EP3183891B1 - Calculation of fir filter coefficients for beamformer filter - Google Patents

Description

The present invention is concerned with the calculation of FIR filter coefficients for beamforming filters of a transducer array, such as e.g. an array of microphones or speakers.

Beamforming technologies, such as those used in the audio field, specify - in the case of a microphone array for the evaluation of the individual signals of the microphones or in the case of a loudspeaker array for the reproduction of the signals of the individual speakers - as the signals of an individual Filtering with a respective discrete-time filter are subjected. For broadband applications, such as Music, are determined from the specification of the optimal frequency response coefficients for these time-discrete filters.

The literature on beamforming and signal control deals almost exclusively with the design of the drive weights in the frequency domain. It is implicitly assumed that the determination of FIR filters in the time domain by an inverse discrete Fourier transform (DFT), referred to as FFT, takes place. This approach can be interpreted as a frequency sampling design [Smi11, Lyo11], a very simple, variously detrimental method of filter design: The frequency response of the filters must be specified in an equidistant grid over the complete time discrete frequency axis up to the sampling frequency. If for individual frequency ranges (eg very low frequencies where no satisfactory directivity is possible or high frequencies in which due to spatial aliasing no targeted influencing of the radiation can take place), no meaningful specifications for the frequency response can be made, there is a risk that the resulting FIR filters are not usable (eg due to strong fluctuations between the frequency sampling points very high gain values at certain frequencies etc.)

The resulting FIR filters accurately map the given frequency response in the frequency raster given by the DFT, but the frequency response can assume arbitrary values between the raster points. This often leads to useless designs with strong oscillations of the resulting frequency response.

Furthermore, in frequency sampling design, the length of the FIR filter automatically results from the resolution of the frequency response specification (and vice versa).
Filters created using Frequency Sampling Design are susceptible to temporal aliasing, ie periodic convolution of impulse responses (eg [Smi11]). Additional techniques such as zero-padding the DFTs or windowing the generated FIR filters may need to be used.
An alternative approach is to determine the FIR coefficients in a one-step process directly in the time domain [MDK11]. In this case, the radiation behavior of the array for a given pattern of frequencies is represented directly as a function of the FIR coefficients of all transducers (ie loudspeakers / microphones) and formulated as a single optimization problem, by the solution of the optimal filter coefficients for all beamforming filters are determined simultaneously. The problem here is the size of the optimization problem, both in terms of the number of variables to be optimized (filter length times the number of beamforming filters) and with respect to the dimension of the determination equations and, if necessary, secondary conditions. The latter dimension is usually proportional to both the number of frequency raster points and the spatial resolution used to determine the desired beamformer response. As a consequence of this rapidly increasing complexity, this method is limited to low element count arrays and very small filter orders. For example, [MSK11] microphone arrays of six elements and a filter length of 8 are used.

EP 1 919 251 A1 shows a beamforming filter, designed as an FIR filter and applied to data coming from an array of sensors. The characteristics of the filters can be determined in the frequency domain. The FIR filter coefficients are then derived from the determined characteristics.

The object of the present invention is to provide a concept for calculating FIR filter coefficients for the beamforming filters of a transducer array, which is more effective, such as in relation to the ratio between achieved beamforming quality and the amount of computation required.
This object is solved by the subject matter of the appended independent claim.
One idea on which the present application is based is to have realized that the effectiveness of calculating FIR filter coefficients for beamforming filters for transducer arrays, such as arrays of microphones or loudspeakers, can be increased if the calculation is performed in two stages is, on the one hand by the calculation of frequency domain filter weights of the beamforming filters in a predetermined frequency raster, ie coefficients describing the transmission function of the beamforming filters in the frequency domain or for a respective frequency or for a sinusoidal input signal with a respective frequency to target frequency responses for the To obtain beamforming filters such that application of the beamforming filters to the array approximates a desired direction selectivity and followed by a calculation of the FIR filter coefficients for the beamforming filters, ie coefficients describing the impulse response of the beamforming filters in the time domain such that frequency responses of the beamforming filters approximate the intermediate frequency responses. The two-step nature allows for independent choice of the frequency resolution resulting from the discrete Fourier transform of the Implus responses described by the FIR filter coefficients. Furthermore, specific secondary conditions can be specified both in the calculation of the beamforming drive weights in the frequency domain and in the calculation of the time domain FIR filter coefficients, in order to influence the respective calculation in a targeted manner.

Fig. 1

ein schematisches Blockschaltbild eines Lautsprecherarrays mit Beamforming-Filtern zeigt, für welches die Ausführungsbeispiele der vorliegenden Anmeldung verwendet werden könnten;

Fig. 2

ein schematisches Blockschaltbild eines Mikrofonarrays mit Beamforming-Filtern zeigt, für welches Ausführungsbeispiele der vorliegenden Anmeldung verwendet werden könnten;

Fig. 3

ein Blockschaltbild einer Vorrichtung zur Berechnung von FIR-Filterkoeffizienten für die Beamforming-Filtern gemäß einem Ausführungsbeispiel zeigt;

Fig. 4

schematisch veranschaulicht, wie gemäß einem Ausführungsbeispiel bei Fig. 3 die optimierungsbasierte Berechnung der Zielfrequenzgänge der Beamforming-Filter stufenweise über die Modellierung eines DSB-Designs durchgeführt wird;

Fig. 5

schematisch veranschaulicht, wie gemäß einem Ausführungsbeispiel die zwischen den zwei Berechnungseinrichtungen angeordnete Modifikationseinrichtung in Fig. 3 das Optimierungsziel für die Zeitbereichsoptimierung der zweiten Berechnungseinrichtung geeigneter macht;

Fig. 6

schematisch veranschaulicht, wie gemäß einem Ausführungsbeispiel die in dem Verzögerungsanpassungsmodul von Fig. 3 durch Phasennivellierung entnommenen Verzögerungen in die berechneten FIR-Filterkoeffizienten re-integriert werden können; und

Fig. 7

schematisch darstellt, wie sich gemäß einem Hybrid-Ansatz zur Durchführung der Zielfrequenzgangberechnung in der ersten Berechnungseinrichtung von Fig. 3 der Zielfrequenzgang aus einem optimierten Anteil in einen Niederfrequenzabschnitt und einer DSB-Übertragungsfunktion in einem Hochfrequenzabschnitt zusammensetzt.

Advantageous embodiments of the present invention are subject-matter dependent claims. Preferred embodiments of the present application are explained in more detail below with reference to the figures, among which

Fig. 1

shows a schematic block diagram of a speaker array with beamforming filters for which the embodiments of the present application could be used;

Fig. 2

shows a schematic block diagram of a microphone array with beamforming filters, for which embodiments of the present application could be used;

Fig. 3

shows a block diagram of an apparatus for calculating FIR filter coefficients for the beamforming filters according to an embodiment;

Fig. 4

schematically illustrates how according to an embodiment at Fig. 3 the optimization-based calculation of the target frequency responses of the beamforming filters is carried out step by step via the modeling of a DSB design;

Fig. 5

schematically illustrates how, according to one embodiment, the arranged between the two calculating means in Fig. Fig. 3 makes the optimization target for the time domain optimization of the second calculation means more appropriate;

Fig. 6

schematically illustrates how in the delay adjustment module of FIG Fig. 3 can be re-integrated into the calculated FIR filter coefficients by phase-leveling delays; and

Fig. 7

schematically illustrates how according to a hybrid approach for performing the target frequency response calculation in the first calculation means of Fig. 3 the target frequency response is composed of an optimized portion into a low frequency section and a DSB transfer function in a high frequency section.

wobei h_BFFn (i) die Filterkoeffizienten des FIR-Filters 14_n mit der FIR-Ordnung I_BFFn bzw. der Filterlänge I_BFFn +1 ist. Fig. 1 shows first an example of an array 10 of loudspeakers 12, which is to be enabled by the application of beamforming filters (BFF) 14 to have a desired directional selectivity, ie, for example, to radiate in a particular direction 16. In Fig. 1 For example, an index is used to distinguish the individual speakers 12 from each other. The number N of speakers 12 may be two or more. As it is in Fig. 1 can be seen, each speaker 12 _n with i = 1 ... N is preceded by a beamforming filter 14 _n , which filters the corresponding speaker input signal. In particular, the loudspeaker 12 _{n is} connected to a common audio input 18 via its corresponding beam-forming filter 14 _n . This means that all speakers 12 _n receive the same audio signal, but filtered by the respective beamforming filter 14 _n . The audio signal s () at the input 18 is a discrete-time audio signal consisting of a sequence of audio samples and the beamforming filters 14 _n are configured as FIR filters and thus fold the audio signal with the impulse response of the respective beamforming filter 14 _n as defined by the FIR filter coefficients of the respective beamforming filter 14 _n . For example, if the audio signal at input 18 is described by the sequence of audio samples s (k), for example, the resulting filtered loudspeaker signal s ' _{BFF n} ( k ) for the respective speaker 12 _{n are} described as $$s{\text{'}}_{\mathit{BF}{F}_n}\left(k\right)={\displaystyle \underset{i=0}{\overset{I_{\mathit{BF}{F}_n}}{\Sigma }}{H}_{\mathit{BF}{F}_n}\left(i\right)\cdot s\left(k-i\right).}$$

where h is _{BFF n} ( i ) the filter coefficients of the FIR filter 14 _n with the FIR order I _{BFF n} or the filter length I _{BFF n} +1 is.

The art of FIR coefficient calculation is that the loudspeaker array 10 emits the audio signal at the input 18 with a desired directional selectivity, such as in the desired direction 16. In doing so Fig. 1 by way of example only, the loudspeakers 12 _n are arranged equidistantly in a line and the array 10 is a linear array of loudspeakers. However, a two-dimensional arrangement of loudspeakers would also be conceivable, as well as a non-uniform distribution of the loudspeakers 12 in the array 10 and also an arrangement deviating from an arrangement along a straight line or a plane. The emission direction 16 can be measured, for example, by an angular deviation of the direction 16 from a mid-perpendicular of the straight line or the surface along which the loudspeakers 12 are arranged. However, there are also variations here. For example, it is possible that the radiation should preferably be audible at a particular location in front of the array 10. However, the filter coefficients h of the beamforming filters 14 _n can also be selected more precisely such that the directional characteristic or directional selectivity of the array 10 not only experiences a maximum in a certain direction 16 when irradiated, but also fulfills other desired criteria, such as an angular one Beamwidth, a particular frequency response in a direction 16 maximum radiation or even a specific frequency response as far as an area that includes the direction 16 and directions around it affected.

wobei h_BFFn wiederum die FIR-Filterkoeffizienten der Beamforming-Filter 14_n sind. Die Summierung durch den Addierer 24 ergibt dann das gesamte Ausgangssignal s' gemäß $$s\prime \left(k\right)={\displaystyle \sum _{n=1}^{N}s{\prime }_{\mathit{BF}{F}_n}\left(k\right).}$$

In the following, embodiments for an effective manner of calculating the just mentioned FIR filter coefficients of the beamforming filters 14 _{n of} a transducer array 10 will be described. However, the embodiments described below are also applicable to calculate the beamforming filters of other arrays of transducers, such as ultrasonic transducers, antennas, or the like. Transducer arrays for reception can also be the object of beamforming. Thus, embodiments described below can also be used to design the beam-forming filters of a microphone array, ie to calculate their FIR filter coefficients. Fig. 2 shows such a microphone array. The microphone array of Fig. 2 is exemplarily also provided with the reference numeral 10, but in each case consists of microphones 20 ₁ ... 20 _N together. Regarding the arrangement of the microphones, the same applies as with respect to the speaker 12 of Fig. 1 : They can be arranged one-dimensionally along a line or two-dimensionally along a surface, where the line can be straight or the surface can be a plane, and also a regular distribution is not necessary. Each microphone generates a received audio signal S _{BFF i} and is connected via a respective beamforming filter 14 _n to a common output node 22 for outputting the received output signal s ', so that the filtered audio signals s ' _{BFF s} the beamforming filter 14 _n additively contribute to the audio signal s'. For this purpose, an adder 24 is connected between the outputs of the beamforming filters 14 _n and the common output node 22. The beamforming filters are again configured as FIR filters and form from the respective audio signal of the respective microphone 20 _n , ie s' _{BFF n} , the filtered audio signal s ' _{BFF n} for example according to $$s{\text{'}}_{\mathit{BF}{F}_n}\left(k\right)={\displaystyle \underset{i=O}{\overset{I_{\mathit{BF}{F}_n}}{\Sigma }}{H}_{\mathit{BF}{F}_n}\left(i\right)\cdot S_{\mathit{BF}{F}_n}\left(k-i\right).}$$

where h is _{BFF n} again the FIR filter coefficients of the beamforming filters 14 _n . The summation by the adder 24 then gives the total output signal s' according to $$s\text{'}\left(k\right)={\displaystyle \underset{n=1}{\overset{N}{\Sigma }}s{\text{'}}_{\mathit{BF}{F}_n}\left(k\right),}$$

The following embodiments in turn then allow the microphone array 10 Fig. 2 has a desired directional or directional characteristic to primarily or exclusively absorb the sound scene from a particular direction 16, so that it is reflected in the output signal s', the direction 16 again as in the case of Fig. 1 can be defined by the angulare deviation φ or in the two-dimensional case φ and θ from a perpendicular of the array 10 and the desired direction selectivity may possibly also be more accurate than just specifying a direction of maximum sensitivity, namely more precisely in terms of spatial dimension or frequency dimension.

Fig. 3 now shows an embodiment of an apparatus for calculating FIR filter coefficients for the beamforming filter of a transducer array, such as an array of microphones, as for example in Fig. 2 was shown, or speakers, such as in Fig. 1 was shown.

The device is indicated generally at 30 and may be implemented, for example, in software executed by a computer, in which case all of the devices and modules described below may be, for example, different sections of a computer program. An implementation in the form of a dedicated hardware, e.g. in the form of an ASIC or in the form of a programmable logic circuit, e.g. an FPGA, however, is also possible.

The device 30 calculates the FIR filter coefficients 32, such as the h _BFF just mentioned above _n for the beamforming filters 14 _n , specific to the array 10, to which the device 30 has interfaces to obtain information about the array 10 or information about the desired direction selectivity. In Fig. 3 It is shown by way of example that the device 30 receives converter data 34 from outside, which will be described in more detail below and for example the positions and orientations of the transducer elements, ie for example the loudspeakers or microphones, and their individual direction-selective sensitivity or emission characteristic and / or specify the frequency response. Other information relates, for example, to the desired directional selectivity. For example, shows Fig. 3 in that the device 30 obtains data 36 which indicate the desired directional behavior of the array 10, such as a direction of maximum radiation and possibly more precise information, such as the radiation behavior or the sensitivity around the just mentioned maximum radiation / sensitivity. The data 36 are supplemented, for example, by further data 38 which can be specified from the outside of the device 30 and, for example, the desired transfer characteristic or the frequency response of the array 10 in the direction of the radiation or sensitivity of the array 10, ie the frequency-dependent desired description the sensitivity or emission intensity of the array adjusted with the final FIR filter coefficients in a certain direction or directions. Other information may also be provided to the device 30 for calculating the FIR filter coefficients 32, such as specifications regarding robustness to be maintained of the calculated FIR filter coefficients against deviations of the transducer data 34 from actual physical conditions of an actual array 10, these specifications in Fig. 3 40, as well as data on a frequency restriction, 42, whose exemplary meaning for the calculation will be described below and possibly related to the transducer data 34.

It should be noted that all of the information 34 to 42 used for the device 30 of FIG Fig. 3 can be specified from outside, are optional. The device 30 could also be specific to a particular array setup, and it would also be possible for the device to be specific to particular settings of the other data. In the case of an input facility, this may be implemented via an input interface, such as via user input interfaces of a computer or read interfaces of a computer, such that, for example, the data is read from one or more particular files.

The device of Fig. 3 includes first calculating means 44 and second calculating means 46. The first calculating means 44 calculates frequency-domain filter weights of the beamforming filters, ie complex-valued samples of the transfer function of the beamforming filters. They are used to set a target frequency response for the beamforming filters. In particular, the first calculation device 44 calculates the frequency range drive weights in a frequency raster defined by specific, not necessarily equidistant frequencies ω ₁ ... Ω _k , such that it has a transfer function H _{BFF n} describe the beamforming filter which approximates the desired direction selectivity when applying such beamforming filters to the array 10. In the following, it is described that the first calculation device uses, for example, a suitable optimization algorithm, for example a method for solving linear, quadratic or convex optimization problems. The frequency raster may, for example, in accordance with requirements of the beamforming application, such as different requirements for the accuracy of the radiation specification in certain frequency ranges, or according to other requirements, such as the subsequent and below-mentioned FIR time domain design method, such as necessary sampling rate for the definition of the desired frequency response, to be selected.

While the first calculation means 44 thus the transfer function H _{BFF n} the beamforming filter describes over the frequency ω or calculates the transfer function, namely at certain nodes ω ₁ ... ω _k, for example, the second calculation means 46 is for determining the FIR filter coefficients of the beamforming filters which describe the impulse response of the beamforming filters. The second calculation device 46 carries out the calculation in such a way that the frequency responses of the beamforming filters, as they correspond to the FIR filter coefficients via the relationship between transfer function and impulse response, approximate the target frequency responses predetermined by the first calculation device 44. The second calculation device 46 also uses optimization according to the following embodiment description, which can again be implemented as a method for solving linear, quadratic or convex optimization problems.

The functioning of the device 30 of FIG Fig. 3 for a possible implementation case described in more detail. The description also refers to various implementation options. According to an implementation possibility, the first calculation means 44 performs the calculation by solving a first optimization problem, after which a deviation between a directional selectivity of the array, as reflected by the frequency range drive weights H _{BFF n} (ω _k ), and the desired direction selectivity that may be predetermined by the data 34 and / or 38 is minimized. As it is in Fig. 3 For this purpose, the first calculation means 44 may use the robustness specifications 40 as a constraint of the optimization problem, and the conversion data 34 is used to determine the relationship between the optimization variables, namely the frequency domain drive weights H _{BFF n} (ω _k ) on the one hand and the resulting directional selectivity on the other hand to set or define. The following description will then turn to possible implementations of the second calculator 46, from which it will be seen that the second calculator may also solve an optimization problem to make the calculation. After the second optimization problem on which the second calculation device 46 is based, a deviation from the target frequency responses H _{BFF n} (ω _k ) minimized in the frequency domain. As stated, the FIR filter coefficients to be calculated by the second calculator 46 correspond to the impulse response, and the device 46 tries to calculate them by optimization according to the following embodiments such that the transfer functions corresponding to these impulse responses correspond to the transfer functions H _{BFF n} (ω _k ) as close as they have been calculated by the first calculating means 44. From the description below In this case, it will become clear that, advantageously, in the optimization of the calculation device 46, ancillary conditions provided specifically for this optimization can be taken into account, as specified by the data 42. The following description will also deal with a target frequency response modification device 48, optionally provided between the two calculation devices 44 and 46, which optionally modifies the target frequency responses of the beamforming filters as determined by the first calculation device 44 before being used as the approximation target by the second calculation device 46 are used. Various modification options are described. They are designed to not cause the effectiveness of the calculation of the FIR filter coefficients 32 by the computing device 46 or even the calculation of lower-quality FIR filter coefficients. According to one of the modification possibilities, the device 30 may optionally include an optional modification device 50 for modifying the calculated FIR filter coefficients, as calculated by the second calculation device 46, so that the respective modification is taken into account. Fig. 3 will also exemplarily describe a possible modular structure for the first calculation device 44 and the target frequency response modification device 48, but the respective modular design is merely exemplary.

• In einer ersten Stufe, wie sie durch die erste Berechnungseinrichtung 44 bereitgestellt wird, wird der Frequenzgang der Beamforming-Ansteuerfilter BFF im Frequenzbereich in einen vorgegebenen Frequenzraster ω_k entworfen, das eine bestimmte Frequenzauflösung festlegt, wie z.B. Δω= ω_k-ω_k-1. Das Frequenzraster muss dabei jedoch nicht äquidistant gewählt werden, sondern kann auch unregelmässig sein. Hier kann auf die in der Literatur beschriebenen Beamforming-Techniken zurückgegriffen werden. Optimierungen können verwendet werden. Ein solches Frequenzbereichs-Optimierungsverfahren wird beispielsweise in [MSK09] beschrieben.
• In einer zweiten Stufe, wie sie durch die zweite Berechnungseinrichtung 46 bereitgestellt wird, wird für jedes Beamforming-Ansteuerfilter BFF_n aus dessen Zielfrequenzgang, wie er durch die erste Stufe vorgegeben wurde, ein FIR-Filter erzeugt, indem dessen FIR-Filterkoeffizienten h_BFFn berechnet werden. Hier können ebenfalls Optimierungsverfahren verwendet werden, um eine bestmögliche Approximation des gewünschten Zielfrequenzganges für die gegebene FIR-Filteranordnung, eine frei wählbare Filternorm sowie gegebenenfalls eine Anzahl zusätzlicher Nebenbedingungen zu erzielen. Die Frequenzauflösung des FIR-Filterdesigns, festgelegt durch beispielsweise die Nyquist-Frequenz des FIR-Filters geteilt durch die Hälfte der FIR-Filterlänge, bzw., ein wenig exakter ausgedrückt, die Nyquist-Frequenz (halbe Abtastrate) des zeitdiskreten Systems, in dem der Beamformer und damit auch die FIR -Filter implementiert sind, kann zu der Frequenzauflösung der Frequenzbereichsauflösung unterschiedlich gewählt werden.

As already outlined above, the device 30 of Fig. 3 To find the time domain FIR filters or the FIR filter coefficients for the beamforming filter, use solutions of optimization problems. The time-domain FIR filter calculation using optimization-based filter design techniques, as described below, avoids both the disadvantages of frequency sampling design and the complexity, and hence the demands on computation time and resources, such as memory, for direct time-domain design of the filters. as described in the introductory part of the present application. By the first and second calculation means 44 and 46, the design of the beamforming filters according to Fig. 3 in a two-step process:

• In a first stage, as provided by the first calculating means 44, the frequency response of the beamforming Ansteuerfilter BFF in the frequency range ω in a predetermined frequency grid is designed _k, which determines a particular frequency resolution, such as Δω = ω _k ω _k-1 , However, the frequency grid does not have to be chosen equidistantly, but can also be irregular. Here may refer to the beamforming techniques described in the literature be resorted to. Optimizations can be used. Such a frequency domain optimization method is described, for example, in [MSK09].
• In a second stage, as provided by the second calculating means 46, for each beamforming drive filter BFF _n, from its target frequency response, as dictated by the first stage, an FIR filter is generated by having its FIR filter coefficients h _{BFF n} be calculated. Optimization methods can also be used here in order to achieve the best possible approximation of the desired target frequency response for the given FIR filter arrangement, a freely selectable filter standard and optionally a number of additional secondary conditions. The frequency resolution of the FIR filter design, defined by, for example, the Nyquist frequency of the FIR filter divided by half the FIR filter length, or, to a lesser extent, the Nyquist frequency (half the sampling rate) of the time-discrete system in which Beamformer and thus the FIR filters are implemented, can be selected differently to the frequency resolution of the frequency domain resolution.

The filter design process, as implemented by the device 30, provides for a variety of individual interrelated measures and precautions in accordance with the embodiments described below. All in all, they enable the generation of particularly stable, robust control filters or beamforming filters. The operation of the device 30 will now be described in detail. However, some of the measures can also be left out depending on the application.

As already mentioned above, in the first calculation by the calculation device 44, the transducer characteristics, ie the properties of, for example, microphones or loudspeakers, are included. The transducer data 34 describes the transducer characteristics that are typically derived from measurements or modeling, such as simulation. The transducer data 34 may represent, for example, the directional and frequency dependent transfer function of the transducers of (in the case of loudspeakers) and to (in the case of sensors or microphones, respectively) different points in space. For example, a module 52 of the computing device 44 may perform directional characteristic interpolation, ie, interpolation of the transducer data 34 to determine the transfer function of the transducers from / to points or Allow directions that are not included under the original data 34, ie, not in the original records.

The converter data of the module 52 thus obtained are used in two function blocks or modules 54 and 56 of the first calculation device 44, namely a delay and sum beamformer module and an optimization module 56. The delay and sum (delay and summation Beamformer module 54 calculates a delay and an amplitude weight, ie, for each transducer n , based on a desired specification for the directional behavior of the transducer array, which specifies, for example, a desired magnitude in the emission direction or emission directions, using the individual transducers of the array in the respective direction frequency-independent quantities, such as a time delay and a gain factor per converter 12 and 14. The optimization 56 operates in the frequency domain. It optimizes as optimization variables the frequency range shaping coefficients already mentioned above or the frequency range control weights H _{BFF n} ie frequency dependent quantities. The latter optimization 56 of the frequency range drive weights can be improved by the inclusion of specific converter transfer functions, especially if they deviate greatly from an ideally assumed behavior, such as a monopole characteristic. For example, transducer data 34 obtained by measurements often have pure delays, such as acoustic propagation, and a delay extraction module 58 connected between the directional characteristic interpolation module 52 and the optimization module 56 could be provided to remove common delay times of all transducer data. This simplifies the optimization process in the optimization module 56, because the delays no longer have to be included in the desired optimization target function, or the beamforming filters achieved do not have to compensate for the array delay common to the transducers. It will become apparent from the following description that an advantage of the use of the delay-and-sum block is that by the same with the used converters with high robustness feasible design specification for the frequency response of the transducer array in the desired direction of radiation / incident with high sensitivity can be obtained.

Once again, it should be pointed out that the just described inclusion of converter characteristics in the calculation by the calculation device 44 is merely optional, ie the presetting of the data 34 as well as the modules 52 and 58 may be missing. Rather, the calculation by the calculation device could also be based on the assumption of idealized transfer characteristics. On the other hand, the use of real transducer data 34 often allows for a higher performance of the finally calculated beamforming filters.

• eine oder mehrere bevorzugte Abstrahlrichtungen oder -Punkte;
• Richtungen oder Bereiche, in denen die erzielte Schallabstrahlung nur in definierter Weise (typischerweise durch maximale Abweichungen vorgegeben) von der gewünschten Schallabstrahlung abweichen darf;
• Bereiche, in denen keine Vorgaben über die Schallabstrahlung gemacht werden, welche auch als Übergangsbereiche oder räumliche "don't care"-Bereiche bezeichnet werden können;
• Bereiche, in denen die Schallabstrahlung minimiert werden soll, optional mit einer Gewichtungsfunktion, um die Priorität einzelner Teilbereiche anzupassen.

The specification of the desired directional behavior or beamforming behavior is determined according to Fig. 3 made via the data 36. They form the starting point of the beamformer design by describing a desired directional characteristic. For example, they describe a desired radiation of the desired sound in one or more directions or areas in the case of loudspeakers for one or more directions or areas in the case of microphones, while the radiation is in sensitivity for other directions / Areas should be suppressed as possible. This description of the data 36 is converted, for example, by a module 60 into a target pattern specification, ie a mathematical formulation of the desired directional behavior. The target function output by the target pattern specification 60 describes, for example, the desired complex sound radiation in different spatial directions φ or φ and θ. The objective function can be either frequency-independent or frequency-dependent, ie with different specifications for different frequencies or frequency ranges. In addition, the mathematical formulation of the directional behavior may include one or more of the following elements:

• one or more preferred radiating directions or points;
• Directions or areas in which the sound radiation achieved may deviate from the desired sound radiation only in a defined manner (typically given by maximum deviations);
• Areas where noise exposure is not provided, which may also be referred to as transition areas or "do not care"areas;
• Areas in which the sound radiation is to be minimized, optionally with a weighting function, to adjust the priority of individual partial areas.

In general, it should be noted that the desired complex sound radiation, which is described by the objective function, is not necessarily limited to directions. Other arguments are also possible, for example, such as the desired emission along a line or across a surface / volume.

With regard to the robustness specifications 40, the following applies. In the context of beamforming applications robustness refers to the property of showing only a relatively small deterioration of the radiation behavior in the case of deviations of the transducer array 10 or of the transmission system, eg due to deviations of the control filters from ideal behavior, positioning errors of the transducers in the array or deviations from the modeled transmission behavior , A measure of robustness frequently used for microphone arrays, for example, is the so-called "White Noise Gain" [BW01, MSK09], ([WNG]), which results as the quotient of the signal magnitude in the direction of incidence and the L ₂ standard of the drive weights for the array , This measure can also be usefully used for loudspeaker arrays [MK07], whereby here the signal magnitude in the desired emission direction assumes the role of the magnitude in the direction of incidence.

• Basierend auf der gewünschten Abstrahlrichtung bzw. den Daten 36 zum gewünschten Richtungsverhalten wird die Übertragungsfunktion der Ansteuerfilter für den Delay- und Sum-Beamformer (DSB) in dem Modul 54 erstellt. Das heißt, Modul 54 geht von einfachen Filtern aus, die nur von der Position der Wandler und der Abstrahlrichtung abhängen und lediglich aus einem frequenzunabhängigen Verstärkungswert und einer frequenzunabhängigen Verzögerung, jeweils pro Wandlerelement, bestehen. Nur solche frequenzunabhängigen Werte pro Wandler werden durch das Modul 54 berechnet, ausgehend von dem gewünschten Richtungsverhalten 36 und unter Einbeziehung der Wandlerdaten 34. Ein DSB entspricht also quasi dem Aufbau von Fig. 1 bzw. 2, wobei allerdings einfachere BFFs verwendet werden, nämlich lediglich solche, die eine zeitliche Verzögerung und eine frequenzunabhängige Verstärkung durchführen. Während die Richtwirkung eines solchen DSBs insbesondere für niedrige Frequenzen gering ist, weist er hohe WNG-Werte und damit eine gute Robustheit auf.
• Mit diesem DSB-Ansteuerfiltersatz (bestehend aus lediglich dem frequenzunabhängigen Verstärkungswert und der frequenzunabhängigen Verzögerung pro Wandlerelement) wird die Abstrahlung des Arrays in der gewünschten Abstrahlrichtung berechnet/simuliert. In die Berechnung dieser frequenzunabhängigen Wertepaare pro Wandlerelement durch das Modul 54 fließen, wie bereits erwähnt, die modellierten oder gemessenen Wandlercharakteristiken aus den Daten 34 ein.
• Der aus dem DSB-Ansteuerfiltersatz des Moduls 54 resultierende Frequenzgang des Wandlerarrays in Abstrahlrichtung kann als Referenz-Frequenzgang (bzw. Magnitudengang) bezeichnet und in den nachfolgenden Schritten der Berechnung durch die Berechnungseinrichtung 44 verwendet werden. Der Vorteil des Vorgehens besteht darin, dass hierdurch eine Vorgabe für die Magnitude vorliegt, welche durch das Wandlerarray innerhalb der vorgegebenen Maximalaussteuerungen für die Einzelwandler realisiert werden kann, und welches (weil aus einem DSB-Design resultierend) gute Robustheitseigenschaften besitzt bzw. so entworfen werden kann, dass es gute Robustheitseigenschaften besitzt.

As shown in the previous section, the magnitude in the direction of radiation (respectively direction of incidence) has a direct effect on the WNG and thus on the robustness in relation to an allowed standard of the drive weights. In the same way, the achievable level in the emission direction depends both on the maximum permissible amount of the drive weights and on the emission characteristics of the converters. It is therefore necessary to specify the magnitude (or amplitude of the desired radiation pattern) so that both robustness and radiation amplitude requirements are achieved. To get a good starting point for this specification, it is possible to use the following procedure:

• Based on the desired emission direction or the data 36 for the desired directional behavior, the transfer function of the drive filters for the delay and sum beamformer (DSB) in the module 54 is created. That is, module 54 is based on simple filters, which depend only on the position of the transducers and the emission direction and consist only of a frequency-independent gain value and a frequency-independent delay, each per transducer element. Only such frequency-independent values per converter are calculated by the module 54, starting from the desired directional behavior 36 and taking into account the converter data 34. A DSB thus corresponds to the structure of Fig. 1 or 2, but using simpler BFFs, namely only those that have a time delay and perform a frequency-independent amplification. While the directivity of such a DSB is low, especially for low frequencies, it has high WNG values and thus good robustness.
• With this DSB control filter set (consisting of only the frequency-independent gain value and the frequency-independent delay per transducer element), the radiation of the array in the desired emission direction is calculated / simulated. In the calculation of these frequency-independent value pairs per transducer element by the module 54, as already mentioned, the modeled or measured transducer characteristics flow from the data 34.
• The frequency response of the transducer array in the emission direction resulting from the DSB drive filter set of the module 54 may be referred to as the reference frequency response (or magnitude response) and used in the subsequent steps of the calculation by the calculation device 44. The advantage of the approach is that it provides a magnitude constraint that can be realized by the transducer array within the given maximum drive levels for the individual transducers, and that has (because of a DSB design) good robustness characteristics can, that it has good robustness properties.

According to the example of Fig. 3 For example, the calculation device 44 has another module, namely a module 58, which determines the final specification of the frequency response of the transducer array in the emission direction from the acquired reference magnitude response of the module 54 in combination with the specifications 38 for the desired frequency response or desired frequency response. That is, the starting point for the determination of the module 58 is the frequency response of the transducer array, as determined by the DSB values of the module 54, ie the frequency response that results for the transducer array with the DSB values in the corresponding direction. From this Magnitudengang starting, are made by the module 58 modifications. For example, modifications are made to the reference magnitude response, for example to equalize the frequency response. Also, the directivity of the array can be increased within certain limits (either globally or for certain frequencies) by reducing the magnitude response in the direction of emission from the reference magnitude response. The use of the DSB reference design and its WNG value allows a good estimation of the robustness properties of the final design specification.

In an optional application example, psychoacoustic findings flow into the frequency response determination 58. In this case, for example, the knowledge can be exploited that certain frequency ranges of a signal are more important for the perception of a sound event, and that therefore a less advantageous, because less directed, radiation in other frequency ranges can be compensated or less perceptible by a targeted increase in these frequency ranges , It should be noted here that this equalization is, for one thing, independent of the signal and is also limited to only one emission characteristic, that is to say is not based on psychoacoustic masking between different emission characteristics or audio signals.

Based on the determined frequency response target for the transducer array, as determined by the module 58, optimization is then performed in module 56. The beamforming filter is designed here in the frequency domain for a series of discrete frequencies ω _k . In the context of the present application, optimization methods based on convex optimization are preferably used [M07, MSK09]. These allow a best possible approximation of the predetermined or selected by the module 58 Abstrahlcharakteristik as it is determined from the data 36 by the modules 60, 54 and 58, with respect to a selectable error standard, such as the L ₂ - (least squares, least square error) or the L∞ norm (Chebyshev, Minimax norm) The result of the optimization in module 56 is a complex drive value for each discrete frequency, so that a vector H _n (ω _k ) complex of other weights per transducer n is obtained. In the optimization problem that is solved by the module 56, measured or modeled transducer data, or the data can be included 34 in order to obtain _n on the frequency response and radiation pattern optimized Ansteuerfilter frequency responses H. Furthermore, the optimization-based approach allows for numerous constraints that affect both the radiation achieved and the driving power can relate to. For example, a limitation on the minimum white noise gain can be set. In the same way it is possible to set maximum amounts for the control weights in order to limit the control of the individual transducers.

The previous description of the possible implementation of the operation of the first calculation means 44 summarized once again in an illustrative manner, becomes Fig. 4 directed. The starting point of the target frequency response calculation by the calculation device 44 forms the desired direction selectivity, which in Fig. 4 described with Ω is and is provided with the reference numeral 70. The desired direction selectivity Ω is illustrated here by way of example as a function Ω dependent on the emission angle φ. However, as stated above, the directionality may be defined other than angular. Further shows Fig. 4 by a dashed θ, the desired direction selectivity 70 can be defined in space sense, not just in one plane. Top right is in Fig. 4 indicated how the angles φ and θ could be defined. In the desired direction selectivity, a frequency dependence could already be included, ie Ω could depend on ω. In this respect, there has often been talk of a "frequency response" Ω, because direction-dependent certain frequencies are attenuated less or more. However, this frequency response Ω is to be distinguished from the frequency response H _n (ω _k ) for the individual beamforming filters, as they are to be calculated by the calculation device 44. Both act like a filter with a transfer function as determined by the dependence on ω, but the frequency response Ω is affected by the finally calculated frequency responses H _{n of} the individual beamforming filters.

The desired direction selectivity 70, as dictated by data 36, is now to be achieved with the particular transducer array. In Fig. 4 In the upper right corner loudspeakers were used as the elements of the array, but as already mentioned, an array of other transducers, such as microphones, is also possible. The array is thus determined from certain transducer positions, transducer orientations, a transducer frequency response, wherein the frequency response may in turn be direction-dependent, and / or a directional dependence of the radiation or the sensitivity, which in turn may be frequency dependent. In module 54, a pair of values ψ _n and a _n , namely frequency-independent delay ψ and a gain value a, which is also frequency-independent, are now determined for each transducer n, so that assuming only these frequency-independent values in the BFFs the transducer n are applied, the directional selectivity Ω '72 results, which is direction-dependent, that is, for example, depending on φ and optionally θ and frequency-dependent, ie depending on ω. The determination in module 54 is performed so that the desired direction selectivity 70 is achieved or approximated where possible. This is only to a limited extent, of course, as per converter yes only be determined frequency independent delay and gain n. But the directional selectivity Ω 'is achieved with great robustness. As described above, Ω '72 now serves as a starting point for the actual desired direction selectivity 74, which will later be the basis of optimization 56. From the directional selectivity 72 one uses the foreknowledge that it is due to its DSB property is robust. The module 58 now modifies the directionality Ω '72 to be closer to the desire for a particular frequency dependence of directional selectivity. For example, in the module 58 by the transfer characteristic 38, a frequency dependence of the directional selectivity Ω in a predefined direction φ ₀ or (φ ₀ , θ ₀ given, such as in the direction of maximum radiation or maximum selectivity, ie the direction for which Ω The optimization target 74 of the optimization 56 is thus a frequency-dependent and direction-dependent directional selectivity Ω _Ziei and the optimization 56 is carried out in such a way that it finds target frequency responses or transfer functions H _n (ω _k ) for the beamforming filters n . Optimization goal 74 is achieved or approximated as well as possible by its use in the beamforming filters of transducer array 10, ie, a deviation according to a certain criterion is minimized Optimization 56 could thus be regarded as a fine adjustment of beamforming filter transfer functions 76 which when used for the beamforming filters, to d frequency independent delays and gains are equivalent. However, it should be noted that, nevertheless, the DSB design is actually used only for the optimization target formulation and the frequency domain optimization 56 may start independently of the DSB design. In other words, according to a preferred embodiment, the DSB design is not adapted or used as a basis, thus serving merely as a template for the desired frequency response in the emission direction, ie for the optimization target definition, and the optimization algorithm 56 starts "from Scratch ", ie without knowledge of the DSB weighting. Namely, the frequency-independent delays and gains Ψ _n and a _n , as calculated in the module 54, can be generated in the same way by filters with transfer functions H _n whose 2π-phase-jump-adjusted linear phase curve has a slope that corresponds to ψ _η , and whose magnitude or magnitude corresponds to a _n and is therefore constant. For which frequency support points these sampling points ω _k with k = 1... K the optimization 56 is carried out, may be suitably set by the application. Thus, since the transfer function H _{n is} a complex valued function, the variables to be optimized are 2 · N · K, where N is the number of converters and K is the number of frequency samples for which optimization 56 is performed. The optimized target frequency responses 78, which result from the optimization 56, can be achieved by optionally additionally subjecting the optimization to additional constraints, such as, for example, ancillary conditions regarding compliance with certain robustness criteria, as specified by the data 40. The optimization 56 can therefore in particular be a quadratic program with a secondary condition that does not fall below a certain robustness measure.

It has often been pointed out above that the calculation of the target frequency responses 78 could also be carried out differently.

In the embodiment of Fig. 3 Now, before the target frequency response 78 of the beamforming filters of the optimization in the second calculation device 46 is taken as a basis, one or more modifications are carried out, which, however, as already mentioned, are optional.

As described below, the frequency responses of the individual drive filters n result from the drive weights H _n (ω _k ) obtained in the optimization 56, since the weights of the filter are taken in each case. These filters often contain a significant delay or delay, which manifests itself for example by the phase or group delay. This delay is a hindrance for the further processing stages, such as in particular the subsequent optimization in the second calculation means 46. The optional smoothing step described below is also made more difficult or requires a significantly higher resolution of the frequency raster in the optimization 56 in the first calculation means, since the smoothing is a Determination of the continuous phase involved by a phase unwrapping. The greater the increase in the phase function contained in the frequency response, the more difficult is the correct detection and subsequent compensation of the phase jumps. This has a negative effect on the correctness of the "phase-unwrapping" algorithms.

Furthermore, it is advantageous for the optimization step in the second calculation device 46 if the local optimization target, ie target frequency response 78, is in a version that is as close as possible to a zero-phase frequency response, in which the phase terms caused by delays are eliminated as far as possible become. Further requirements of the optimization step in the calculation device 46 will be described in more detail below. In general, the following aspects should be considered:
The causality of the resulting filters is not relevant at this stage of the design process. It is possible to work with non-causal, near zero-phase transfer functions desired frequency responses for the drive filter. The causality can be made causal again after the FIR design (by reinserting the extracted delays, possibly supplemented by additional delays).

• Die Anpassung erfolgt für jedes Filter BFF_n einzeln.
• Durch einen Algorithmus zum "phase unwrapping" wird die kontinuierliche Phase des Frequenzgangs bestimmt.
• Der lineare Anteil (d.h. der Anstieg) der Phasenfunktion wird durch eine Least-Squares-Fit mit einem Polynom erster Ordnung bestimmt. Daraus kann der lineare Anteil der Verzögerung bestimmt werden.
• Optional: Der lineare Verzögerungsanteil wird auf ein ganzzahliges Vielfaches der Sampling-Periode gerundet bzw. abgerundet. Dies kann die spätere Rekombination vereinfachen, die dann nur eine Verschiebung der Impulsantwort erfordert (z.B. durch Voranstellen einer entsprechenden Zahl von Nullen oder durch eine Implementierung dieser Delays in Form einer Delay Line (Verzögerungsleitung).
• Auf Basis dieses linearen Terms wird ein Vektor aus komplexen Exponentialen berechnet, welches einen zu diesem linearen Phasenterm negierten Phasenverlauf hat.
• Durch Multiplikation des ursprünglichen Frequenzgangs 78 mit diesem Vektor aus komplexen Exponentialen wird die Verzögerung des Frequenzgangs angepasst.
• Die Berechnungsvorschrift kann leicht variiert werden, z.B. Zerlegung des komplexen Frequenzgangs in Magnitudengang (besser: Zero-Phase-Frequenzgang) und kontinuierliche Phase, Bestimmung des linearen Verzögerungsanteils, Subtraktion dieses Anteils von der kontinuierlichen Phase, gefolgt von einer Rekombination von Magnitude und Phase, oder einer Übergabe beider Teile an die folgende Glättung.

Extraction of the delays from the transducer data, already shown above to include transducer characteristics, already reduces some delay in the desired frequency response H _n 78 of the drive filter n . However, this may not be usable here and there and be supplemented by the delay adjustment module 80. The following procedure can be used to adjust the gain values.

• The adaptation is done for each filter BFF _n individually.
• A phase unwrapping algorithm determines the continuous phase of the frequency response.
• The linear portion (ie, slope) of the phase function is determined by a least squares fit with a first order polynomial. From this the linear part of the delay can be determined.
• Optional: The linear delay component is rounded to an integer multiple of the sampling period. This can simplify the later recombination, which then requires only a shift of the impulse response (eg by prefixing a corresponding number of zeros or by implementing these delays in the form of a delay line).
• On the basis of this linear term, a vector of complex exponentials is calculated which has a phase characteristic negated to this linear phase term.
• By multiplying the original frequency response 78 by this vector of complex exponentials, the delay of the frequency response is adjusted.
• The calculation rule can easily be varied, for example, decomposition of the complex frequency response in magnitude response (better: zero-phase response) and continuous phase, determination of the linear delay component, subtraction of this component from the continuous phase, followed by a recombination of magnitude and phase, or a transfer of both parts to the following smoothing.

Fig. 5 illustrates once again the operation of the delay adjustment module 80 of the modifier 48. As stated, the starting point is the set of target frequency responses 78 to be modified, ie H _n (ω _k ). Fig. 5 Illustratively shows the phase curve 82 of H _n (ω _k ). It has exemplary phase jumps 84. The 2π phase-shift-adjusted phase profile is shown at 86 and this can be approximated by a linear curve 88, such as a least square fit, where the linear portion 88 has a slope corresponding to a frequency-independent delay ψ ' _η equivalent. The modification of the target frequency response 78 by the module 80 now provides that this linear component 88 is eliminated or reduced, ie the 2π phase-jump-adjusted phase characteristic is leveled or straightened Fig. 5 at 90 shows the phase characteristic of the thus modified target frequency responses H ' _n (ω _k ). The delays ψ ' _η are reserved or stored.

Another module of the modification device 48 is the optional frequency-domain smoothing module 92. The frequency-domain smoothing by the module 92 has the following meaning. The frequency responses 78 and H ' _n (ω _k ) of the drive filters _n generated by the optimization-based filter design typically have large fluctuations of the magnitude and also of the phase. Such design specifications are difficult to implement in an FIR filter design or require a very high FIR filter order or FIR length of the beamforming filters. In the latter case, although a good agreement with the given interfaces can be achieved, however, strong overshoot _phenomena frequently occur between the interpolation points ω _k , which deteriorate the frequency response of the resulting beamformer. Even from psychoacoustic considerations, it often does not make sense to map such narrowband fluctuations. Therefore, the desired frequency responses 78 of the drive filters are subjected to a smoothing algorithm. This is done, for example, for psychoacoustic considerations with a frequency-dependent window width of, for example, 1/3 octave or 1/6 octave [HN00]. Since the frequency responses are complex-valued, for example, the smoothing is carried out separately for magnitude and phase, ie a separate smoothing of the magnitude transfer function (to be more precise of the "zero-phase" frequency response (cf., for example, [Sar93, SI07]) and the continuous ( It is possible that magnitude and phase are generated and independently by a phase unwrapping algorithm in the module 92 from the complex frequency response H _η (ω _k ) or H ' _n (ω _k ) is smoothed by convolution with a frequency-dependent smoothing filter, also referred to as "window." The phase unwrapping in the module 92 may, in the case of the presence of the module 80, occur if necessary because phase unwrapping was already performed in module 80. Subsequently, both smoothed parts, ie magnitude and phase, are combined to form the smoothed complex frequency response, more or less to H " _η (ω _k ) Alternatively, the separation of the frequency response into" zero-phase component "and continuous phase obtained in module 80, which are smoothed directly in module 90 and then combined. Fig. 5 indicates the combination of application of modules 80 and 92.

By the optimization in the calculation means 46 now FIR filter coefficients h _{BFF n} ( i ) with i = 1 ... l determined such that the target frequency responses of the beamforming filters are approximated, such as H " _n (ω _k ) in the case of using both modification modules 80 and 92. For details, see below As has already been mentioned, however, optimization methods for linear, quadratic or more generally convex compression problems can be used, and this optimization problem may be accompanied by constraints, which for example concern the course of the transfer function of the beamforming filters, ie a secondary condition that the The transfer function or the frequency range of the beamforming filters is concerned if the optimization in the calculation device 46 otherwise relates to the FIR filter coefficients of the beamforming filters which correspond to the impulse response of the beamforming filters as optimization variables.

For the sake of completeness, however, the meaning of the modification device 50 will be discussed for the sake of completeness prior to a more detailed description of the optimization in the calculation device 46. It is responsible for "integrating" the modification by the module 80, ie the leveling of the phase response of the target frequency responses of the beamforming filters, back into the FIR filter coefficients obtained by the optimization in the calculation means 46, if necessary, by adding a kind of delay Recombination performed, such as the zeros insertion described in more detail below, after which the FIR filter coefficients are prefixed zeros. This will be described below. Fig. 6 shows by way of example by a double arrow that the FIR filter coefficients h _BFF obtained by the optimization in the calculation device 46 _n Beamforming filter mode, the impulse response of the respective beam-forming filter n describe and pass over an FFT or Fourier transforms in the transfer function H _n (ω) of the respective beamforming filter or correspond to her. Fig. 6 shows by way of example at 96 the impulse response and at 98 exemplarily the 2π phase-jump-corrected phase characteristic of the transfer function. The modification device 50 now uses the phase delay value ψ _η stored for the respective beamforming filter n, in which the FIR filter coefficients are shifted accordingly in accordance with h ' _{BFF n} ( i ) = h _{BFF n} ( i ) ± ψ ' _n , for which purpose, as already mentioned, it is advantageous if, in the leveling module 80, the gradient ψ' _n used for leveling is limited to integer multiples of the time intervals of the FIR filter taps, since then the consideration of the leveling by the module 80 in the modification device 50 only a shift of the FIR filter coefficients h _{BFF n} otherwise, interpolation of the FIR filter coefficients is additionally required. For the modified FIR filter coefficient h ' _{BFF n} corresponding phase course this means as in Fig. 6 indicated at 100 that quasi leveling is reversed again.

Alternatively to the procedure after Fig. 6 in the modifier 50, in addition to the FIR filter coefficient h, _{BFF n} each beamforming filter n in the beamforming filter n in each case not only by the beamforming FIR filter coefficients h _{BFF n} , but also by the frequency-independent delay ψ ' _η , the latter in beamforming filters of the Fig. 1 and 2 could be considered by a simple delay connected in series with the FIR filter.

mit ƒ_s als Samp-lingfrequenz durchzuführen. Für sehr niedrige Frequenzen, insbesondere auch für f = 0 Hz, d.h. dem Gleichanteil, ist eine dezidierte Vorgabe des Abstrahlverhaltens nicht sinnvoll, gerade bei Modulierung realer Wandler. Ebenso sind für sehr hohe Frequenzen, wie z.B. relativ zur räumlichen Aliasing-Frequenz des Arrays, in der Regel keine sinnvollen Vorgaben möglich: 1) die Entstehung ausgeprägter Nebenkeulen kann nicht durch eine entsprechende Wunsch-Charakteristik verhindert werden. 2) Die Breite des "Beams" der gewünschten Abstrahlrichtung wird mit zunehmender Frequenz immer geringer. Somit ist es nicht oder nur mit hohem Spezifikationsaufwand möglich, sinnvolle, erfüllbare Vorgaben zur Breite der Beams in diesen Frequenzbereichen zu machen.It is usually not possible, the frequency domain design or the frequency range optimization 56 over the entire frequency range of the time-discrete filter, ie the FIR filter of the beamforming filter, namely from f = 0 Hz to $f=\frac{f_s}{2}$

with ƒ _s as a sampling frequency. For very low frequencies, especially for f = 0 Hz, ie the DC component, a dedicated specification of the radiation behavior is not useful, especially when modulating real converter. Similarly, for very high frequencies, such as relative to the spatial aliasing frequency of the array, usually no meaningful guidelines possible: 1) the formation of pronounced side lobes can not be prevented by a corresponding desired characteristic. 2) The width of the "beam" of the desired direction of radiation decreases with increasing frequency. Thus, it is not possible or only with high specification effort to make meaningful, achievable specifications for the width of the beams in these frequency ranges.

The statements just made relate to the frequency domain optimization 56, but also allow conclusions to be drawn about the time domain optimization in the time calculation device 46. Generally, the optimization process in the calculator 46, i. the optimization-based design of FIR filters, the introduction of frequency ranges or frequency sections for which no specifications are made, i. for which there is no desired frequency response or target frequency response, i. for which no optimization goal is specified. Such areas may be referred to as transition bands or "do not care bands". For the considered beamforming applications, however, it can be seen that even very narrow frequency ranges without design specification or without optimization target in the optimization of the second calculation means 46 lead to uncontrolled behavior of the designed FIR filters, such as e.g. to an extremely high magnitude and to fluctuations of the beamforming filter frequency response in these frequency sections.

wobei X eine diskretisierte Repräsentation der Transitions- bzw. "don't care"-Bänder darstellt, d.h. derjenigen Frequenzabschnitte, für die kein Optimierungsziel bei der Optimierung in der zweiten Berechnungseinrichtung 46 vorliegen soll, und |Ĥ(ω)| die maximal erlaubte Magnitude des Frequenzganges bei der Frequenz ω innerhalb der Transitionsbänder X bezeichnet.That's why Fig. 3 the optional possibility, according to which restrictions 42 are made for the optimization target with regard to the frequency response of these frequency sections. As is the dashed line in Fig. 3 indicates, and as it represented the penultimate paragraph, the frequency sections may be selected depending on characteristics of the converter. For example, the frequency constraint 42 is included in the optimization problem to be solved by the calculation means 46 by specifying a maximum magnitude as a constraint for the convex optimization problem: $$\mathrm{...}\mathrm{under\; the\; constraint\; that}\left|H\left(\omega \right)\right|\le \left|\widehat{H}\left(\omega \right)\right|\forall \omega \in X.$$

where X represents a discretized representation of the transition or "do not care" bands, ie those frequency segments for which there is no optimization target in the optimization in the second calculation means 46, and | Ĥ ( ω ) | denotes the maximum allowable magnitude of the frequency response at the frequency ω within the transition bands X.

An alternative to the use of frequency restrictions 42 or restrictions for high and low frequencies, respectively, is the use of a hybrid design approach, which will be described below.

The aim of the optimization in the second calculation device 46 is the frequencies obtained by the frequency domain design for the beamformers, which are denoted above as H _n (ω _k ) and H ' _n (ω _k ) and H " _n (ω _k ), respectively hereinafter referred to as the desired frequency response with the variable name Ĥ ( ω ) to generate FIR filters, with which the filtering of the source signals, ie the speaker signals in the case of a loudspeaker array, as shown in FIG Fig. 1 and the microphone output signals in the case of a microphone array as shown in FIG Fig. 2 shown can be done. For this purpose, a mathematical optimization method is used, which can be, for example, a method of convex optimization. With them, the frequency response H (w) of the designed FIR filter h (i) is determined so that Ĥ ( ω ) is approximated as best as possible, ie that the error with respect to a selectable standard p becomes minimal. The optimization problem can generally be represented in the following form: $$\begin{array}{c}\underset{H\left(i\right)\mathrm{,,\; 0}\le i\le I}{\mathrm{minimize}}{\Vert H\left(\omega \right)-\widehat{H}\left(\omega \right)\Vert }_p\\ \mathrm{under\; the\; constraint\; that\; <constraint}\left(s\right)\mathrm{>}\end{array}$$

The suffix <constraint (s)> is optional. Secondary conditions do not have to be present, but may be present, as described above with regard to the high-frequency restrictions, as an example. A single constraint is also possible. In general, these constraints represent a variety of possible constraints, including, but not limited to, the frequency response or coefficients of the FIR filter. The frequency variable ω, used here as a normalized angular frequency ω = 2πf / f _s , is usually discretized. Thus, both the optimization problem according to equation (2) and the secondary conditions can typically be represented in matrix form.

The target frequency responses for the time domain optimization in the second calculation device 46 which arise in the context of the frequency domain optimization 56 (or with modification 80 and / or 92) are generally complex-valued and have a non-trivial, in particular neither linear nor minimal-phase, frequency response. Thus, the optimization problem of the above equation (2) corresponds to a filter design problem for FIR filters with arbitrary phase characteristics. For this purpose, a large number of methods are described in the literature, for example in [PR95, KM95; KM99].

verwendet wird. Aus diesem Grund wäre es möglich, wie in [KM99] vorgeschlagen, das Design auf Basis eines nichtkausalen FIR-Filters mit der Übertragungsfunktion $$H_{\mathit{nc}}\left(\omega \right)={\displaystyle \sum _{n=0}^{N}h\left[n\right]G\left(n,\omega \right)}\mathrm{mit}G\left(n,\omega \right)=e^{-\mathit{j\omega }\left(n-\frac{N}{2}\right)}$$

vorzunehmen. Der kausale (3) und der nichtkausale Filter (4a) unterscheiden sich durch den reinen Delay-Term, nämlich $$H\left(e^{\mathit{j\omega }}\right)=e^{-j\frac{N}{2}\omega }{H}_{\mathit{nc}}\left(\omega \right).$$

During the implementation of the design algorithm , the delays contained in the filters Ĥ ( ω ) and Ĥ (ω) , ie the linear term of the phase response which has been adjusted by 2π phase jumps, are of particular importance. As shown in [KM99], the use of arbitrary phase responses results in very poorly conditioned optimization problems or degenerate solutions. This is especially true when the standard formulation of a causal FIR filter with the frequency response $$H\left(\omega \right)={\displaystyle \underset{n=0}{\overset{N}{\Sigma }}{e}^{-\mathit{j\omega n}}}$$

is used. For this reason, it would be possible, as suggested in [KM99], to design based on a non-causal FIR filter with the transfer function $$H_{\mathit{nc}}\left(\omega \right)={\displaystyle \underset{n=0}{\overset{N}{\Sigma }}H\left[n\right]G\left(n.\omega \right)}\mathrm{With}G\left(n.\omega \right)=e^{-\mathit{j\omega }\left(n-\frac{N}{2}\right)}$$

make. The causal (3) and the non-causal filter (4a) differ by the pure delay term, viz $$H\left(e^{\mathit{j\omega }}\right)=e^{-j\frac{N}{2}\omega }{H}_{\mathit{nc}}\left(\omega \right),$$

When using the non-causal frequency response, the desired function Ĥ ( ω ) should be adjusted so that the linear component of the phase is as close to 0 as possible. This is effectively realized by the modifications 80 and 50.

After the impulse responses of the FIR filters, ie h (i), have been determined in the optimization of the second calculation device 46, the modification device 50 optionally integrates the previously compensated delay components back into the drive filters. According to an alternative embodiment, the integration of the delays ψ ' _η into the filters n is bypassed by applying the pure delays ψ' _n at runtime of the beamforming application be applied to the input or output signals of the control filters by means of suitable signal processing means, such as digital delay lines (English Delay Lines ). In this case it is only necessary to ensure that the impulse responses of the obtained FIR filters are causal, ie that the indices of the impulse responses begin at zero. Such a modification does not require active arithmetic operations at run-time, but merely corresponds to the introduction of a constant implementation-related delay for all drive filters n. It should be ensured that this delay is constant for all drive filters of a beamformer. For the separate application of the delay, it may be advantageous to select the delays extracted in delay adaptation 80 as multiples of the sampling period. Namely, in this case, the delay lines as with respect Fig. 6 as already described, are used for integer delays that do not require filtering operations but merely require indexed access to the signal and also do not cause distortion. Alternatively, any delay values can be mapped. However, this requires delay lines with access to arbitrary fractional delay lines , which can cause distortion, require processing power, and possibly require additional latency or delay.

In the context of high-frequency restriction 42, it has already been discussed that optimization that applies equally to all frequencies does not always make sense. This also goes for frequency range optimization 56. Above, it has already been suggested that frequency domain optimization 56 could also use a hybrid design approach. According to this approach, an optimization-based approach for obtaining the frequency domain drive functions H _m (ω _k ) as described so far is combined with a design corresponding to the DSB design as calculated in the module 54, wherein the DSB Design approach is used for the high frequencies. The aim is to reduce the required filter order while improving robustness. It is exploited that for high frequencies, the emission characteristics of the transducer array due to the spatial aliasing can not be completely controlled. Therefore, for frequencies above a fixed fundamental frequency, such as a frequency that is relatively close to the spatial aliasing frequency of the transducer array, a DSB design approach is used. For this purpose, the frequency domain specification of the complete filter is composed of two parts: the frequency responses obtained by optimization up to the cutoff frequency and the frequency responses corresponding to those of the DSB for the frequencies above it. The combination of both methods is followed by the subsequent smoothing already described above and the optimization-based FIR design. A critical step here is the alignment of the signal delays of both design approaches. For example, it is possible to use a least-square fitting to determine a delay offset for the DSB in such a way that the delay jumps of the individual control filters are minimized in the root mean square.

In various exemplary designs, the hybrid design approach allows for more robust high frequency radiation, resulting in less erratic fluctuations in performance without significant loss of performance, with partially improved low frequency directivity, and consistent filter ordering. The reason for this can be assumed that the degrees of freedom provided by a certain filter order are better used with the hybrid design approach for the frequency ranges in which the characteristic can be influenced, while for high frequencies in which due to spatial aliasing hard restrictions for the Suppression of unwanted radiation, less resources are spent.

Fig. 7 illustrates again the hybrid design approach: The transfer function to be used for time domain optimization in the second calculating means 46 is composed of the obtained according to the frequency range optimization 56 transfer function, as far as a portion of lower audio frequencies is concerned 100, where the the frequency-independent pairs of values ψ _η a _η corresponding transfer functions H _{n be used} in the higher audio frequency section 102. Section 100 and section 102 can be concatenated to a cutoff frequency ω _cross connect to each other, for example, corresponds to the spatial aliasing frequency border of the transducer array or from the latter deviates less than 10%. It is also possible that, as indicated by dashed dots, low-frequency section and high-frequency sections 100 and 102 overlap each other. For example, if section 100 extends over [ωN _{, b,} ωN _{, e} ] and section 102 over [ωH _{, b,} ωH _{, e],} then ωN _{, b} <ωH _{, b} ΛωN _{, e} <ω _{H, e,} where possibly ω _{N, b} = 0 and / or ω _{H, b} ≤ ω _{N, e} or even ω _{H, b} = ω _{N, e} and / or 0.9 · ω _limit <ω _{H, b,} ω _{N, e} <1.1 · ω _limit applies. In the overlapping area of both sections, the time-domain optimization transfer function finally to be used could be obtained, for example, by averaging between both transfer functions (DSB design and optimization result of FIG. 56).

In summary, the above embodiments thus described a possibility for the creation of a design of robust FIR filters for beamforming applications. From complex-valued frequency responses of the individual beamforming filters, FIR filters with arbitrary phase responses can be generated. Particular value of the above embodiments is that robustness properties of the beamformer can be obtained.

Particular advantages of the above embodiments are, for example, that robust FIR filters can also be obtained for complex beamforming problems, such as e.g. in broadband operation beyond the aliasing frequency of the transducer array, or in the case of complex behavior of the transducers, e.g. a limited level at low frequencies. Another advantage is that the frequency raster of the frequency response specification, i. in the frequency domain optimization 56, and the filter order of the FIR filters of the beamforming filters can be selected independently of each other. In addition, a variety of design specifications for beamformers and the filters are possible: constraints, e.g. Level limits, behavior of the filter in regions where there is no beamforming frequency response, etc. can be easily integrated.

The present invention can be used in a variety of beamforming applications, e.g. in loudspeaker arrays for room-selective sonication, for generating "quiet zones" or for reproducing surround material via loudspeaker lines (soundbars). Likewise, the above embodiments may also be used by microphone arrays to record sound directionally selective.

Possibly beamforming applications for electromagnetic waves, e.g. conceivable for mobile or radar antennas. However, the bandwidths required there are significantly lower than for audio applications, so that an implementation as an FIR filter or the need for a design approach for broadband filters can be estimated only with difficulty here.

Although some aspects have been described in the context of a device, it will be understood that these aspects also constitute a description of the corresponding method, so that a block or a component of a device is also to be understood as a corresponding method step or as a feature of a method step. Similarly, aspects described in connection with or as a method step also provide a description of a corresponding one Some or all of the method steps may be performed by a hardware device (or using a hardware device), such as a microprocessor, a programmable computer, or an electronic circuit. In some embodiments, some or more of the most important method steps may be performed by such an apparatus.

The inventive set of FIR filter coefficients 32 for the beamforming filters may be stored on a digital storage medium, or may be transmitted on a transmission medium such as a wireless transmission medium or a wired transmission medium such as the Internet.

Depending on particular implementation requirements, embodiments of the invention may be implemented in hardware or in software. The implementation may be performed using a digital storage medium, such as a floppy disk, a DVD, a Blu-ray Disc, a CD, a ROM, a PROM, an EPROM, an EEPROM or FLASH memory, a hard disk, or other magnetic disk or optical memory are stored on the electronically readable control signals that can cooperate with a programmable computer system or cooperate such that the respective method is performed. Therefore, the digital storage medium can be computer readable.

Thus, some embodiments according to the invention include a data carrier having electronically readable control signals capable of interacting with a programmable computer system such that one of the methods described herein is performed.

In general, embodiments of the present invention may be implemented as a computer program product having a program code, wherein the program code is operable to perform one of the methods when the computer program product runs on a computer.

The program code can also be stored, for example, on a machine-readable carrier.

Other embodiments include the computer program for performing any of the methods described herein, wherein the computer program is stored on a machine-readable medium.

In other words, an embodiment of the method according to the invention is thus a computer program which has a program code for performing one of the methods described herein when the computer program runs on a computer.

A further embodiment of the inventive method is thus a data carrier (or a digital storage medium or a computer-readable medium) on which the computer program is recorded for carrying out one of the methods described herein.

A further embodiment of the method according to the invention is thus a data stream or a sequence of signals, which represent the computer program for performing one of the methods described herein. The data stream or the sequence of signals may be configured, for example, to be transferred via a data communication connection, for example via the Internet.

Another embodiment includes a processing device, such as a computer or a programmable logic device, that is configured or adapted to perform one of the methods described herein.

Another embodiment includes a computer on which the computer program is installed to perform one of the methods described herein.

Another embodiment according to the invention comprises a device or system adapted to transmit a computer program for performing at least one of the methods described herein to a receiver. The transmission can be done for example electronically or optically. The receiver may be, for example, a computer, a mobile device, a storage device or a similar device. For example, the device or system may include a file server for transmitting the computer program to the recipient.

In some embodiments, a programmable logic device (eg, a field programmable gate array, an FPGA) may be used to to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor to perform one of the methods described herein. In general, in some embodiments, the methods are performed by any hardware device. This may be a universal hardware such as a computer processor (CPU) or hardware specific to the process, such as an ASIC.

The embodiments described above are merely illustrative of the principles of the present invention. It will be understood that modifications and variations of the arrangements and details described herein will be apparent to others of ordinary skill in the art. Therefore, it is intended that the invention be limited only by the scope of the appended claims and not by the specific details presented in the description and explanation of the embodiments herein.

literature

[ACL93] Ashraf S. Alkhairy, Kevin G. Christian, and Jae S. Lim. Design and characterization of optimal FIR filters with arbitrary phase. IEEE Transactions on Signal Processing, 41 (2): 559-572, February 1993 , [BW01] Michael Brandstein and Darren Ward, editors. Microphone Arrays: Signal Processing Techniques and Applications. Springer 2001 , [HM00] Panagiotis D. Hatziantoniou and John N. Mourjopoulos. Generalized fractional-octave smoothing of audio and acoustic responses. Journal of the Audio Engineering Society, 48 (4): 259-280, April 2000 [KM95] Lina J. Karam and James H. McClellan. Complex Chebyshev approximation for FIR filter design. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42 (3): 207-216, March 1995 , [KM99] Lina J. Karam and James H. McClellan. Chebyshev digital FIR filter design. Signal Processing, 79 (1): 17-36, July 1999 [Lyo11] Richard G. Lyons. Understanding Digital Signal Processing (3rd Edition) (hardcover), Pearson, Upper Saddle River, NJ, 3rd edition, 2011 , [MK07] Edwin Mabande and Walter Kellermann. Towards superdirective beam-forming with loudspeaker arrays. In Conf. Rec. International Congress on Acoustics, 2007 , [MSK09] Edwin Mabande, Adrian Schad, and Walter Kellermann. Design of robust superdirective beamformers as convex optimization problem. In the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2009), pages 77-80, April 2009 , [MSK11] Edwin Mabande, Adrian Schad, and Walter Kellermann. A time-domain implementation of data-independent robust broadband beamfomers with low filter order. In Workshop on Hands-free Speech Communication and Microphone Arrays (HSCMA), pages 81-85, Edinburgh, UK, May 2011 , [PF04] Jörg Panzer and Lampos Ferekidis. The use of continuous phase for interpolation, smoothing and forming. At 116th AES Convention, Berlin, Germany, May 2004 , [PR95] Alexander W. Potchinkov and R Reemtsen. The design of FIR filters in the complex plan by convex optimization. Signal Processing, 46 (2): 127-146, October 1995 , [Sar93] Tapio Saramaki. Finite impulse response filter design. In SK Miter and JF Kaiser editors, Handbook for Digital Signal Processing, chapter 4, pages 155-278. John Wiley & Sons, Inc., 1993 , [S107] Julius O. Smith III. Introduction to Digital Filters with Audio Applications, W3K Publishing, 2007 http://w3k.org/books/http://www.w3k.org/books /. [Smi11] Julius O. Smith. Spectral Audio Signal Processing. W3K Publishing 2011. [online] http: //ccrma.stanford.edu~jos/sasp ,

Claims (12)

1. Device for calculating FIR filter coefficients for beam-forming filters of a transducer array (10), comprising:

   first calculation means (44) for calculating frequency domain filter weights of the beam-forming filters (14₁...,14_N) for a predetermined frequency raster so as to obtain target frequency responses (78) for the beam-forming filters, so that application of the beam-forming filters to the transducer array (10) approximates a desired directional selectivity (36; 38; 70; 74); and

   second calculation means (46) for calculating the FIR filter coefficients (32) for the beam-forming filters so that frequency responses of the beam-forming filters approximate the target frequency responses;

   further comprising a target frequency response modification means (48) connected between the first calculation means (44) and the second calculation means (46) so as to modify the target frequency responses of the beam-forming filters as obtained by the first calculation means (44), so that the second calculation means (46) calculates the FIR filter coefficients for the beam-forming filters in such a manner that the frequency responses of the beam-forming filters approximate the target frequency responses in a form modified by the target frequency response modification means (48), said modification including

   frequency domain smoothing (92) and/or

   for each beam-forming filter, leveling (80) of a phase response (86), adjusted by 2π phase jumps, of the target frequency response of the respective beam-forming filter by removing a linear phase function portion (88), and storing a delay for the respective beam-forming filter, said delay corresponding to a slope of the linear phase function portion.
2. Device as claimed in claim 1, wherein the first calculation means (44) is configured to perform the calculation by solving a first optimization problem according to which a deviation between a directional selectivity of the array, as results from the frequency domain filter weights, and the desired directional selectivity (74) is minimized.
3. Device as claimed in claim 2, wherein the first calculation means (44) is configured such that the first optimization problem is a convex optimization problem.
4. Device as claimed in claims 2 or 3, wherein the first calculation means (44) is configured to combine the calculation within a first range of relatively low audio frequencies (100) by solving the first optimization problem so as to obtain low-frequency domain target frequency responses for the beam-forming filters, and within a second range of relatively high audio frequencies (102) by calculating global-frequency delays and amplitude weights for the array as a function of the desired directional selectivity, and to subsequently combine the low-frequency domain target frequency responses with high-frequency domain target frequency responses which correspond to global-frequency delays and amplitude weights.
5. Device as claimed in any of the previous claims, said device further comprising an FIR filter coefficient modification means (50) configured to subject the FIR filter coefficients (32) as are calculated by the second calculation means to a time-domain shift corresponding to the stored delay for the respective beam-forming filter.
6. Device as claimed in any of the previous claims, wherein the second calculation means (46) is configured to perform the calculation by solving a second optimization problem according to which a deviation between the frequency responses of the beam-forming filters corresponding to the FIR filter coefficients and the target frequency responses is minimized.
7. Device as claimed in claim 6, wherein the second calculation means (46) is configured such that the second optimization problem is a convex optimization problem.
8. Device as claimed in claim 6 or 7, wherein the second calculation means (46) is configured such that the second optimization problem defines the deviation in a frequency-selective manner, or defines frequency-dependent tolerance thresholds for the deviation.
9. Device as claimed in any of claims 6 to 8, wherein the second calculation means (46) is configured such that as a secondary condition, the second optimization problem comprises, in at least one frequency section wherein the deviation is not minimized, a restriction of the magnitude of the frequency responses of the beam-forming filters which correspond to the FIR filter coefficients.
10. Device as claimed in any of claims 1 to 9, wherein a frequency resolution of the beam-forming filters as is defined by the FIR filter coefficients differs from a frequency resolution of the frequency raster for which the frequency domain filter weights of the beam-forming filters are calculated.
11. Method of calculating FIR filter coefficients for beam-forming filters of a transducer array (10) comprising:

    calculating frequency domain filter weights of the beam-forming filters (14₁..., 14_N) for a predetermined frequency raster so as to obtain target frequency responses (78) for the beam-forming filters, so that application of the beam-forming filters to the transducer array (10) approximates a desired directional selectivity (36; 38; 70; 74); and

    modifying the target frequency responses of the beam-forming filters, said modification including

    frequency domain smoothing (92) and/or

    for each beam-forming filter, leveling (80) of a phase response (86), adjusted by 2π phase jumps, of the target frequency response of the respective beam-forming filter by removing a linear phase function portion (88), and storing a delay for the respective beam-forming filter, said delay corresponding to a slope of the linear phase function portion;

    and

    calculating the FIR filter coefficients (32) for the beam-forming filters so that frequency responses of the beam-forming filters approximate the target frequency responses in a form modified by the target frequency response modification means (48).
12. Computer program having a program code for performing the method of claim 11, when the program runs on a computer.

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