sample frequency of
44.1 kHz. The results are illustrated in figure 17. As can be seen, even a short
filter shows already a good approximation to the desired behaviour (original).

Upon determining the phase equalizing function for an individual
loudspeaker, subsequently a new reference signal is derived through superposition
of the old reference signal with the new phase equalized loudspeaker group (or channel).
The new reference signal serves as a reference for the next loudspeaker to be investigated.
Although each group of loudspeakers (or channel) can be used as a reference the
front left position may be preferred since most car stereo systems will have a loudspeaker
in this particular position.

Figure 18 illustrates the sound pressure levels over frequency
at four positions in the interior of a vehicle with the already mentioned difference
between front and rear seats. Figure 19 shows the sound pressure levels over frequency
upon filtering the respective electrical sound signals according to the above mention
method using the phase equalizing function with no phase limitation. Figure 20 illustrates
the case of applying such a phase limitation of ±10° per frequency step.
Figure 21 shows the performance of the bass management system as sound pressure
level over frequency using a FIR filter with 4096 taps.

Apparently, all kinds of bass management systems discussed
above create similar situations for each of the positions with frequencies below
150 Hz with no decrease in the average sound pressure level. Further, only above
approximately 100 Hz there is a significant difference between the cases of having
a phase limitation or not. Finally, there is no significant difference between the
theoretically optimum behaviour (figure 20) and the behaviour of an approximation
thereof by a 4096 taps FIR filter (figure 21).

Upon such phase equalization filtering, a reference is
derived from the average amplitude over frequency of all positions under investigation.
Said reference is then adapted to a target function by means of an amplitude equalization
function which is the same for all positions to be investigated. The target function
may be, for example, the manually modified sum amplitude response of the auto equalization
algorithm that, in turn, follows automatically its respective target function. The
resulting target function for the bass management system is depicted "Target" in
figures 22 and 23. By subtracting the target function from the average amplitude
response of all positions a global equalizer function (figure 23: "original") is
derived. In order to avoid a decrease in the low frequency range by this measure,
the global amplitude equalizing function (figure 2: "half wave rectified") is applied
to compensate for the decrease. Figure 24 shows as a result the transfer functions
of the sums of all speakers at different positions after phase and global amplitude
equalization.

Although FIR filters in general have been used in the examples
above, all kind of digital filtering may be used. However, emphasis is put to minimal
phase FIR filters which showed the best performance, particularly, in view of the
acoustical results as well as the filter length.

Figure 25 illustrates the signal flow in a system exercising
the methods described above. In the system of figure 25, two stereo signal channels,
a left channel L and a right channel R, are supplied to a sound processor unit SP
generating five channels thereof. Said five channels are a front right channel FR,
a rear right channel RR, a rear left RL, a front left channel FL, and a woofer and/or
subwoofer channel LOW. Each of said five channels is supplied to a respective equalizer
unit EQ_FR, EQ_RR, EQ_RL, EQ_FL, and EQ_LOW for amplitude and phase equalization.
The equalizer units EQ_FR, EQ_RR, EQ_RL, EQ_FL, and EQ_LOW are controlled via a
equalizer control bus BUS_EQ by a control unit CONTROL which also performs the basic
sound analysis for controlling other units of the system. The equalizer units EQ_FR,
EQ_RR, EQ_RL, EQ_FL, and EQ_LOW comprise preferably minimal phase FIR filters.

Such other units are, e.g., controllable crossover filter
units CO_FR, CO_RR, CO_RL, and CO_FL having a controllable crossover frequency and
being connected downstream of the respective equalizer units EQ_FR, EQ_RR, EQ_RL,
and EQ_FL for splitting each respective input signal into two output signals, one
in the high frequency range and the other in the mid frequency range. The signals
from the crossover filter units CO_FR, CO_RR, CO_RL, and CO_FL are supplied via
respective controllable switches S_FR_H, S_RR_H, S_RL_H, S_FL_H, S_FR_M, S_RR_M,
S_RL_M, and S_FL_M as well as controllable gain units G_FR_H, G_RR_H, G_RL_H, G_FL_H,
G_FR_M, G_RR_M, G_RL_M, and G_FL_M to loudspeakers LS_FR_H, LS_RR_H, LS_RL_H, LS_FL_H,
LS_FR_M, LS_RR_M, LS_RL_M, and LS_FL_M. The signal from the equalizer unit EQ_LOW
is supplied via two controllable switches S_LOW1 and S_LOW2 as well as respective
controllable gain units G_LOW1 and G_LOW2 to (sub-)woofer loudspeakers LS_LOW1 and
LS_LOW2. The controllable switches S_FR_H, S_RR_H, S_RL_H, S_FL_H, S_FR_M, S_RR_M,
S_RL_M, S_FL_M, S_LOW1, S_LOW2 and the controllable gain units G_FR_H, G_RR_H, G_RL_H,
G_FL_H, G_FR_M, G_RR_M, G_RL_M, G_FL_M, G_LOW1, G_LOW2 are controlled by the control
unit CONTROL via control bus BUS_S or BUS_G, respectively.

For sound analysis, two microphones MIC_L and MIC_R are
arranged in a dummy head DH which is located in the room where the loudspeakers
are located. The signals from the microphones MIC_L and MIC_R are evaluated as described
herein further above wherein, during the analysis procedure, a certain group of
loudspeakers (including groups having only one loudspeaker) may be switched on while
the other groups are switched of by means of the controlled switches S_FR_H, S_RR_H,
S_RL_H, S_FL_H, S_FR_M, S_RR_M, S_RL_M, S_FL_M, S_LOW1, S_LOW2. The groups may be
switched on sequentially according to a given sequence or dependant on the deviation
from a target function.

Although various examples to realize the invention have
been disclosed, it will be apparent to those skilled in the art that various changes
and modifications can be made which will achieve some of the advantages of the invention
without departing from the spirit and scope of the invention. It will be obvious
to those reasonably skilled in the art that other components performing the same
functions may be suitably substituted. Such modifications to the inventive concept
are intended to be covered by the appended claims. Although only shown in connection
with AutoEQ, e.g., the adaptation method of the crossover frequencies and the bass
management method may be each used in a stand alone application or in connection
equalizing methods as well.