Method for the direction-dependent correction of the frequency response of sound wavefronts

Abstract

The invention relates to a method for operating and / or setting up a two-dimensional sound transducer assembly (1) comprising a plurality of discretely controlled sound transducers (9), wherein the sound transducers (9) of the sound transducer assembly (1) each generate elementary waves which are superposed according to the principle of wave field synthesis and / or according to beamforming methods to form at least one sound wavefront, wherein a local propagation direction for the at least one sound wavefront is known or can be determined at each transducer (9) of the transducer assembly (1). At least one acoustic disturbance factor, which causes frequency-dependent and / or direction-dependent variations in the sound pressure of at least one first sound transducer (9) of the sound transducer assembly (1), is detected, and an input signal of the at least one first sound transducer (9) of the sound transducer assembly (1) is coupled to at least one correction device, in particular a filter device, which influences the acoustic disturbance factor depending on the local propagation direction of the at least one sound wavefront at the at least one first sound transducer (9), in particular by minimising it by means of a forward correction.

Description

[0001] Method for the direction-dependent correction of the frequency response of sound wave fronts Description The proposed solution relates to a method for the direction-dependent correction of the frequency response of sound wave fronts that are generated in two-dimensional sound transducer arrangements according to the principle of wave field synthesis or using beamforming methods. Using a large number of discretely controlled sound transducers, it is possible to radiate several acoustic wave fronts simultaneously in different directions. A vector-based method, as known from German patent application DE 102021207302 A1, adapts the shape and level of each of the wave fronts generated from a large number of elementary waves to the audience area in such a way that even under unfavorable acoustic conditions hardly any unwanted reflections from the playback room are excited. This leads to exceptionally high speech intelligibility throughout the entire audience area.In addition, the signal levels are adjusted by the described method so that a very balanced sound pressure level is achieved in the entire audience area, even if its shape is irregular and the distances of the listeners from the sound transducer surface vary greatly. For this purpose, the delay times and levels are calculated separately for each individual sound transducer in the sound transducer array and for each individual wavefront. A mathematical method for calculating the delay times is described, for example, in DE 102021207302 A1. In one embodiment, coordinates in the audience area are assigned to each sound transducer in the sound transducer array. A vector calculation of the distances between the sound transducer and the assigned point in the audience area, with appropriate level correction, leads to a very uniform sound pressure distribution in the audience area for each individual input signal.According to the principle of wave field synthesis (A.J. Berkhout, A Holographic Approach to Acoustic Control, J.Audio Eng.Soc, Vol.36, No.12, 1988), a large number of sound transducers generate a wave front that supplies a given audience area with a very uniform level of high audio quality, without undesirably illuminating adjacent reflecting surfaces. As the size of the audience areas at large events grows, the demands on the sound reinforcement systems increase. Often, the differences in sound pressure between the individual audience seats are intolerable with a poorly directed radiation of the sound waves. Reproduction, frequency response and speech intelligibility suffer due to level drop, airborne sound insulation and unwanted reflections. For this reason, loudspeaker arrangements consisting of several individual sound sources direct the sound more strongly into the more distant audience areas. A typical application is so-called line arrays, which, for example,are arranged to the left and right above the front of the stage. Their curvature is adjusted to the audience area so that the radiated wave front in the elevation plane is directed towards the more distant audience areas. This creates almost a cylindrical wave around this part of the loudspeaker arrangement. The surface area of ​​a cylinder grows linearly with its radius, which is why the sound pressure decreases by 3 decibels for every doubling of the distance. In the lower area of ​​the transducer arrangement, the greater curvature of the transducer surfaces results in a larger vertical aperture angle. In this area, the wave front is almost a section of a sphere. The surface area of ​​a sphere, which grows quadratically with the radius, results in a sound pressure drop of 6 dB for every doubling of the distance.Due to the rapid sound pressure drop in the near field and the longer-reaching cylindrical wave for the distant seats, the differences in sound pressure between the front and rear audience areas are significantly reduced. In recent years, array speakers with electronic control of the individual transducers have also been used. Each transducer has its own amplifier, which is controlled by a signal processor. Mathematical processes allow for radiation that is much better adapted to the audience area than would be possible with the mechanical alignment of individual transducers. The curvature of the transducer arrangement can be simulated and electronically adjusted according to Huygens' principle with minimal delays in the control of the individual transducers. However, these possibilities are limited to the elevation plane with the available array speakers.Because the directivity, even with this improved dispersion, can only be adjusted in the elevation plane, the sound field remains only roughly tailored to the given audience area. In the azimuth plane, dispersion is only determined by the mechanical alignment of the loudspeaker array. Adaptation to the audience area can only be achieved by selecting loudspeaker elements with wider or narrower horizontal directivity. Loudspeaker arrays such as those available for audio reproduction based on the principle of wave field synthesis (such as in WO 2015 / 036845 A1) are significantly more flexible. Here, each transducer is driven by a separate power amplifier. According to Huygens' principle, the superposition of the elementary waves of each individual transducer creates a wavefront that reconstructs a spherical section of the wavefront of a real sound source.The center of this spherical section is the virtual sound source of the wave field synthesis. The boundaries of the spherical section are determined by the size of the sound transducer field in conjunction with the position of the virtual sound source. The individual sound transducers of the at least one sound transducer arrangement radiate - during operation - elementary waves which overlap to form a common wave front. Whenever the radiation of elementary waves from the sound transducers is mentioned below, the acoustic center of the sound transducers is meant. The at least one sound transducer arrangement and the audience area are assigned to a common coordinate system, in particular a Cartesian coordinate system. As will become clear below, the coordinate system on the side of the at least one sound transducer arrangement serves in particular to provide starting points for position vectors ^. ^ to determine which together with direction vectors ^ ^determine the sound radiation from the at least one transducer array. The coordinate system thus links the at least one transducer array and the at least one audience area. Between the position vectors ^ ^ and the physical positions of the transducers are spatially related. In the simplest case, the acoustic centers of the transducers are located at the origin of the position vectors ^ ^ . However, it is also possible that the transducers are not exactly at the origins of the position vectors ^ ^ If the positions of the acoustic centers of the transducers deviate from the intersection points of the auxiliary grid, the associated change in delay time and level can be corrected by spatial interpolation or other methods. The position vectors ^ ^can be stored, for example, in the form of a list. By introducing the coordinate system, points in the audience area and points on the at least one transducer arrangement – ​​and thus indirectly also the transducers themselves – can be easily geometrically related to one another, such as when calculating the distance of a transducer to a point in the audience area. The method assumes an assignment of points of the coordinate system to points in at least one audience area and assigns a position vector ^ ^ to. The position vector ^ ^ thus points to a specific location in the audience area 3. From the position vectors ^ ^ , from which the positions of the individual sound transducers can be determined directly or indirectly, direction vectors, in particular standardized direction vectors ^ ^ ^= determine the radiation direction of the wavefront in the area of ​​the respective transducers. Now, depending on the spatial assignment of the position vectors ^ ^ and the transducer delay times ^ ^ for the sound transducers, which then emit acoustic elementary waves. The delay times ^ ^ the transducers are chosen so that the local direction of the common wavefront corresponds to the direction of the direction vector, in particular the normalized direction vector ^ ^ ^ The transducers of the at least one transducer arrangement are thus each provided with a specific delay time ^ ^ operated. The delay time ^ ^ of a transducer determines the time of generation of an elementary wave at the respective transducer. In particular, the delay times ^ ^of the individual transducers relative to the input signal. In other words, each transducer is assigned an individual delay time ^ ^ The delay times of the individual transducers can generally differ, but some transducers can also be assigned the same delay time ^ ^ The total delay times with which the individual transducers of the transducer array are operated influences the shape of the common wavefront, which is composed of the elementary waves generated by the individual transducers. In particular, the total delay times ^ ^ the shape of the common wavefront can be determined. In particular, by choosing the delay times ^ ^ produce complex wavefronts. The result is different delay times ^ ^in the transducer arrangement, a correspondingly shaped wavefront, e.g., with different curvatures. The wavefront formed by the elementary waves is thus no longer a spherical section, as generated by a virtual sound source with a two-dimensional wave field synthesis transducer arrangement. Depending on the shape and size of the coverage area (i.e., the at least one audience area), stronger curvatures and flatter curved areas result. The convex curvature of the wavefront is usually smaller towards the farthest audience seats; a stronger curvature towards the front audience seats causes the sound pressure level to drop more rapidly with distance and distributes the energy over a larger audience area. The delay times ^ ^of the individual transducers can be determined in such a way that the common wavefront adapts to the geometry of the audience area. In particular, the delay times ^ ^the local directions of the wave front are controlled. The resulting, irregularly shaped wave front is in principle assigned the same number of grid points (i.e. the coordinate system in the area of ​​the sound transducer arrangement) of the sound transducer arrangement and thus also of sound transducers for the same size of the audience area. In this respect, such a wave front differs fundamentally from the spherical section of a point-like virtual sound source of wave field synthesis, in which the audience area supplied by the same number of sound transducers increases continuously with distance. The local direction of the common wave front at a position on the wave front describes the direction in which the common wave front propagates at the respective position. The local direction of the common wave front can be described by the direction vector that is perpendicular to the respective point on the common wave front.The direction vector describes a local propagation direction of the common wavefront when the wavefront moves perpendicular to the direction vector. Adaptation of the common wavefront to the geometry of at least one audience area is enabled by a definable assignment that defines the position vectors ^. ^ (which can be assigned to individual surge transducers, for example) each have a position in the audience area corresponding to a position vector ^ ^ The respective assignment results in normalized direction vectors ^ ^ ^ = The delay times ^ ^ are then chosen so that the local direction of the common wave front at the position in the audience area, which is determined by the position vector ^ ^ is described, the direction of the direction vector ^ ^ ^In particular, local propagation directions of the common wavefront are given by the normalized direction vectors ^ ^ ^given. The sound transducers of the at least one sound transducer arrangement can be arranged on or in a plane. Alternatively, the sound transducers of the sound transducer arrangement can be arranged on or in an at least partially curved surface. The arrangement can, for example, be grid-like. In particular, the distances between the sound transducers can be uniform. For example, the distances in a first direction, in particular in the vertical direction, and / or the distances in a second direction, in particular in the horizontal direction, can each correspond to one another or result in a regular sequence of distance sizes. The geometric shape in or on which the sound transducers are arranged can be complex. For example, the sound transducers can lie in one area on a flat surface, with other sound transducers of the same sound transducer arrangement lying on a curved surface.Different parts of the surface can also have different radii of curvature. Alternatively, the sound transducers of the at least one sound transducer arrangement are arranged in a three-dimensional area, in particular a room. The arrangement of the individual sound transducers can be determined starting from a reference surface, for example a plane or a curved surface, wherein at least a subset of the sound transducers of the at least one sound transducer arrangement is arranged on the reference surface and the positions of the remaining sound transducers of the at least one sound transducer arrangement can be determined by a spatial offset in the three-dimensional area. The operation of the sound transducer - which corresponds to the position vector ^. ^ is assigned - with delay time ^ ^ can be controlled by a computer system. In particular, the control can be done with a delay time ^ ^be digitally influenced or caused by digital control. The delay times can be on the order of milliseconds. For neighboring transducers, the time difference is usually only a few microseconds, so the overall system requires a very stable system clock. Additionally or alternatively, the delay time with which a transducer is operated can be influenced mechanically or geometrically. For example, the delay time of a transducer can be controlled by means of a spatial offset, particularly in the radiation direction of the transducer arrangement, compared to other transducers in the transducer arrangement. The audience area can have at least partially a flat or concave and / or at least partially a convex shape.The audience area can be described as a contiguous area or as a discontinuous area consisting of at least two contiguous parts. An example of an audience area composed of multiple areas is the main hall of the Berlin Philharmonic Hall or an opera hall with several tiers. However, the audience area can also be represented by a set of coordinate points. In the coordinate system, the position vectors^ can be ^ , which are assigned to the transducers of the transducer array, form a regular grid. Additionally or alternatively, the position vectors ^ ^ a regular grid on the reference area ^ assigned to the audience area. The assignment, which corresponds to each position vector ^ ^ in the transducer array a point in the audience area corresponding to the position vector ^ ^can be determined by means of connecting lines from the transducer array to the audience area. In particular, the connecting line can be a half-line starting from the position vector ^ ^ which intersects the audience area or the reference area assigned to the audience area ^. The sound transducer can then be assigned a position vector ^ ^ which results from the intersection of the half-line with the audience area or the reference area ^ assigned to the audience area. Additionally or alternatively, the levels at which the sound transducers of the at least one sound transducer arrangement are operated can be determined by means of a relative amplification factor, in particular based on the rule ^ ^ ^ = ^ ^ ^ ∙ ^ ^ , where ^ ^ the normal to the reference surface ^ at the position vector ^ ^By operating the transducers according to the relative gain factors ^ ^ ^ ensures that the sound pressure level at the receiver position ^ ^ independent of the angle of the direction vector ^ ^ to the normal ^ ^ This ensures a homogeneous volume in the audience area to be sounded. Furthermore, the proposed solution includes a method for determining delay times ^ ^ for a sound transducer arrangement with a plurality of sound transducers ^ for generating elementary waves according to the delay times ^ ^for providing sound to at least one audience area. The method comprises the steps of determining a coordinate system by which the at least one sound transducer arrangement is approximately described as a reference surface ^ and the audience area is approximately described as a reference surface ^; determining position vectors ^ on the reference surface ^ of the at least one sound transducer arrangement, from which the positions of the sound transducers of the at least one sound transducer arrangement can be determined; determining standardized directional vectors ^ ^ starting from the position vectors ^, where the normalized direction vectors ^ ^ directed to the reference area ^ of the audience area and the determination of delay times ^ ^ for sound transducers ^, so that the elementary waves of the sound transducers of the sound transducer arrangement during operation according to the delay times ^ ^superimpose to form a common wavefront, where the normalized direction vectors ^ ^ describe the local propagation directions of the common wavefront. In other words, the common wavefront propagates essentially perpendicular to the normalized direction vectors ^ ^ In this way, the normalized direction vectors ^ ^ the propagation path of the common wavefront. In particular, the common wavefront is determined by a suitable choice of the normalized direction vectors ^ ^ can be adapted to the geometry of the audience area. To adjust the sound levels, the relative gain factors ^ ^ ^ for at least a subset of the position vectors ^ according to the rule ^ ^ ^ = ^ ^ ∙ ^ be determined, where ^ is a normal to the reference surface ^ of the transducer array at the point determined by the position vector ^ and ^ ^the normalized direction vector starting from the position vector ^. The position vectors ^ may correspond entirely or partially to the positions of the transducers on the transducer array; in any case, there is a correlation between the physical positions of the individual transducers in the at least one transducer array and the position vectors ^ ^for defining coordinates in the area of ​​the at least one sound transducer arrangement, a spatial assignment. The number of position vectors ^ can correspond to the number of sound transducers in the sound transducer arrangement or can also be different from this. In particular, the number of position vectors ^ can be higher than the number of sound transducers on the sound transducer arrangement. The position vectors ^ can describe intersection points of an auxiliary grid described on the reference surface ^ of the at least one sound transducer arrangement. However, position vectors ^ do not have to lie on all intersection points of the auxiliary grid. The auxiliary grid can, for example, describe a rectangular plane. The number of grid lines in the horizontal and / or vertical direction can each correspond to a number of rows and / or columns of sound transducers in the sound transducer arrangement.The number of grid lines in the horizontal and / or vertical direction can also be greater than the number of rows and / or columns of sound transducers in the sound transducer array. The method can further comprise determining position vectors ^ on the reference surface ^ of the audience area, wherein a position vector ^ is assigned to each position vector ^. The assignment can be made by means of a connecting line from the position vector ^ to the position vector ^, on the basis of which the respective normalized direction vector ^ is determined. ^ can be determined. In particular, the direction vector ^ ^ each using the calculation rule ^ ^ =^^ ^ |^^^| be determined. In one embodiment, the entirety of the connecting lines is such that they do not cross or overlap in pairs. In particular, no connecting line intersects the other connecting lines. The assignment of the position vectors ^ to the position vectors ^ can be done automatically, in particular using a 3D CAD file of the audience area. This can be done using a suitable mapping method. In particular, points and / or areas of the reference surface of the audience area can be omitted during the assignment, for example those that correspond to areas of the audience area that are not to be hit by the common wavefront. The position vectors ^ can be evenly distributed on the reference surface ^ of the audience area. In this case, they can correspond to evenly distributed points in the audience area.A uniform distribution of the points is ensured, for example, by ensuring that any two neighboring points are the same distance from each other. The reference surface ^ of the audience area can be described by an auxiliary grid. The position vectors ^ can at least partially correspond to intersection points of the auxiliary grid. Likewise, the reference surface ^ of the sound transducer arrangement can be described by an auxiliary grid on which the position vectors ^ at least partially correspond to intersection points. Such an auxiliary grid is particularly important for numerical treatment because, for example, numerical integrations can be easily carried out in it using the trapezoidal rule. Auxiliary grids on the reference surface ^ of the at least one sound transducer arrangement and auxiliary grids on the reference surface ^ of the audience area can be converted into one another. In particular, they can have the same number of lines in the horizontal and / or vertical plane.By connecting the intersection points of the auxiliary grids, a suitable connection can be created between the reference plane ^ of the at least one sound transducer arrangement and the reference plane ^ of the audience area. The reference surface ^ of the at least one sound transducer arrangement can be a plane or, for example, an at least partially curved surface. In particular, a curvature of the reference surface ^ of the sound transducer arrangement in the horizontal direction can differ from a curvature in the vertical direction. In one embodiment, the reference surface ^ of the sound transducer arrangement is parameterized using coordinates ^(^, ^) = [^(^, ^) ^(^, ^) ^(^, ^)], where ^ and ^ are real, continuous variables. To determine the respective individual delay times ^. ^for sound transducers ^ a scalar-valued function of delay times ^(^, ^) can first be determined for a finite set of position vectors of the form ^ = ^(^, ^) and then the determinations of the delay time ^ ^ for sound transducers ^ at least partly by interpolations of at least two values ​​of the form ^ ( ^, ^ ) The delay times ^ ( ^, ^ ) are in one embodiment by means of numerical integration of the discrete 2D vector field [ ∆ ^ ^ ∆ ^ ^ ] The delay differences ∆ ^ ^ in ^ - direction or ∆ ^ ^ in ^ - direction given by respectively where ∆^ and ∆^ describe discrete step sizes in ^ - direction and ^ - direction respectively, ^ describes the speed of sound and where ^ ^ ^ and ^^^ by the scalar products ^ ^ ^ = ^ ^ ∙ ^^ or ^ ^ ^ = ^ ^ ∙ ^ ^ , are given, where ^ ^ describes the normalized direction vector starting from the position vector ^ = ^(^, ^) and ^ ^ and ^ ^ Describe tangent vectors to the reference surface ^ starting from the position vector ^ = ^(^, ^). The tangent vectors ^ ^ and ^ ^ are given by the partial derivatives or . In other words, it can be used in a method for determining the delay times ^ ( ^, ^ ) first the two-dimensional discrete vector field [ ∆ ^ ^ ∆ ^ ^ ] in accordance with the regulations or based on tangent vectors ^ ^ and ^ ^ the reference surface ^ of the transducer arrangement, the normalized direction vectors ^ ^and the speed of sound ^ can be determined. The vector field can then be integrated using a numerical integration method. The function ^ obtained by the integration ( ^, ^ ) then describes the desired delay times. The values ​​of the function ^ ( ^, ^ ) describe the delay times at the position vectors ^(^, ^). For each individual combination of the parameters u and v, ^ ( ^, ^ ) your own position ^ ^ . The delays at the driver positions can then be determined by spatial interpolation. The calculated time is then multiplied by the time of the nearest sample, which is determined by the sampling frequency of the entire system. In particular, the desired delay times are described by a function ^ ( ^, ^ ) , whose gradient is the two-dimensional vector field [ ∆ ^ ^ ∆ ^ ^] where the components ∆ ^ ^ and ∆ ^^ as given above. A wavefront can be viewed as a type of relief which assigns a height at each intersection point of the grid. The gradient at that point is then a vector pointing in the direction of the greatest height increase. The magnitude of this vector indicates the greatest gradient at that point. The speed of sound ^ can depend on the location, for example if there is a higher temperature at a higher level of the sound propagation region, which influences the speed of sound. The speed of sound can also depend on the location, which is then taken into account in the calculation. The numerical integration method can include the composite trapezium method, the Simpson method, the Romberg method or the more advanced inverse gradient method.In case that the reference surface ^ of the sound transducer arrangement is parameterized by means of a function ^(^, ^) = [^(^, ^) ^(^, ^) ^(^, ^)], as described above, the normal ^ to the reference surface ^ of the sound transducer arrangement, which can be used in the determination for sound level correction, is given by the cross product of ^ at the point described by ^ = ^(^, ^). ^ and ^ ^ ^ = ^ ^ × ^ ^ , where ^ ^ and ^ ^are given by the partial derivatives, as described above. Embodiments are described below by way of example with reference to figures. These show: Fig. 1 an embodiment for operating a sound transducer arrangement; Fig. 2 a schematic representation of the method for direction-dependent correction of the frequency response; Fig. 3 a schematic representation of the wavefront of a virtual sound source of wave field synthesis in a two-dimensional sound transducer arrangement; Fig. 4 a schematic representation of the wavefront of a wavefront shape of a two-dimensional sound transducer arrangement adapted to the audience area; Fig. 5 the determination of normal vectors on a curved reference surface of a sound transducer arrangement; Fig. 6 the assignment of the auxiliary grid of a sound transducer arrangement to an auxiliary grid in the audience area; Fig.Fig. 7 shows the formation of a local directional vector of the wavefront, which arises from surrounding elementary waves starting from a sound transducer and shows the audience area; Fig. 8 shows the formation of a normalized directional vector of length one; Fig. 9 shows an embodiment in which the audience area is divided into individual sub-areas with different signal content; Fig. 10 shows an adapted sound transducer configuration for a non-variable audience area; Fig. 11 shows an embodiment with a mechanically curved sound transducer surface; Fig. 12 shows the frequency response of a woofer (left) and a tweeter (right) with and without a semi-transparent plate, without signal processing; Fig. 13 shows a spatial transfer function of MDI Strong Panel; and Fig. 14 shows a transfer function of the optimized 120° beam at the angles 0°, 30°, and 60°. Fig. 1 briefly shows an embodiment of the method from DE 102021207302 A1 as an example for explanation.The method is based on assigning a point in the audience area 3 to each transducer 9 in the transducer array 1. The procedure is performed separately for each transducer 9, each intersection point of a grid in the audience area 3, and each of the simultaneously reproduced input signals of the system. The mathematical method described in DE 102021207302 A1 thus provides the delay time τ and the relative gain factors ^ for each of the input signals. ^ ^for the respective transducer. The superposition of the elementary wave with the elementary waves of the neighboring transducers results in the desired local direction within the wavefront. The local propagation directions combine to form a wavefront, the shape of which can be irregular depending on the shape and structure of the audience area. This is the only way to achieve level consistency across a wide, irregularly shaped audience area. The individual input channels Ch 1…Ch n are processed in the same way with their associated data, and the sum of all signals results in the contribution of the respective transducer to the wavefronts, which are radiated simultaneously in different directions and to different audience areas with independent signal content.In the method according to DE 102021207302 A1, the vector d for the local propagation direction of each wavefront is also available, which is used to determine the distance for each individual sound transducer. The system thus knows the path that the respective wavefront must travel from the sound transducer to the listener. The polar coordinates φ and θ (i.e. spatial / 3D polar coordinates or spherical coordinates), with which the local radiation direction of each individual wavefront is determined, are also available from the calculations. The proposed solution describes how the spectral balance of the spatial radiation of the sound transducer arrangement 1 can be significantly improved. In principle, the proposed solution can always be applied if the local radiation direction is known for each of the radiated wavefronts, which results from the superposition of the elementary waves of the surrounding loudspeakers.In the method according to DE 102021207302 A1, this radiation direction is known from the direction of the vector d. However, it can also be derived from the geometric position of the respective sound transducer in relation to the virtual sound source in which the respective wavefront originates, or it can be determined using other methods. The goal of any audio reproduction is not only a uniform level distribution but also the consistency of the audio spectrum across the entire audience area. In practice, however, there are several factors that largely prevent this goal from being achieved. First and foremost, the spatial radiation characteristics of the sound transducers used must be mentioned. Their diameter and other factors result in direction- and frequency-dependent level changes that lead to location-dependent spectral errors in the reproduction area.In addition, grilles or other structures positioned in front of the radiation source, such as a sound-permeable LED wall as described in WO 2020 / 252063 A1, can significantly alter the spectral reproduction depending on the radiation direction. In very large audience areas, airborne sound insulation, depending on relative humidity, air pressure, and temperature, severely limits reproduction, especially in the upper audio frequency range, with increasing distance from the transducer arrangement. Targeted, direction-dependent frequency response modification, for example, to specifically target specific preferences for individual audience groups, correct hearing loss for individual individuals, or expand the artistic possibilities for sound field design, is not yet possible. In Fig.Figure 2 describes an embodiment of the proposed solution in the form of a method for correcting the direction-dependent frequency response of sound wavefronts generated by a two-dimensional sound transducer arrangement according to the principle of wave field synthesis or beamforming. The illustration is limited to an exemplary signal processing for a single sound transducer. A method illustrated in Figure 2 can, for example, be applied to the method described in DE 102021207302 A1 by adding software, provided the hardware resources are sufficient. The signal lines of channels 1 ... n carry the system's input signals to all sound transducer units and to all modules. They can also be assigned to individual groups of sound transducers designed to emit different frequency ranges.The corresponding frequency response roll-off in the crossover area is then already implemented, and the sum signal of all frequency ranges is already equalized to a linear frequency response of the entire system in its main radiation direction. After the delay with τ and the level control with the relative gain factor dn for each individual loudspeaker, each input channel is fed to a summation unit before the signal drives the loudspeaker. The extension of the system for correcting the direction-dependent frequency response is added before the signal delay in each input channel for the respective loudspeaker. The order in which the subsequent corrections are carried out is not important. Individual corrections can also be omitted or others added. In the example representation, the correction of the direction-dependent frequency response changes of the individual loudspeakers is arranged first in the signal path.As with the other frequency response corrections, they are to be compensated for by a forward correction. For this purpose, the 3D polar coordinates of the respective sound transducers installed in the module are determined and saved individually in an anechoic chamber. In principle, it would also be possible to use the half-space radiation data provided by the manufacturer or the data from measurements in an infinite baffle. However, unevenness in the baffle surface of the modules, especially when multi-way arrangements are used, result in significant differences compared to radiation on a flat baffle. The measurement data is saved in angular steps in a spherical coordinate system with a radius of 1, so that with the help of the polar coordinates φ and θ, which determine the local radiation direction of each individual wavefront, the corresponding frequency response can be read out from the memory related to the sound transducer.The data for the local direction of the wavefront from the relationship G(f,φ,θ) known from [1] provide a frequency response curve which, in a downstream inversive filter Ginv (f), can largely compensate for the frequency response error of the respective sound transducer in the local radiation direction of the respective wavefront. The second point in the signal path shows an example of a compensation for acoustic obstacles in the signal path. This can be a loudspeaker grille that has a low-pass function and forms standing waves to the baffle, or a perforated projection surface that is used as a projection surface in front of the sound transducer modules. In practice, there are also far more complex requirements, such as massive projection surfaces that only have local openings for the sound to escape, or very complex, coarsely structured obstacles, such as the LED structure in front of the sound transducer modules described in [2].Here, too, the compensation is based on a forward correction of the sound transducers. The only difference is that for the measurement of the polar radiation of the sound transducers, the difference between the measurement of the individual sound transducers without the acoustic obstacle and the measurement of the polar radiation with the upstream obstacle is used and saved. The further steps are analogous to the correction of the sound transducers; in a subsequent normalization element, the correction is compensated in an inversive filter using the function Hinv (f). The third correction element in the signal curve serves to compensate for the airborne sound insulation in the signal curve. Its influence on the frequency response depends on relative humidity (in %), air pressure (in kPa), and temperature (in K), and increases with the distance of the sound transducer from the listener.In principle, a data set with stored values ​​could be created here as well, but each of the three factors mentioned changes the curve in a different way; this would require creating a data set for individual distance steps for each of the values. Therefore, it makes more sense to provide the values ​​for relative humidity (in %), air pressure (in kPa), and temperature (in K) that are valid for the entire system. To calculate the resulting frequency response of the airborne sound insulation at 1 meter directly for a distance of 1 meter using the known mathematical relationships, and to multiply the values ​​by the distance of the sound transducer from the viewer, which is known from DE 102021207302 A1 using the length of the vector d. The resulting value A is then calculated. inv(f) The inverse filter then compensates for the airborne sound insulation of the wavefront in question toward the audience area. To calculate the compensation filters for each of the three filter blocks, the data must be preprocessed. First, the data is normalized to change the overall gain in all directions by a fixed value to achieve a desired level. The data is then regularized, which involves frequency limiting and spatial and spectral smoothing of the data. The degree of smoothing depends on the required quality of compensation and the available filter resolution. Finally, the normalized and regularized frequency response data are inverted for the given angles φ and θ (or d in the third block), yielding the final inverse filter.Since compensation can lead to undesirably high filter gains at certain frequencies or in certain directions, the maximum level of compensation can be limited using the control factors wG, wH, and wA. For this purpose, a limit value can be entered for the overall system, for example, for maximum compensation of up to +12 dB. In principle, it is also possible to adapt this limit value to the current level of the input signal in question, so that the maximum available headroom is always used for compensation. Narrowband frequency response dips below a third of an octave, such as those caused by direction-dependent nulls in the sound transducers, are subjectively hardly disturbing. The situation is different with the roll-off of the entire high-frequency range, which becomes clearly audible at great distances, especially in dry ambient air. Here, the aim is to make maximum use of the available headroom.One possibility for increasing it for distant areas has already been described in DE 102021207302 A1. In this case, a larger number of transducers are assigned to audience areas of equal size as the distance from the transducer arrangement increases. With the extension of the method described in DE 102021207302 A1, a very balanced level curve without noticeable sound coloration can be achieved over a wide, irregularly shaped audience area. The described method allows for further developments. As an example, the direction-dependent frequency response modification mentioned at the beginning can be added as an additional correction element in order to specifically shape certain preferences of individual audience groups or to correct hearing loss of individual people, or to expand artistic possibilities.Or the system can operate independently as a single module with permanently programmed directivity and permanently programmed direction-dependent correction of the frequency response. In this case, a given audience area can be provided with very high-quality sound in fixed installations using one or more correspondingly programmed modules. The use of such modules with permanently programmed directivity and correspondingly stored values ​​for the direction-dependent correction of the frequency response of its sound transducers is also conceivable in the home. For example, when used as a stereo loudspeaker with a single input channel, a specifically adjusted radiation angle can achieve a spectral consistency of reproduction that would never be achievable with individual loudspeakers for the individual frequency range. Further embodiments and / or modifications are possible. Figures 3 to 11 describe aspects of operating a sound transducer arrangement 1, which, for example,can also be operated using the proposed solution (method, computer program product, sound transducer arrangement). Fig. 3 shows a given audience area 3 which is to be sound-treated using a planar sound transducer arrangement 1 according to the principle of wave field synthesis (WFS). During operation, the sound transducers of the sound transducer arrangement 1 generate elementary waves 8 which superimpose themselves to form a common wavefront 4. The common wavefront 4 is designed as if it were emanating from a virtual sound source 12. Accordingly, the surface of the wavefront 4 formed from the elementary waves 8 of the sound transducers 9 corresponds to a section of a sphere. For illustrative purposes, the common wavefront 4 is divided into rectangles 105 which represent the proportions of elementary waves 8 generated by approximately the same number of sound transducers of the sound transducer arrangement 1 on the common wavefront 4.In the spherical section 4, the respective sub-area 105 assigned to a given number of sound transducers of the sound transducer arrangement 1 is approximately the same size. Accordingly, the sound pressure is evenly distributed across the surface of the wavefront 4 at the same time. However, the audience areas 106 assigned to these sub-sections have very different areas over which the same energy of the assigned spherical wave section is distributed. The sound pressure levels in the various parts of the audience area 3 are correspondingly different. The virtual sound source 12 is located behind the sound transducer arrangement 1 in Fig. 1. The position of the virtual sound source 12 determines both the curvature of the common wavefront 4 and the direction in which it propagates.If the virtual sound source 12 is positioned close to the sound transducer arrangement 1, the coverage area is wide and the curvature of the common wavefront 4 is strong. The surface area of ​​the common wavefront 4 grows correspondingly rapidly with distance, and the sound pressure level therefore decreases rapidly. The further the virtual sound source 12 is positioned from the WFS sound transducer arrangement 1, the narrower the radiation angle and the smaller the curvature of the spherical section. At very great distances, a virtually parallel wavefront results, the level of which hardly decreases with distance. However, this narrows the coverage area 10 to such an extent that only part of the audience area 5 is supplied. The position of the virtual sound source 12 is therefore a compromise between a wide coverage area and an acceptable sound pressure drop in the rear rows of the audience area 3 to be sound-covered. As shown in Fig.1, the same number of transducers of the transducer arrangement 1 supplies a portion of the audience area 3 to be sounded, which increases significantly with distance; accordingly, the sound pressure drops significantly here. Furthermore, it is clear that even surfaces outside the audience area 3 to be sounded are unintentionally impacted by the common wavefront 4 throughout the entire coverage area 10. It is known to supply the given audience area using several virtual sound sources that have the same signal content. A method for this is described in WO2015 / 022579 A3. A three-dimensional further development of the method is described in patent application DE 102019208631 A1. The combination of several wavefronts emanating from different virtual sound sources allows for a very balanced level curve across large audience areas 3.Reflecting surfaces can be deliberately left out and the level can be set separately for each individual wavefront. Even in reverberant environments, a high direct sound level with correspondingly good speech intelligibility can be achieved in the entire audience area 3. These methods come close to the goal of completely and very evenly sounding a given audience area 3 with a two-dimensional sound transducer arrangement 1 according to the principle of wave field synthesis. However, due to the different positions of the virtual sound sources, these methods result in a time offset between the individual beams (e.g. sound radiation in a certain solid angle range). This leads to comb filter effects in the frequency response in the boundary region of the beams if the time differences between them are not compensated for.Such temporal compensation is possible because the individual virtual sound sources can be controlled independently of one another. However, in the boundary areas of the individual beams, the offset can only be fully compensated for one point; at other points, perceptible comb filter effects in the upper playback frequency range are unavoidable when wave fronts with coherent signal content overlap in the transition areas. The audience area 3 at the venue is essentially predetermined; in practice, its shape and size can hardly be adapted to the acoustic requirements for high-quality sound reinforcement. The area to be served is rarely a flat rectangle. Often the area is asymmetrical and rises more sharply towards the rear to ensure a clear view of the stage.The position of the two-dimensional sound transducer arrangement 1, which can operate according to the principle of wave field synthesis, is also predetermined in principle because the sound source is to be localized in the stage area. Embodiments of methods with an essentially two-dimensional sound transducer arrangement 1, as is known from wave field systems, for generating a closed wavefront without transitions between individual beams, the shape of which in the azimuth and elevation planes is designed to ensure a uniform distribution of the sound pressure level across the given audience area 3, are explained below with reference to Figures 4 to 11. This can be achieved if the solid angle Ω of the share of a given number of sound transducers in the wavefront to be generated is adjusted for a given part of the audience area 3 so that it each supplies an equally large part of the audience area 3.This would not be possible with discrete virtual sound sources of wave field synthesis. Fig. 4 shows a sound transducer array 1 with a plurality of sound transducers. The sound transducer array 1 is used to provide sound to an audience area 3. During operation, the individual sound transducers 9 of the sound transducer array 1 each emit elementary waves 8, which overlap to form a common wavefront 4. The sound transducers 9 of the sound transducer array 1 are provided with individual delay times ^. ^ operated, ie the sound transducers 9 radiate elementary waves 8 at individual delay times. By operating the sound transducer arrangement 1 with the individual delay times ^ ^ the common wavefront 4 is formed. In particular, the common wavefront 4 can be formed by operating with individual delay times ^ ^be shaped so that it is adapted to the geometry of the audience area 3. The sound transducer arrangement 1 and the audience area 3 are assigned to a common coordinate system 2, in which the positions of the individual sound transducers of the sound transducer arrangement 1 are determined by position vectors ^ ^ The exact delay times of the individual transducers can be determined by interpolation from the calculated delay times of the surrounding intersection points of the auxiliary grid if the transducers are not exactly at the origin of a position vector ^ ^ are arranged. The position vectors ^ ^ assigned transducer is connected to the individual delay time ^ ^ driven to emit elementary waves 8. In principle, the individual delay times differ ^ ^of the transducers 9, but they may also be at least partially identical. Determining the delay times ^ ^ is carried out by means of an assignment that assigns each intersection point of the auxiliary grid 5 to an intersection point of an auxiliary grid 6 in the audience area 3. In particular, this assignment assigns the sound transducer 9 with position vector ^ ^ a point in the audience area 3 corresponding to a position vector ^ ^ From the assignment, the direction vectors 7 result, which point from the intersection points of the auxiliary grid 5 in the direction of the assigned intersection points of the auxiliary grid 6 in the audience area 3. The normalized direction vectors in the cuboid 60, starting from the position vectors ^ ^ are each regulated by the regulation determined. The position vectors assigned to them ^ ^ determined delay times ^ ^of the transducer are then chosen so that the local direction 50 of the common wavefront 4 at the position vector ^ ^ each of the direction of the normalized direction vector 61 ^ ^ ^According to the proposed solution, the normalized direction vectors 61 therefore determine the shape of the common wavefront 4. In particular, local directions 50 of the common wavefront 4 can be determined by the direction vectors 7. The normalized direction vectors 61 are each perpendicular to the common wavefront 4. By a suitable choice of the assignment (see Fig. 8) - and thus of the normalized direction vectors 61 - the common wavefront 4 can be shaped such that it adapts to the geometry of the audience area 3. This is achieved by assigning the grid points. The wavefront 4 is then shaped such that approximately the same number of sound transducers of the sound transducer arrangement 1 is assigned to equally sized sub-areas 106 of the audience area 3. The corresponding sub-areas 105 of the wavefront 4 then have a different size at the same time.The upper sub-area in the sketch is still significantly smaller than the lower one at this distance. Accordingly, in this area the sound pressure within the same wavefront is significantly higher than in the lower sub-area intended for the nearby spectator seats. Fig. 5 shows a reference surface 30 ^ which models the sound transducer arrangement 1 in a coordinate system 2. On the reference surface 30 ^ of the sound transducer arrangement 1, a regular, curved auxiliary grid 5 is arranged, to which the positions of the individual sound transducers 9 of the sound transducer arrangement 1 are aligned. By means of the reference surface 30 ^, in particular by means of the auxiliary grid 5, coordinates for the individual sound transducers 9 of the sound transducer arrangement 1 can be determined in 3D space. The reference surface 30 ^ is parameterized by a system of curved coordinates using the equation ^(^, ^) = [^(^, ^) ^(^, ^) ^(^, ^)], where ^ and ^ are real variables.A normal 202 ^ on the reference surface 101 ^ at ^(^, ^) is by definition a normal to the surface formed by the tangent vectors 201 ^. ^ and ^ ^ , spanned tangent plane, given by the partial derivatives of ^ ( ^, ^ ) , where ^^ ^^ ^^ ^ ^ ^^ ^ ^ ^ = = ^^ ^^ ^^^ (1a) The normal 31 ^ to ^(^, ^) is given by the cross product of ^ ^ and ^ ^ as ^ = ^ ^ × ^ ^. (2) The transducers 9 of the transducer array 1 themselves do not have to be mounted at the intersection points of the auxiliary grid 5; their respective delay and level are interpolated to the intersection points in three-dimensional space. The curvature of the reference surface 30^, as well as of the auxiliary grid 5, can be different in the azimuth plane than in the elevation plane; it is also possible to curve the auxiliary grid 5 only in one plane. In practice, the reference surface 30^ of the transducer array 1 will usually be a flat surface, and thus the auxiliary grid 5 will be a flat auxiliary grid. This corresponds to the case where the transducers 9 are essentially mounted in a two-dimensional arrangement. A flat surface is considered a special case of a curved surface. Fig. 6 shows the assignment of the auxiliary grid 5 of a transducer array 1 to an auxiliary grid 6 in the audience area 3.The solution approach presented here is not based on the position of a virtual sound source (as shown in Fig. 3), but on the given geometry of the audience area 3 to be sound-covered and the geometry of the sound transducer arrangement 1. In principle, the audience area 3 to be sound-covered can have any shape: flat, curved, or even rising. Fig. 6 shows an irregularly shaped audience area 3 to be sound-covered, which is particularly not symmetrical and rises more sharply in the rear right-hand area than on the left-hand side. With conventional approaches, but also with virtual sound sources of wave field synthesis, the task of supplying an audience area such as the one shown in Fig. 6 with direct sound very evenly can only be inadequately solved because the curvature of the wavefronts of virtual sound sources of wave field synthesis is always a section of a sphere.However, with the help of the illustrated assignment of the auxiliary grids 5 and 6, a common wavefront 4 can be generated whose shape is adapted to the geometry of the audience area 3 to be sound-covered. To solve the problem, a coordinate system 2 is determined. Coordinate points distributed across the audience area 3 to be sound-covered are assigned to the coordinate system 2. In Fig. 6, these coordinate points are arranged in the audience area 3 at the intersection points of an auxiliary grid 6, but they can also be distributed in the audience area 3 using other mapping methods. In addition, an auxiliary grid 5 is assigned to the coordinate system 2, by means of which the positions of the sound transducers 9 of the sound transducer arrangement 1 can be determined. The auxiliary grid is shown in Fig. 5 as a flat, regular auxiliary grid. In principle, however, the auxiliary grid can also be curved, i.e. have curved lines.In principle, the auxiliary grid 5 can be arranged on a reference surface, which models the sound transducer arrangement 1. The number of coordinate points in the audience area 3 corresponds to the number of intersection points of the auxiliary grid 6. Thus, each intersection point of the auxiliary grid 5 can be assigned a coordinate point of the auxiliary grid 6 in the audience area 3. The distribution of the coordinate points should be across the entire audience area 3, with the distances between the individual coordinate points as uniform as possible. Each intersection point of the grid 5 is assigned a coordinate point with the position ^. ( ^, ^, ^ )in the audience area 3. The connecting line 7 between the intersection points of the auxiliary grid 5 and its associated coordinate point in the audience area 3 then forms a vector in the coordinate system 2, which is the basis for calculating the propagation time and level of the audio signal. The illustrated flat auxiliary grid 5 of the sound transducer arrangement 1 has the shape of a rectangle whose aspect ratio is the same as that of the planned sound transducer arrangement 1, for example in the form of a sound transducer array. It should have at least as many intersection points as there are sound transducers 9 planned in the sound transducer arrangement 1. In principle, the aspect ratio is not defined, so it would also be possible to construct a single line of sound transducers if this is appropriate to the given spatial situation in the audience area 3.The spacing of the grid lines of the auxiliary grid 5 can vary in the horizontal and vertical planes, but should at least correspond to the number of rows and columns of the two-dimensional sound transducer array 1. The sound transducers 9 of the sound transducer array 1 can be mounted with their acoustic center at the intersection points of the auxiliary grid 5. However, their position can also deviate from these intersection points, with their respective propagation times and levels being determined by interpolating the values ​​calculated for the surrounding grid points. A higher number of grid lines improves the accuracy of the interpolation. A lower number of grid lines results in a wavefront composed of flat partial surfaces rather than a uniformly curved one. The resulting diffraction effects lead to local irregularities in the frequency response.In principle, physical transducers 9 do not need to be assigned to all intersection points of the auxiliary grid 5. This allows for interrupted placement in the areas where the bass-midrange transducers 9 have their sound outlets. Furthermore, all transducers 9 can be distributed slightly irregularly across the area, as described in DE 102009006762 A1. This reduces unwanted aliasing effects in the audience area 3 because the resulting comb filter effects statistically balance each other out somewhat in the frequency response. The auxiliary grid 6 placed over the audience area 3 completely encloses it. The shape of the auxiliary grid 6 is adapted to the audience area 3. This can, in principle, be done manually.In practice, however, several hundred to several thousand grid points are necessary to ensure that the distance between the sound transducers 9 is sufficiently small to achieve reproduction that is largely free of audible aliasing effects. The small number of grid lines in the sketches serves to provide clarity when explaining the operating principle. It is therefore advantageous to automatically determine the coordinate points in the audience area 3 using a 3D CAD file of the audience area 3 and a suitable mapping process. This way, even areas that should not be directly hit by the common wavefront 4 because they emit unwanted reflections can remain free of assigned grid points. This means that no sound transducers 9 are assigned to them whose wavefront is directed directly in their direction. The coordinate points are moved from these areas without changing their number.Surrounding coordinate points shift accordingly to maintain an even distribution across the audience area 3. Each intersection point of the auxiliary grid 5 in the plane of the two-dimensional sound transducer arrangement 1 should be assigned a reference point in the audience area 3 to be sound-covered. Visualization in a 3D CAD file facilitates the shutdown of unoccupied audience areas 3. The calculations remain fundamentally unchanged; only the sound transducers assigned to unoccupied audience areas 3 are not supplied with a signal. This results in a lower diffuse-field sound level at the event location, which contributes to better speech intelligibility in the occupied audience areas 3. Fig. 7 illustrates by way of example how the local curvature 50 of the wavefront 4, which according to the described method does not have to be a spherical section, arises from the superposition of the elementary waves 8 of the surrounding sound transducers 9.For simplicity, the acoustic centers of the sound transducers 9 are mounted in the example at the intersection points of the auxiliary grid. The individual sound transducer 9, shown in black in the sketch, has an omnidirectional half-space radiation according to the principle of wave field synthesis. Accordingly, the elementary wave 8 generated by it alone cannot form a directional vector. The local directional vector ^ of the wavefront assigned to it only arises at some distance from the sound transducer arrangement 1 through the superposition of the elementary waves 8 of the surrounding sound transducers. The directional vector 7 ^ can be determined for this intersection point using the rule ^ = ^ − ^ (3). It is always orthogonal to the local wavefront 50. In the exemplary representation in Fig. 7, the point described by the vector ^ lies at an intersection point of the auxiliary grid 6 of the audience area 3.In principle, the direction vector 7 ^ can also be determined without the aid of the auxiliary grids 5 and 6. In this case, the direction vector 7 ^ starts from a position vector ^ on a reference surface 30 ^, which models the sound transducer arrangement 1, and points to a position vector ^ in the audience area 3, or to a position vector ^, which describes a point on a reference surface ^ 30 models the audience area 3. The following describes a method of deriving delay times and levels for the individual sound transducers 9 from given direction vectors 7, so that the superposition of their elementary waves 8 superposes to form a wavefront that is consistently aligned with the given audience area 3. In Fig. 8, the direction vector 7 ^ selected as an example from Fig. 6 is scaled to the length of the normalized direction vector 61 ^. ^ which is considered The desired wavefront generated by the transducer arrangement 1, in particular in the form of a curved or planar array, can be locally approximated by a plane wave propagating along (i.e., locally in the direction of) the normalized direction vector 61 ^ ^ Each local plane wave can be directed in the desired direction by operating the transducers 9 of the transducer array 1 according to the corresponding delay times of the signal. The delay time ^ ^ at any position ^ ( ^, ^ ) on the reference surface 30 ^ of the transducer arrangement 1 is described by the scalar-valued delay function ^(^, ^). In vector calculus, the gradient of a scalar-valued function ^ of several variables is a vector field ^^, whose components can be determined by partial derivatives of ^, in particular The deceleration gradient ^^ ( ^, ^) can be determined in the following way: The scalar products of the normalized direction vector 61 ^ ^ and tangent vectors ^ ^ and ^ ^ respectively ^^ ^ and ^^ ^ are given by ^ ^ ^ = ^ ^ ∙ ^ ^ (6a) The scalars ^ ^ ^ and ^^ ^ can be physically interpreted as the local differentials of the path lengths between the plane wave and the tangential plane of the transducer arrangement 1. In the special case of a planar transducer arrangement 1, as shown in Fig.8, ^ ^ ^ and ^^ ^ equal to the sizes illustrated in Fig.8 ^^ ^ and ^^ ^ , which are the x- and z-components of the vector ^ ^ The relationship between the delay gradient ^^(^, ^) from equation (5) and the components ^ ^ ^ and ^^ ^is given by the speed of sound ^. Therefore, the partial derivatives of the delay function ^ can be described as ^^ ^^ = ^ ^ ^ ^ (7a) and ^^ ^^ = ^ ^ ^ ^ . (7b) In practice, the distance between the transducers 9 is finite. Therefore, the differential equations in equations (7a) and (7b) must be rewritten as discrete difference equations. The delay differences ∆ ^ ^ and ∆ ^ ^ in ^- and ^- directions are now given by and where ∆^ and ∆^ are the discrete step sizes in the ^- and ^- directions, respectively. The required delay can be determined by numerical integration of the discrete 2D vector field [∆ ^ ^ ∆ ^^] can be found. Several mathematical integration methods are available, such as the composite trapezium, Simpson's, or more advanced inverse gradient methods. The integration constant can be freely chosen. To satisfy the causality condition and minimize system latency, the minimum delay across all drivers is subtracted from the calculated delays. The relative gain factor ^ ^ ^ for each position in the sound transducer arrangement 1 is given by the scalar product of normalized direction vector 61 ^ ^ and normal ^ according to the equation ^ ^ ^ = ^ ^ ∙ ^, (9) where the normal ^ is defined as in equation (2). By operating the transducers 9 according to the relative amplification factors ^ ^ ^it is guaranteed that the sound pressure level at the receiver position ^ is independent of the angle of the directional vector ^ to the normal ^. With increasing inclination of the radiation with respect to the normal ^ the number of sound transducers 9 in a given solid angle Ω increases, so that the sound pressure level would increase here. The compensation according to equation (9) corrects this according to a cosine function of the angle γ in Fig. 6. With a uniform distribution of the coordinate points ^ a very homogeneous distribution of the sound pressure over the entire audience area 3 to be sound-covered is guaranteed. Fig. 9 shows that the audience area 3 to be sound-covered can also be divided into individual sub-areas 701, 702, 703 with different signal content. In principle, sub-areas of the sound transducer arrangement 1 could then also be assigned to these sub-areas.However, a much more precise sound reinforcement is achieved if the high directivity of the entire arrangement is used to direct the signal content to the desired audience areas 3. In each of the sub-areas 701, 702, 703, the number of crossing points 6 then corresponds to the number of crossing points 5 of the auxiliary grid of the sound transducer arrangement 1. With the same signal content, the division into sub-areas is not useful if the sub-areas are not sufficiently spatially separated. With a coherent signal content, comb filter effects would then arise at the area boundaries. Individual sub-areas can also be smaller than the assigned sound transducer 9 area, provided that the crossing points of the auxiliary grid in the audience area 3 are closer together than in the auxiliary grid of the sound transducer arrangement 1. In this case, concave wave fronts are created whose sound pressure level is higher in the audience area 3 than at the generating radiator area itself.It is also possible to reduce the size of an auxiliary grid in the audience area 3 to a single point. Then, using the vector-based method described above, the two-dimensional transducer array 1 generates the same concave wavefront as would be generated in a two-dimensional transducer array 1 based on the principle of wave field synthesis for a virtual sound source at this point. Using the coordinates of the grid points 5 on the reference surface of the transducer array 1 and their associated coordinates 6 in the audience area 3, it is also possible to compensate for the sound pressure drop at higher frequencies caused by airborne sound insulation. For a given humidity, the frequency-dependent attenuation values ​​of the air per meter are precisely known. A corresponding inverse equalization curve can then be assigned to each transducer 9 because the distance to the corresponding audience seat (given by the length of the directional vector ^ in Fig. 7) is known.In large audience areas 3, the sound pressure drop at the upper limit of the audio range can rise to well over ten dB in dry air. In any case, this frequency range must be driven at a much higher level in a planar sound transducer arrangement 1 because the level gain due to the improved adaptation of the synchronously operating loudspeaker group only takes effect at longer wavelengths. The additional compensation of the airborne sound insulation for the distant audience areas 3 can therefore bring the system to the limits of its controllability at high signal levels in the upper audio frequency range. One solution to this problem is to arrange the coordinate points ^ closer together with the distance to the sound transducer arrangement 1. The distant audience areas 3 are then assigned a smaller sub-area 106 to the same number of sound transducers 9.Each halving of the area results in a level increase of 3 dB, by which the control of the assigned sound transducers 9 would have to be reduced so that the sound pressure level in the entire audience area 3 remains virtually constant. The correspondingly reduced control signal is associated with greater headroom in the assigned amplifiers. This can then be used to further equalize the control signals. The localization of the sound source in the described process differs fundamentally from the localization of a virtual point sound source in wave field synthesis. In wave field synthesis, virtual sound sources are generally localized at their virtual starting point, similar to a real sound source, regardless of the listener's position in the coverage area. However, the wavefront tailored to audience area 3 does not emanate from defined positions of virtual sound sources.It arises, as it were, from an extended source of many different origins in the area behind the transducer surface. The viewer in the front left seat in Fig. 4 will assign the origin of the wavefront to the lower left corner of the transducer array 1, while the viewer in the rear right will perceive the sound to be coming from the upper right corner of the transducer array 1. This is not a disadvantage for reproduction without a visual reference to the sound source, but spatial reproduction is only possible to a limited extent, as shown in Fig. 4.Nevertheless, the method can be assigned to the field of wave field synthesis because the theoretical derivation of wave field synthesis from the Kirchhoff-Helmholtz integral makes it possible to generate any desired wavefront shape (Jens Ahrens: The Single-layer Potential Approach Applied to Sound Field Synthesis Including Cases of Non-enclosing Distributions of Secondary Sources, dissertation, Technical University of Berlin, 2010). Further developments So far it has been assumed that the sound transducers 9 of the sound transducer arrangement 1 are arranged in a regular grid. In practice, however, the distribution of the sound transducers 9 can also be irregular. First, the travel times ^ are calculated for a sufficiently dense regular grid, after which the travel times to the irregularly placed sound transducers are interpolated. Fig.10 shows a complexly designed audience area 3 with sub-areas 802 and illustrates an assembly of the sound transducer arrangement 1 with sound transducers 9, wherein the assembly is adapted to the complex design of the audience area 3. In the illustrated embodiment, the assignment between points on the sound transducer arrangement 1 and points in the audience area 3 is made by assigning intersection points of the auxiliary grid 5 of the sound transducer arrangement 1 to intersection points of the auxiliary grid 6 of the audience area 3. However, not all intersection points of the auxiliary grid 5 are assigned sound transducers 9 of the sound transducer arrangement 1; in other words, intersection points of the auxiliary grid 5 remain unequipped. In particular, unequipped intersection points are found between equipped intersection points. The shape of the sound transducer arrangement 1 can thus be adapted to the complex design and / or geometry of the audience area 3 in fixed installations.This enables more effective use of the sound transducers. The auxiliary grid 6 in the audience area 3 can, for example, be a rectangle; in particular, it can extend beyond the audience area. Irregular shapes of the auxiliary grid 6 can lead to incorrect results in calculations using the method described. Intersecting points of the auxiliary grid 6 in the audience area 3 to which no audience is assigned, i.e. which in this case lies outside the partial areas 5a, 5b, 5c of the audience area 3 to be sound-covered, are assigned auxiliary grid points of the auxiliary grid 5 of the sound transducer area that are not equipped with sound transducers or are switched off. Any woofer-midrange sound transducers used are also aligned with the auxiliary grid 5 of the sound transducer arrangement 1. The calculation of their travel times and levels is based on the nearby grid points. The time shift resulting from any bass offset must be compensated for.The phase position of subwoofers can also be effectively adjusted in this way. According to the method, the shortest of all calculated travel times to the individual sound transducers is subtracted from all calculated travel times, so that the front of the wavefront adapted to the audience area 3 is always generated immediately. A further embodiment relates to a device shaped according to the rules of the described method. With it, a single wavefront, whose shape is adapted to the given audience area, can be generated from a mono signal without electronic time shifting of the signal. This mechanical solution can be advantageous for fixed installations in acoustically problematic environments. In this way, a sound system can be installed with reasonable effort that ensures a high direct sound component with correspondingly good speech intelligibility even under unfavorable acoustic conditions. In Fig.11 illustrates a mechanically curved sound transducer arrangement 1 by way of example. By means of the mechanically curved sound transducer arrangement 90, the audience area 3 to be sounded, as described with reference to Fig. 6, can be supplied with a tailored common wavefront 4. The operation of the sound transducers 9 of the sound transducer arrangement 1 is controlled according to the delay times ^ obtained using the described method. ^mechanically realized. All transducers are supplied with a coherent signal, i.e., from a mono signal source. The mechanical realization is achieved by suitable positioning of the transducers 9 on the mechanically curved transducer arrangement 90, in particular by a suitable spatial offset, in particular an offset in the propagation direction of the common wavefront, of the transducers 9 to each other. In order to determine the respective position of the transducers 9 in the adapted transducer area for the audience area 3 to be sounded, a path distance ^ ^ , starting from the corresponding grid point of a plane auxiliary grid 5 along the extended diagonal of the unit vector 61 ^ ^specific cuboid 40. With the help of the alternating angles ^ and ^ which are therefore known, the new coordinates for the acoustic center of the respective sound transducer 9 and also its orientation can be determined in the right-angled triangles of the cuboid 40. The delay times calculated according to the described methods for the individual sound transducers 9 arise from the mechanical offset of the acoustic centers of the respective sound transducers 9 along the diagonal Sd of the respective cuboid. The different signal levels for the individual sound transducers 9 of this two-dimensional sound transducer arrangement 1 can then be approximately realized at a common power amplifier by suitable parallel and series connection of the sound transducers 9 or by connecting them to different amplifiers, each of which is assigned to sound transducers 9 with approximately the same level values.As long as the sound transducers 9 do not exhibit significant dips in their spatial radiation characteristics, they do not need to be aligned along the diagonals of the cuboid. In this case, the method can also be implemented using a device for transverse displacement of sound transducers, as described in WO 2015 / 004526 / A2. The displacement ^. ^of the acoustic center from the grid point of the original transducer grid is then obtained from the quotient A single mechanical device cannot generate spatial sound reinforcement of the audience area 3. It is suitable for ensuring, with manageable effort, a sound reinforcement in which the distribution of the sound pressure level is very uniform throughout the entire audience area 3 and which ensures high speech intelligibility even in acoustically unfavorable rooms. In the following, some embodiments of methods and devices for sound reinforcement of a given audience area 3 by means of a sound transducer arrangement 1, which are controlled with individual delay times and levels based on the principle of wave field synthesis, are presented. For example, in variant 1, the shape of the common acoustic wavefront 4,which is composed by superposition of elementary waves 8 of the sound transducers 9, are determined by the given geometry of the audience area 3 and the sound transducer arrangement 1 in such a way that, in a common coordinate system 2, each intersection point of a regular, at least partially flat and / or curved grid assigned to the sound transducers is assigned a coordinate point in the audience area 3, whereby a vector results from their connecting line, from which the delay time for the respectively assigned sound transducer 9 can be calculated by mathematical combination, whereby the local curvature of the wavefront, which arises by superposition of the elementary waves 8 of the surrounding sound transducers 9, progresses in the direction of this vector, so that a closed wavefront is created,which can reach the entire audience area 3 and in which, in addition, a level correction for each transducer 9 from its assigned vector is possible, which improves the homogeneity of the sound pressure across the entire audience area 3. In one embodiment of variant 1, for example, the coordinate points in the plane of the two-dimensional transducer arrangement 1 are intersection points of a flat or curved grid, to which coordinate points in the audience area 3 are assigned in a common coordinate system 2,The connecting lines between the respective assigned grid points and points in the audience area 3 do not cross or intersect. In a further embodiment, the number of grid lines in the plane of the two-dimensional transducer array 1 in the horizontal and vertical directions corresponds to the number of transducers installed in the rows and columns of the two-dimensional transducer array 1. Alternatively, the number of grid lines can be greater than the number of transducers 9 in the rows and columns of the two-dimensional transducer array 1.wherein the acoustic center of the individual sound transducers 9 can be arranged at the intersection point of the grid lines. The values ​​for delay time and / or level can be determined, for example, by interpolating the values ​​of the surrounding grid points. that the reference points in the audience area 3 can be adapted in all three spatial dimensions to the requirements of the geometry of the audience area 3, whereby care must be taken to ensure that the areas between the individual grid points remain approximately the same size over the entire audience area 3, resulting in a relatively uniform distribution of the sound pressure level over the entire audience area 3. In a further embodiment of variant 1 or one of the above variants, the vectors,which result from the difference between the coordinates of the grid point assigned to the respective sound transducer 9 in the plane of the two-dimensional sound transducer arrangement 1 and the respective position of the assigned coordinate point in the audience area 3, on components of the unit vector ^, ^to create a mathematical basis for determining the time differences between adjacent transducers. In principle, not all intersection points of the auxiliary grid need to be assigned physical transducers 9 that radiate the same frequency range. This makes it possible, for example, to interrupt the array in the areas where the woofer-midrange transducers 9 have their sound outlets or to place tweeters in front of the woofer-midrange transducers, with the time differences caused by the mechanical offset being compensated for by interpolation at the intersection points of the auxiliary grid.In a further embodiment of the variants described above, the influence of the angle which the synthesized wavefront takes at a given grid point to the plane of the sound transducer arrangement 1 on the signal level perceived at the associated point in the audience area 3 is compensated by compensating the level of the sound transducer associated with the respective point with the cosine function of the angle in question, the value of this cosine function corresponding to the value of the component. of the unit vector ^ ^The intersection points of the flat or curved grid in the plane of the two-dimensional transducer array 1 can, in principle, also be assigned several auxiliary grids in the audience area, each with the same number of points as the grid in the plane of the two-dimensional transducer array 1, whereby sub-areas within the audience area can, for example, be supplied simultaneously with different signal content. The reference points in the audience area 3 can be distributed more closely with increasing distance from the two-dimensional transducer array 1, for example, with the intention of making the areas between the reference points smaller with increasing distance from the two-dimensional transducer array 1, so that the assigned transducers 9 of the two-dimensional transducer array 1 can be driven at a lower level while maintaining an unchanged sound pressure in the respective area.which provides more headroom for compensating for the drop in high frequencies caused by the airborne sound insulation in these areas. The influence of airborne sound insulation on the signal at the audience seat for the individual transducers 9 can be compensated for by equalizing their respective input signals with the inverse equalization of the influence of airborne sound insulation at a given humidity according to the distance ‖^‖ of the assigned vector. In principle, individual audience areas 3 can be excluded from the supply, for example, temporarily. For example, if they are not occupied during an event, thereby improving the direct sound component in the remaining audience area 3. In a device for sound reinforcement of a given audience area 3, the propagation times with which the individual transducers 9 of the two-dimensional transducer array 1 radiate according to one of the method variants described above areThis is not achieved by electronically delaying the signal content, but by mechanically positioning the transducers, which are controlled with coherent signals, whereby the signal levels for the respective transducer 9 correspond to the values ​​determined for the original intersection points of the grid. Some embodiments of the method for direction-dependent correction of the frequency response of sound wave fronts are described below. For example, in variant 1a, the direction-dependent correction of the frequency response of sound wave fronts generated by a two-dimensional transducer arrangement according to the principle of wave field synthesis or beamforming methods, for example, in an extension of the method described in DE 102021207302 A1 for sound reinforcement of a given audience area, in which several input signals can be assigned simultaneously and independently to different audience areas,whereby the signal levels are adjusted in such a way that a very balanced sound pressure level is guaranteed in the entire audience area, by additionally inserting corresponding correction elements into the signal path of each input channel for each respective sound transducer, non-linearities in the frequency response of individual wavefronts over the entire audience area are largely compensated for by the fact that, depending on the local radiation direction of the respective wavefront to be corrected in relation to the front surface of the two-dimensional sound transducer arrangement based on an inverse forward correction of the factors,which physically influence their radiation, a linearization of the radiation of each transducer is compensated for for each of the system's input channels. In a refinement of variant 1a, nonlinearities in the frequency response of the individual transducers in the transducer array, which depend on the radiation direction, are largely compensated for by a forward correction in which the data stored under the 3D spherical coordinates of the respective transducers installed in the module are individually determined and stored in the anechoic chamber.so that their frequency response in the radiation direction of the respective wavefront is retrieved from the memory using the spherical coordinates φ and θ, and inverted and normalized as a function Ginv (f), the frequency response error of the respective sound transducer in the local radiation direction of the respective wavefront is largely compensated for by an inverse filter additionally inserted into the respective signal path. Additionally or alternatively, in one embodiment, the frequency response errors caused by acoustic obstacles in the propagation direction of the wavefront can be largely compensated for by forward correction by spatially recording and storing the differences between the 3D spherical coordinates of the individual sound transducers between an unobstructed radiation and the radiation behind the structure obstructing the propagation of the respective wavefront as 3D spherical coordinates.so that the differences between the two frequency responses in the direction of radiation of the respective wavefront are retrieved using the polar coordinates φ and θ and, normalized and inverted as a function Hinv (f), largely compensates for the frequency response error caused by the acoustic obstacle in the local direction of radiation of the respective wavefront by an inverse filter additionally inserted into the respective signal path. Additionally or alternatively, the influence of airborne sound insulation on the frequency response of the respective wavefront can be largely compensated by directly calculating the attenuation curve for a distance of 1 meter using the current values ​​for relative humidity (in %), air pressure (in kPa), and temperature (in K) in the audience area from the known mathematical relationships, and by multiplying the inverted and normalized values ​​by the distance of the transducer from the audience area.to which the local part of the respective wavefront is aligned, in order to compensate for the distance-related level loss of the respective wavefront towards the audience area by means of a filter in the signal path with the resulting function Ainv(f). Additionally or alternatively, the inversion of the frequency response resulting from the stored or calculated data can be preceded by the filters in the signal path in order to compensate for a drop in frequency response by a correspondingly higher gain and to reduce a resonance peak by attenuating the signal in the corresponding frequency range. The correction can be carried out in octaves, thirds, or smaller frequency steps, and a shift in the overall level of the respective channel upstream of the filter is compensated for by a corresponding correction of the overall level of the correction curve.in which a maximum compensation value prevents overdriving of subsequent stages in individual frequency ranges. Additionally or alternatively, additional polar frequency response data and inverse or non-inverse filters, which effect a direction-dependent frequency response change for selected wavefronts, and which can be used to accommodate specific preferences of individual audience groups, correct hearing losses of individual individuals, or achieve expanded artistic design options for the spatial sound field, or other acoustic goals, can be inserted into the signal path as an additional correction element. In principle, the order of the correction elements in the signal path can be freely selected, and individual correction options can be bypassed or omitted. Additionally or alternatively, fixed correction values ​​can be stored in the system.if the direction of the wave fronts is fixed in the system. In principle, systems with fixed directivity and fixed direction-dependent correction of the frequency response can operate independently as individual modules or be combined with other appropriately programmed modules to form a fixed transducer array. Additionally or alternatively, the data on the directivity pattern can be stored in the individual modules and read and overwritten from a central memory via a data bus in a setup process. Further embodiments are described below. Example 1: Method for providing sound to at least one audience area (3) by at least one transducer arrangement (1) with a plurality of transducers (9), wherein the individual transducers (9) of the at least one transducer arrangement (1) each emit elementary waves (8).which are superimposed to form a common wavefront (4), characterized in that a) the at least one sound transducer arrangement (1) and the at least one audience area (3) are geometrically linked to one another by a coordinate system (2) and b) between the physical positions of the individual sound transducers (9) in the at least one sound transducer arrangement (1) and position vectors ^, ^ for determining coordinates in the area of ​​the at least one sound transducer arrangement (1) there is a spatial assignment, and further c) an assignment of points of the coordinate system (2) to points in the at least one audience area (5) according to a position vector ^ ^ where d) in the coordinate system (2) there are direction vectors, in particular normalized direction vectors and where e) depends on the spatial assignment of the position vectors ^ ^ and the transducer (9) delay times ^ ^for the sound transducers (1) are determined, with which elementary waves (8) are radiated by the sound transducers (9), where e) the delay times ^ ^ the sound transducer (9) is selected in such a way that the local direction (50) of the common wavefront (4) corresponds to the direction of the direction vector, in particular the normalized direction vector (61) ^ ^ ^Example 2: Method according to Example 1, characterized in that the sound transducers (9) of the at least one sound transducer arrangement (1) are arranged in or on a plane or in or on an at least partially curved or planar surface (30), in particular in a grid-like manner, wherein the position of the acoustic centers of the sound transducers can deviate from the intersection points of the auxiliary grid (5), provided that the associated change in delay time and level is corrected by spatial interpolation or other methods.Example 3: Method according to Example 1, characterized in that the sound transducers (9) of the at least one sound transducer arrangement (1) are arranged in a three-dimensional area, in particular a room, in particular such that at least a subset of the sound transducers (9) of the at least one sound transducer arrangement (1) is arranged on a reference surface (30) and the positions of the remaining sound transducers (9) of the at least one sound transducer arrangement (1) can be determined by an offset (91) in the three-dimensional area. Example 4: Method according to at least one of the preceding examples, characterized in that the operation of the sound transducers (9) with a delay time ^. ^by activation by means of a computer system and / or mechanically, in particular by spatial offsetting (91) of the sound transducers (9) of the at least one sound transducer arrangement (1) relative to one another. Example 5: Method according to at least one of the preceding examples, characterized in that the at least one audience area (3) has at least partially a concave and / or at least partially a convex shape. Example 6: Method according to at least one of the preceding examples, characterized in that the at least one audience area (3) can be described as a continuous surface. Example 7: Method according to at least one of the preceding examples, characterized in that the at least one audience area (3) can be described as a discontinuous surface which is composed of at least two continuous surfaces.Example 8: Method according to at least one of the previous examples, characterized in that the position vectors ^. ^ a regular grid. Example 9: Method according to at least one of the preceding examples, characterized in that the position vectors ^ ^ a regular grid (6) on an area assigned to the at least one public area (3). Example 10: Method according to at least one of the preceding examples, characterized in that the assignment corresponding to each position vector ^ ^ the point in at least one audience area (3) corresponding to the position vector ^ ^assigns, can be determined by means of connecting lines from the at least one sound transducer arrangement (1) to the audience area (3). Example 11: Method according to at least one of the preceding examples, characterized in that the levels at which the sound transducers (9) of the at least one sound transducer arrangement (1) are operated are adjusted such that the sound pressure in the at least one audience area (3) is homogeneous. Example 12: Method according to Example 11, characterized in that the levels at which the sound transducers (9) of the at least one sound transducer arrangement (1) are operated can be determined by means of a relative amplification factor based on the rule ^ ^ ^ = ^^ ^ ∙ ^ ^ , where ^ ^ the normal to the reference surface (30) ^ at the position vector ^ ^which is assigned to the sound transducer (9). Example 13: Method according to at least one of the preceding examples, characterized in that the at least one audience area (3) has at least two sub-areas which are exposed to different signal content. Example 14: Method according to at least one of the preceding examples, characterized in that the common wavefront (4) is shaped such that it is adapted to the geometry of the at least one audience area (3) by assigning the grid points and then shaping the common wavefront (4) such that substantially the same number of sound transducers (9) of the sound transducer arrangement (1) is assigned to equally sized sub-areas (106) of the at least one audience area (3).Example 15: Method according to at least one of the preceding examples, characterized in that sub-areas of the at least one audience area (3) are assigned sub-areas of the sound transducer arrangement (1), to which different audio content can be simultaneously assigned, wherein a directivity of the sound transducer device (1) is used to align signal content to predetermined parts of the at least one audience area (3), wherein in each of the sub-areas (701, 702, 703) the number of intersection points (6) then corresponds to the number of intersection points (5) of the auxiliary grid of the sound transducer arrangement (1). Example 16: Method for determining delay times ^. ^ for operating sound transducers (9) of at least one sound transducer arrangement (1) with a plurality of sound transducers (9) ^ for generating elementary waves (8) according to the delay times ^ ^for providing sound to at least one audience area (3), comprising the following steps - determining a coordinate system (2), by which o the at least one sound transducer arrangement (1) is approximately described as a two-dimensional reference surface (30) ^ of the at least one sound transducer arrangement (1) and o the at least one audience area (3), - determining position vectors ^ on the reference surface (30) ^ of the at least one sound transducer arrangement (1), from which the positions of the sound transducers (9) of the at least one sound transducer arrangement (1) can be determined, - determining an assignment which assigns each position vector ^ on the reference surface (30) ^ of the at least one sound transducer arrangement (1) a position vector ^ corresponding to a point in the at least one audience area (3), - determining direction vectors, in particular standardized direction vectors (61) ^ ^starting from the position vectors ^, where the normalized direction vectors (61) ^ ^ starting from the position vectors ^ in the direction of the position vector ^ assigned to the position vector ^; and - determination of delay times ^ ^ for sound transducer j, so that the elementary waves (8) generated by the sound transducers (9) during operation according to the delay times ^ ^ to form a common wavefront (4), where the normalized direction vectors (61) ^ ^ each describe local propagation directions (50) of the common wavefront (4). Example 17: Method according to Example 16, comprising a determination of relative amplification factors ^ ^ ^ for at least a subset of the position vectors s according to the rule ^ ^ ^ = ^ ^ ∙ ^,where ^ is a normal to the reference surface (30) ^ of the sound transducer arrangement (1) at the point determined by the position vector ^ and ^ ^ the standardized direction vector (61) starting from the position vector ^. Example 18: Method according to example 16 or 17, characterized in that the position vectors ^ describe the positions of the sound transducers (9). Example 19: Method according to at least one of examples 16 to 18, characterized in that each position vector ^ on the reference surface (30) ^ of the at least one sound transducer arrangement (1) is assigned a position vector ^ on a reference surface ^ of the at least one audience area (3), and the determination of the direction vector, in particular the standardized direction vector (61) ^ ^ for at least one position vector ^ by means of a connecting line (7) between the position vector ^ and the position vector ^, in particular ^ ^^ ^ according to the calculation rule ^ = . Example 20: Method according to Example 19, characterized in that the connecting lines (7) for determining the normalized direction vectors (61) ^ ^do not cross or intersect in pairs. Example 21: Method according to at least one of examples 16 to 20, characterized in that the assignment between the position vector ^ and the position vector ^ takes place automatically, in particular using a 3D CAD file of the at least one audience area (3). Example 22: Method according to at least one of examples 19 to 21, characterized in that the position vectors ^ are evenly distributed on the reference surface ^ of the at least one audience area (3) and thus correspond to evenly distributed points in the at least one audience area (3). Example 23: Method according to at least one of examples 16 to 22, characterized in that the reference surface ^ of the at least one audience area (3) is described by an auxiliary grid (6) on which the position vectors ^ are at least partially intersection points.Example 24: Method according to at least one of examples 16 to 23, characterized in that the reference surface (30) ^ of the at least one sound transducer arrangement (1) is described by an auxiliary grid (5) on which the position vectors ^ are at least partially intersection points. Example 25: Method according to at least one of examples 16 to 24, characterized in that the reference surface (30) ^ of the at least one sound transducer arrangement (1) is parameterized by means of the coordinates ^(^, ^) = [^(^, ^) ^(^, ^) ^(^, ^)], where ^ and ^ are real, continuous variables or discrete variables and thus in particular the position vectors ^ can be described in the form ^ = ^(^, ^). Example 26: Method according to example 16 and 25, characterized in that the normal ^ to the reference surface (30) ^ of the sound transducer arrangement (1) at the point described by ^ = ^(^, ^) is given by the cross product of ^. ^ and ^ ^ as ^ = ^ ^× ^ ^ , where ^ ^ and ^ ^ are given by the partial derivatives ^^ ^^ ^^ ^^ ^ ^ = ^^ = ^ ^^ ^^ ^^^ respectively 27: Method according to Example 26, characterized in that for determining the respective delay times ^ ^ first a scalar-valued function of delay times ^ ( ^, ^ ) for a finite set of position vectors of the form ^ = ^(^, ^) and the determination of the delay times ^ ^ for the transducers (9) with position vector ^ ^ at least partly by interpolation of at least two values ​​of the form ^ ( ^, ^ ) Example 28: Method according to Example 27, characterized in that the scalar-valued function of delay times ^(^, ^) is determined by means of numerical integration of the discrete 2D vector field [ ∆ ^ ^ ∆ ^ ^ ]is determined, - where the delay differences ∆ ^ ^ in ^ - direction or ∆ ^ ^ in ^ - direction are given by ∆ ^ ^ = ^ ^ ^ ^ ∆^ respectively - where ∆^ and ∆^ describe discrete step sizes in the ^ - direction and ^ - direction respectively, - where ^ describes the speed of sound and - where ^ ^ ^ and ^^ ^ by the scalar products ^ ^ ^ = ^ ^ ∙ ^ ^ or ^ ^ ^ = ^ ^ ∙ ^ ^ , are given, where ^ ^ describes the normalized direction vector (61) starting from the position vector ^ = ^(^, ^) and ^ ^ and ^ ^ Tangent vectors to the reference surface (30) ^ starting from the position vector ^ = ^(^, ^), in particular where ^ ^ and ^ ^ are given by the partial derivatives ^^ ^ ^= ^^ = ^^^ ^^ ^^ ^^ ^^ ^^^ respectively Example 29: A method according to example 27 or 28, characterized in that the numerical integration method comprises the composite trapezium method, the Simpson method, the Romberg method, or the more advanced inverse gradient method. Example 30: A computer program product for determining delay times ^ ^ for operating sound transducers (2) ^ at least one sound transducer arrangement (1) with a plurality of sound transducers (2) ^ for generating elementary waves (3) according to the delay times for providing sound to at least one audience area (5), characterized in that the computer program product comprises means for executing at least one instruction for determining delay times ^ ^for sound transducers ^ according to at least one of examples 1 to 15 or 16 to 29. Example 31: A device for providing sound to at least one audience area (3), which device comprises at least one sound transducer arrangement (1) with a plurality of sound transducers (9), wherein the at least one sound transducer arrangement (1) is operable according to a method according to at least one of examples 1 to 15. Example 32: Device according to example 31, wherein the at least one sound transducer arrangement (1) and the at least one audience area (3) are geometrically linked to one another by a coordinate system (2) and between the physical positions of the individual sound transducers (9) in the at least one sound transducer arrangement (1) and position vectors ^ ^for determining coordinates in the area of ​​the at least one sound transducer arrangement (1) there is a spatial assignment, and furthermore an assignment of points of the coordinate system (2) to points in the at least one audience area (5) according to a position vector ^ ^ exists, wherein in the coordinate system (2) direction vectors, in particular normalized direction vectors (61) ^ ^ ^ = result, characterized by a means for controlling the sound radiation of the sound transducers (9), which depends on the spatial assignment of the position vectors ^ ^ to the transducers (9) delay times ^ ^ for the sound transducers (1), with which elementary waves (8) are radiated by the sound transducers (9), whereby the delay times ^ ^the sound transducer (9) is selected in such a way that the local direction (50) of the common wavefront (4) corresponds to the direction of the direction vector, in particular the normalized direction vector (61) ^ ^ ^ and means for assigning each sound transducer (9) to a point in the at least one audience area (3) according to a position vector ^ ^ , so that normalized direction vectors (61) ^ ^ ^ ^ ^ ^ ^ ^ = |^ ^ ^^ ^ | and a means of determining the delay time ^ ^ the sound transducer (9) so that the local direction (50) of a common wavefront (4) corresponds to the direction of the normalized direction vector (61) ^ ^ ^corresponds, wherein in particular the individual sound transducers (9) of the at least one sound transducer arrangement (1) each emit elementary waves (8) which are superimposed to form a common wave front (4) and the at least one sound transducer arrangement (1) and the at least one audience area (3) are assigned to a common coordinate system (2) in which the positions of the individual sound transducers (9) of the at least one sound transducer arrangement (1) and the sound transducers are each determined with a delay time ^ ^is operable to emit elementary waves (8). Example 33: Device according to example 31 or 32, characterized in that the different propagation times for the sound transducers (9) of the sound transducer arrangement (1) are realized using a mechanical or geometric positioning of the sound transducers (9), which are controlled with coherent signals, wherein in particular the signal levels for the respective sound transducer (9) can correspond to the values ​​determined for the original intersection points of the grid. Further exemplary embodiments are described below: Concealing a sound reinforcement system behind an acoustically semi-transparent panel leads to absorbed or reflected sound energy, which leads to gain changes in the audio spectrum.The transfer function (TF) is the frequency-dependent reduction or amplification of the sound level of a sound source as it passes through the panel used to conceal the sound reinforcement system. Traditionally, compensation of the TF of the concealed loudspeaker is achieved by equalizing the average TF over several angles or simply taking the TF on-axis and applying the inverse curve as the profile of an equalization stage. A preliminary evaluation of the TF in the anechoic chamber led to the conclusion that the evaluated panel introduced very different gain variations at different angles for the same frequency. This would result in the spectral balance in the audience area deviating significantly at different angles and distances from the concealed audio module, reducing spectral homogeneity.TF compensation as described above would not be sufficient; instead, an angle-dependent spatial transfer function would be required. Wave field synthesis and 3D audio beamforming technology are based on the high-resolution sensitivity and 3D directivity balloons of the transducers built into the audio module. Using 3D audio beamforming algorithms, individually shaped wavefronts can be defined through level and phase manipulation, which fully adapt to the audience area. Furthermore, the resulting wavefronts are optimized for spatial and spectral homogeneity using a reference target curve. If compensating the spatial transfer function becomes a challenge, a solution to improve the spectral balance in the 3D space of concealed audio modules can be used, as described here.If an algorithm knew the spatial transfer function introduced by the acoustic panel in front of the transducer, the optimization and equalization engine would compensate for the panel's effect in every direction, not just on-axis, achieving similar performance as if the panel were absent. Changes in the transducer's radiation balloon caused by panel resonances, reflections, or acoustic absorption at certain angles would be known in advance and partially compensated to achieve the desired spectral profile across the entire audible range. The challenge here is to capture the transducer's directional balloon when mounted, for example, behind a carbon fiber panel. One possibility is to use a holographic measurement approach to determine the directivity of a loudspeaker.This method uses special solutions of the wave equation (spherical harmonics, Hankel function) to determine the 3D sound pressure of the audio device. Compared to conventional measurement methods, this provides more comprehensive and accurate measurement data while minimizing costs (e.g., for an expensive test room) and measurement time. The device under test remains in a fixed position in the center of the scanner. This simplifies the handling of heavy devices and ensures constant room excitation and thus constant room reflections during the scanning process. The robot arm moves a microphone around the device under test and records the sound pressure in the near field. By scanning along a double layer, for example, direct sound separation can be used. This uses additional phase information to detect the direction of the sound wave and can remove all room reflections from the direct sound of the loudspeaker. This means that the measurement system delivers accurate measurements in any environment (e.g., in a studio).B. Workshop or office) precise free-field data. For example, using an example pair of woofer and tweeter, the effect of an acoustic panel used to cover the audio module can be evaluated. Since the near-field measurements do not include signal processing, the spectral power outside the operating range of the transducer is also shown. The frequency responses of the individual transducers with and without the acoustic panel are shown in Fig. 12. Comparing the acoustic results of both measurements shows a transmission loss in the near-axis frequency response. In a conventional approach, these frequency responses would serve as the basis for calculating the transmission gain and compensate for this energy loss with a DSP. However, if the off-axis frequency responses are also taken into account, the acoustically semi-transparent panel causes further interference.There are additional resonances that affect the radiation pattern at certain frequencies, particularly in the range between 2 kHz and 5 Hz. Above f>7 kHz, measurements show higher on-axis transmission losses than off-axis, resulting in a lower directivity index and a slightly larger radiation angle when the panel is in place. The spatial transfer function of the acoustic panel in Fig. 13 shows the angular dependence of the gain changes across the spectrum. The spatial transfer function is the absolute spectral gain difference between the bare transducer and the same transducer behind the acoustic panel after applying a 1-octave frequency smoothing and a 15-degree spatial smoothing.Spatial smoothing was performed to prevent isolated artifacts caused by the panel used for the measurements from being incorporated into the overall compensation for other panels with different properties: differences in bracing, panel stiffness, and manufacturing, or slight differences in panel positioning. To illustrate the advantage of the 3D audio beamforming approach described here compared to conventional audio solutions, the 3 kHz frequency was used as an example in Fig. 13. The level difference between 0° (on-axis) and 45° is approximately 2 dB; therefore, any global spectral correction at 2 kHz would work effectively for one angle, but over- or undercompensate for other angles. Spatial transfer function differences are difficult to address with a single, global equalizer.On the other hand, with 3D spectral compensation as part of the optimization engine, the transducers used to reproduce the beam can be individually spatially balanced, resulting in optimal spectral balance as the listener moves across the audience area. Once the transducer balloon data has been corrected using the panel's spatial transfer function and incorporated into the algorithms as an audio module variant, hidden audio modules can be optimized, simulated, and benchmarked. Fig.Figure 14 shows example transfer functions of an optimized beam with an opening angle of 120º under different scenarios for different angles (0º, 30º, and 60º) at 1 / 3-octave resolution: a simple audio module (black), the same module and the same beam configuration masked with the MDI panel in front (red), and finally the audio module masked with the MDI panel and spatially compensated with the algorithms. Figure 14 illustrates the different spectral fluctuations at different angles, which can only be resolved with individual equalization. The spatial compensation for the acoustic panel was implemented to restore the overall spectral balance of the desired frequency response. Isolated local artifacts or spectral colorations resulting from panel resonances or reflections were not part of the correction, as their compensation proved ineffective.Audio systems can be concealed in a variety of ways. Acoustically transparent materials such as fabric or perforated screens allow sound to pass through with minimal loss of acoustic performance and can be effective in certain environments. Visible distortion can be a potential problem when projecting video content. To overcome this, a high-resolution video projection solution using a micro-perforated carbon fiber panel can be used. This proved very effective, providing a seamless projection surface, but introduced some disadvantages for the sound system behind it, namely angle-dependent fluctuations in the transfer function. A near-field scanning system has proven to be an effective and robust method for detecting the directivity of loudspeakers, even those concealed behind a panel.The three-dimensional behavior of the drivers built into the audio modules and installed behind the panel was captured to provide the data required for spatial spectral balance correction. Spectral balance correction compensates for level differences between different angles in 3D space for the same frequency across the entire audio spectrum. This feature significantly increased the spectral homogeneity of the audio beams used and represents a clear advantage over traditional compensation methods.

[0002] List of reference symbols 1 Sound transducer arrangement 2 Common coordinate system 3 Audience area 4 Wavefront formed from elementary waves 5 Auxiliary grid on the reference surface of the sound transducer arrangement 6 Auxiliary grid in the audience area 7 Direction vector 8 Elementary waves 9 Sound transducer 10 Coverage area of ​​the wavefront 105 Partial areas of the wavefront 106 Partial areas of the audience area 12 Virtual sound source 30 Curved sound transducer surface 31 Normal 40 Cuboid for vector determination 50 Local direction of the common wavefront 60 Normalized cuboid with diagonal one 61 Normalized direction vector 701, 702, 703 Partial areas of the audience area 801 Intersection points used 802 Fixed audience areas 90 Mechanically curved sound transducer arrangement 91 Spatial offset 1

Claims

AMENDED CLAIMS received by the International Bureau on 09 April 2024 (09.04.2024) 1. A method for operating and / or setting up a two-dimensional sound transducer arrangement (1) with a plurality of discretely controllable sound transducers (4) which are arranged on a flat or curved surface and which are controlled according to the wave field synthesis method or according to the beamforming method, characterized in that frequency-dependent and / or direction-dependent variations in the sound pressure of the wavefronts (6) emanating from the sound transducers of the sound transducer arrangement (1) are compensated for by assigning to each sound transducer of the sound transducer arrangement (1) for each input signal at least one inverse filter for correcting a) the radiation characteristic of the respective sound transducer, which is determined with the spherical coordinates φ and θ and stored in the system and which causes variations in the frequency response or sound pressure level of the reproduction in the propagation direction of the local wavefront (6) determined by the direction vector d,b) the transmission attenuation of the wavefront through at least one partially sound-transparent obstacle in the sound path, which depends on the direction vector d of the relevant local direction of the wavefront (6) and c) the frequency-dependent sound insulation of the air between the respective sound transducer and the audience area, which depends on the path length of the local direction of the wavefront (6) to the audience area (2) and on the temperature, humidity and air pressure in the audience area, is connected upstream in the signal path in order to linearise the frequency response of the radiation of the local wavefront (6) in the direction of the direction vector d.

2. Method according to claim 1, characterized in that the frequency response of the sound transducer (4) of the sound transducer arrangement (1) assigned to the respective correction element is determined for a plurality of radiation directions, which can be described in particular by means of spherical coordinates φ and θ, in the anechoic chamber and stored in the system and the reproduction-side correction device has an inverse filter of the function G inv(f) which, depending on the propagation direction d of the associated local wavefront (6), compensates for the corresponding non-linearities in the frequency response of the respective sound transducer (4), based on a direction-dependent frequency response error of the respective sound transducer (4) stored in the system in the local propagation direction of the associated wavefront, whereby, in cooperation with the surrounding sound transducers (4) of the sound transducer arrangement (1), the frequency response of the respectively emitted local wavefront (6) becomes independent of its propagation direction d, which is why the entire wavefront of the sound transducer arrangement (1) is linearized for the corresponding channel independently of its radiation direction by applying the method separately for each individual sound transducer of the sound transducer arrangement (1) and each individual input channel.

3. Method according to claim 1, characterized in that the attenuation of a partially sound-transparent acoustic obstacle in a propagation direction d of the associated sound wave front is compensated by the difference of the frequency response stored in the system of the unhindered radiated local wave front (6) emanating in the direction of propagation d, and the measured frequency response of the direction of propagation d emanating from the local wavefront (6) radiated through a partially sound-transparent acoustic obstacle for discrete spherical coordinates φ and θ is stored in order to determine the amplitude and frequency response of the signal of the associated local wavefront (6) during reproduction as a function of the propagation direction d by an inverse filter with the function H inv(f) to correct separately for each individual transducer of the transducer arrangement (1) and each individual input channel, whereby in cooperation with the surrounding transducers the frequency response of the respective radiated wavefront becomes independent of its propagation direction d or of the direction-dependent attenuation of the acoustic obstacle.

4. Method according to claim 1, characterized in that the acoustic disturbance factor airborne sound insulation in an audience area (2) is determined based on current values ​​for relative air humidity (in %), air pressure (in kPa) and temperature (in K) in the audience area (2) and is compensated for in accordance with the path length to the audience area, which path length is dependent on the direction vector d (3) of the local wave front (6), by a reproduction-side correction device for each individual sound transducer of the sound transducer arrangement (1) and each individual input channel separately with an inverse filter of the function Ainv(f).

5. Method according to claim 1, characterized in that the order of the correction elements in the signal path can be freely selected and individual correction options can be bridged or omitted.

6. Method according to claim 1, characterized in that fixed correction values ​​can be stored in the system if the direction of the wave fronts in the system is fixed.

7. Method according to claim 1, characterized in that systems with fixed programmed directivity and fixed programmed direction-dependent correction of the frequency response can work independently as individual modules or can be combined with other modules which are programmed accordingly to form a fixed programmed sound transducer array.

8. Method according to claim 1, characterized in that a targeted, direction-dependent frequency response change, for example in order to shape certain preferences of individual audience groups or to correct hearing losses of individual persons or to expand the artistic possibilities for sound field design, is possible by targeted manipulation of the inverse filters for correction.

9. Method according to claim 1, characterized in that the data of the compensation filters are preprocessed for each of the three filter blocks by being normalized in a first step in order to change the overall gain in all directions by a fixed value, then by frequency limitation and spatial and spectral smoothing of the data, the degree of smoothing of which depends on the required quality of the compensation and the available filter resolution and finally by the normalized and smoothed frequency response data for the given angles cp and θ, yielding the final inverse filter.

10. Method according to claim 1, characterized in that the data relating to the directional characteristic are stored in the individual modules and can be read and overwritten from a central memory via a data bus in a setup process.

11. Two-dimensional sound transducer arrangement (1) arranged and designed to carry out at least one of the methods according to claims 1 to 10.

12. A computer program product adapted to be executed on a processor that executes at least one method according to claims 1 to 10.

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