Method and device for obtaining digital audio signal filter, method and device implementing said filter

Abstract

There is described a computer-implemented method for obtaining M filters of a digital audio signal defined in the time domain, where M is an integer greater than or equal to 1, each filter being associated with a respective sound source, referred to as a secondary source, emitting a sound pressure field, the invention relates to a method for operating a sound pressure field that minimizes a reflected sound pressure field of a set of sound sources, referred to as primary sources, located in a room, comprising:-for each primary sound source and secondary sound source, obtaining (S601) an impulse response of reflected sound pressure at N respective different positions in the room, where all primary and secondary sound sources are placed in an operating position, the N positions are the same for all sound sources; determining (S602) a set of M filters by solving a regularization optimization problem based on said set of impulse responses and formulated in the time domain, the optimization problem being defined as (a) minimizing the norm of the sum of impulse responses at N positions; and (b) introducing a non-zero action delay for each filter; each secondary source is combined with a primary source referred to as an associated primary source.

Description

Technical Field

[0001] The present invention relates to a method and device for obtaining a digital audio signal filter, wherein the digital audio signal filter is used in a device for generating a sound source signal, and also relates to a signal processing method for realizing the filter.

[0002] The present invention serves to reduce reflections of sound waves generated by the source. Background Art

[0003] When a sound source transmits sound within an enclosed space, the sound waves are reflected by the various walls until the waves are completely attenuated either through absorption by the walls or (for higher frequencies) through thermal heating in the air.

[0004] At low frequencies, the attenuation of sound waves is limited, and even if there is absorbing material on the wall, the time required for the sound waves to be completely absorbed may be long (more than a second).

[0005] This is because most absorbing materials used dissipate acoustic energy by visco-thermal friction, and their effectiveness is related to the thickness of the material, which is related to the wavelength under consideration.

[0006] As a reminder, wavelength is equal to the speed of sound in air divided by the frequency. Therefore, for lower frequencies, the wavelength is longer. For example, the wavelength associated with 50 Hz is equal to 6.8 meters.

[0007] This means that a very thick absorbing material is required to attenuate sound waves in this frequency range, a thickness that is naturally not suitable for use in a medium-sized room (less than 100m). 2 ) is not compatible.

[0008] Furthermore, at certain frequencies, for which the corresponding wavelength is a multiple of one of the room's dimensions, resonances occur, characterized by a highly non-uniform pressure field, with regions of very high acoustic energy (called pressure antinodes) and other regions of very low acoustic energy (called pressure nodes). These resonances are also known as "acoustic modes" or "room modes" and significantly reduce the acoustic quality of the source compared to when it radiates in a free field (e.g., outdoors).

[0009] There are various types of damage caused by acoustic modes:

[0010] - Spatial: For a given frequency, areas of very high pressure coexist with areas of very low pressure, resulting in a high spatial variability of the sound level.

[0011] - Frequency: Thus, for a fixed position, the magnitude of pressure based on frequency (often referred to as the "frequency response") varies greatly.

[0012] - Time: Acoustic modes with low sound energy decay may result in very long decay times (also called reverberation times). This is often referred to as smearing.

[0013] The number of acoustic modes per frequency band (also called "modal density") depends on the volume of the room. Larger rooms tend to have a greater number of acoustic modes in a given frequency band than smaller rooms. However, low modal density is more problematic because the modes that do exist tend to be more distinguishable (because they are further apart in the frequency domain) and have higher energy.

[0014] Therefore, room modes are particularly problematic in mixing and listening rooms, as well as small to medium-sized concert halls, because they can strongly modify low frequencies (between 20 Hz and 100 to 200 Hz).For larger rooms, the higher modal density makes the room's acoustic impact less problematic.

[0015] The Schroeder frequency simply quantifies the transition between modal behavior, where the different acoustic modes are clearly identifiable and have higher energy, and statistical behavior, where the modes are too close in frequency to be clearly identified and the modes have lower energy.

[0016] This frequency is inversely proportional to the volume of the room. Therefore, for large concert halls, when the frequency is low enough that no correction is needed, a switch is made to a less problematic statistical behavior. This type of control is too complex to be established.

[0017] Several methods have been proposed to attenuate acoustic modes by adding so-called "secondary" sound sources whose function is to absorb the sound waves emitted by the so-called "primary" sources. These secondary sources are located, for example, on the wall opposite the primary source. These methods include the "CABS" (Controlled Acoustic Bass System) method by Adrian Celestinos et al. (see Reference 1 in the Appendix). Another method is the "impedance matching" method proposed by the Ecole Polytechnique Fédéral de Lausanne. A third method is described by Franz Heuchel et al. in his article "Compensation active d'une pièce pour le renforcement du son utilisant des techniques de séparation de champsonore" ("Active room sound reinforcement compensation using acoustic field separation techniques") (Reference 2). This method uses plane wave decomposition (PWD) to model the incident and reflected fields. The authors then solve a frequency-domain optimization problem aimed at finding the optimal filter for the secondary sources to cancel the reflected fields. The method requires a calibration step using two sets of microphones placed around the room.

[0018] A fourth approach involves adding electronic corrections using filters to modify the frequency response curve at one or more reference locations in the room. These corrections are not intended to suppress acoustic modes, but rather to "equalize" the frequency response at certain locations in a preferential manner, simply by reducing the sound pressure level at the transmitter at frequencies corresponding to pressure antinodes, and sometimes by increasing the sound pressure level at frequencies corresponding to pressure nodes.

[0019] However, this fourth approach is not satisfactory because reducing the sound pressure level at emission also degrades the sound waves before reflection (also known as the "direct field"), which results in a loss of accuracy and impact.

[0020] Document US8660272 describes a technique for reducing acoustic reflections from a device equipped with a loudspeaker in a room. The signal fed to the loudspeaker comprises an audio signal to which is added an identical filtered audio signal, the filtering comprising applying a multi-stage filter, each stage of which comprises a delay and a gain, the characteristics of each stage being obtained iteratively.

[0021] It would be desirable to have a solution for reducing sound wave reflections generated by one or more sound sources in a room that requires few resources during the calibration phase. Summary of the Invention

[0022] A first aspect relates to a computer-implemented method for obtaining M filters of a digital audio signal defined in the time domain, where M is an integer greater than or equal to 1, each filter being associated with a respective sound source, referred to as a secondary source, emitting a sound pressure field that minimizes the reflected sound pressure field of a set of sound sources, referred to as primary sources, located in a room, the method comprising:

[0023] - for each primary sound source and secondary sound source, obtaining an impulse response of the reflected sound pressure at N corresponding different positions in the room, wherein all the primary sound sources and the secondary sound sources are placed in an operating position, the N positions being the same for all the sound sources;

[0024] - The set of M filters is determined by solving a regularized optimization problem based on the set of impulse responses and formulated in the time domain, the optimization problem being defined as

[0025] (a) minimizing the norm of the sum of the impulse responses at the N positions; and

[0026] (b) introducing non-zero action delay for each filter;

[0027] Each secondary source is combined with a primary source called an associated primary source.

[0028] Each filter is intended to be applied to a signal derived from the input audio signal of the corresponding sound source associated with the filter, with the corresponding sound source being configured to broadcast the sum of the input audio signal and the filtered signal. The audio input signals from the sound sources are identical. This reduces reflections of the generated sound waves.

[0029] According to one or more embodiments, M is greater than or equal to 2.

[0030] According to one or more embodiments, for a given secondary sound source combined with its associated primary source, obtaining an impulse response of the reflected sound pressure at a given one of N locations includes:

[0031] - emission of sound waves by a given secondary sound source in combination with its associated primary source in response to an excitation signal;

[0032] - obtaining a signal representing the sound pressure generated by the excitation signal at said location;

[0033] - determining the impulse response of the reflected sound pressure based on the obtained signal representing the sound pressure.

[0034] According to one or more embodiments, the sound pressure signal is obtained using a microphone placed at the given location, and the determining of the impulse response includes applying time windowing to the sound pressure signal so as to suppress direct sound waves received from the given secondary sound source in combination with its associated primary source, while retaining the reflected sound waves.

[0035] According to one or more embodiments, the sound pressure signal is obtained using a pair of microphones placed around the given location, and the determination of the impulse response includes determining the pressure and velocity of the sound wave in order to separate the direct sound wave received from the sound source from the reflected sound wave.

[0036] According to one or more embodiments, the motion delay is substantially equal to an average travel time of a sound wave generated by the source between the source and a wall of the room.

[0037] According to one or more embodiments, the method includes determining a regularization parameter for regularizing the optimization problem, the determination taking into account a maximum magnitude threshold of the filter.

[0038] A second aspect relates to a data processing device comprising means for implementing one of the above methods.

[0039] A third aspect relates to an audio signal processing device, the audio signal processing device comprising:

[0040] an input configured to receive a first audio signal (x(t));

[0041] a first filter for filtering the first signal and obtaining a second audio signal, the first filter being a finite impulse response filter obtained by applying one of the above filter obtaining methods;

[0042] - an adder for adding the first audio signal and the second audio signal to obtain a third audio signal for controlling a sound source associated with the first filter.

[0043] According to one or more embodiments, the audio signal processing device includes a low-pass filter for filtering the first audio signal, and an output terminal of the low-pass filter is connected to an input terminal of the first filter.

[0044] According to one or more embodiments, the audio signal processing device includes: a downsampling circuit for downsampling the audio signal after the low-pass filter and before being provided to the first filter; and an oversampling circuit for oversampling the audio signal after being filtered by the first impulse response filter and before being provided to the adder.

[0045] According to one or more embodiments, the audio signal processing device includes one of the following:

[0046] an adjustable attenuator for applying a gain between 0% and 100% to the second audio signal; and

[0047] A switch is configured to connect or disconnect the second signal to or from the adder input terminal.

[0048] A fourth aspect relates to an audio signal processing method implemented by a device including a processor, a memory, and software code, the method comprising:

[0049] - receiving a first audio signal;

[0050] - filtering the audio signal by a finite impulse response filter obtained by applying one of the above-mentioned filtering methods;

[0051] - summing the first audio signal and the signal filtered by the finite impulse response filter to form a signal suitable for providing to a sound source associated with the finite impulse response filter.

[0052] According to one or more example embodiments, the audio signal processing method includes low-pass filtering the first audio signal before filtering by the impulse response filter.

[0053] According to one or more embodiment examples, the audio signal processing method includes downsampling the audio signal after low-pass filtering and before impulse response filtering, and oversampling the audio signal after impulse response filtering and before summing.

[0054] One or more embodiments relate to a storage medium readable by a device equipped with a processor, the medium including instructions that, when executed by the processor of the device, cause the device to implement at least one of the methods described. Specifically, the recording medium may be non-transitory. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Other features and advantages of the present invention will become apparent from the following detailed description, which can be read with reference to the accompanying drawings, in which:

[0056] Figure 1 is a functional block diagram of a device according to one or more embodiments;

[0057] Figure 2 is a collection of devices that receive the same audio signal as input (such as Figure 1 A functional block diagram of a collection of devices in a

[0058] Figure 3 schematically illustrates a room including a plurality of primary sound sources and a plurality of secondary sound sources designed to reduce reflections of waves generated by the primary sources, according to one or more example embodiments;

[0059] Figure 4 is a graph showing the filter magnitude based on the norm of the correction error for different λ regularization parameters for the optimization problem;

[0060] Figure 5 schematically illustrates a room with several primary and secondary sound sources combined according to one or more example embodiments;

[0061] Figure 6 is a flow chart of a method for determining one or more filters according to one or more embodiments;

[0062] Figure 7 is a block diagram of an example apparatus for determining a filter according to one or more example embodiments. DETAILED DESCRIPTION

[0063] In the following description, the same, similar or like elements will be referred to by the same reference numerals.

[0064] The block diagrams, flow charts, and message sequence charts in the accompanying drawings illustrate the architecture, functionality, and operation of systems, devices, methods, and computer program products according to one or more exemplary embodiments. Each block in a block diagram or each step in a flow chart may represent a portion of a module or software code that includes instructions for implementing one or more functions. Depending on the specific implementation, the order of the blocks or steps may be changed, or the corresponding functions may be implemented in parallel. For all or part of the blocks or steps, circuitry, software, or a combination of circuitry and software may be used to implement the method blocks or steps in a centralized or distributed manner. The described systems, devices, processes, and methods may be modified or have additions and / or deletions made while remaining within the scope of the present disclosure. For example, the components of a device or system may be integrated or separated. Similarly, the disclosed features may be implemented using more or fewer components or steps, or even implemented together with other components or with the aid of other steps. Any suitable data processing system may be used for specific implementations. Suitable data processing systems or devices include, for example, a combination of software code and circuitry, such as a processor, controller, or other circuitry suitable for executing the software code. When executing the software code, the processor or controller causes the system or device to implement all or part of the functionality of the blocks and / or steps of the process or method according to the exemplary embodiments. The software codes may be stored in a memory or readable medium which may be accessed by a processor or controller directly or via another module.

[0065] One embodiment relates to an apparatus for processing an audio signal intended to be broadcast by a sound source, typically an electroacoustic transducer that converts an electrical signal into an acoustic signal. The transducer is, for example, a loudspeaker, although other transducers may also be used. The terms sound source, transducer, and loudspeaker are used interchangeably hereinafter.

[0066] Illustratively, according to one or more embodiments, the signal generated by the audio signal processing device includes an input audio signal (e.g., music content), referred to as a reference signal, and a control signal that attenuates waves reflected in the room broadcast by the transducer. More precisely, the control signal corresponds to the delayed and filtered input audio signal. Thus, when the input audio signal is provided to the transducer, the processed audio signal propagates through the room and is reflected by the walls. As the wave reflects and propagates in the room, it undergoes changes similar to filtering. After a certain delay relative to the reference audio signal, the transducer transmits a copy of the reflected and filtered signal in antiphase. The reflected wave is then canceled, and resonance can no longer be established.

[0067] Depending on the desired implementation, the signal processing device is adapted to generate a signal for one or several transducers.The processing device may be combined with one or more transducers into a device or may be located in a separate device.

[0068] Figure 1 Schematic diagram illustrating, in functional block form, the processing performed on a reference signal and the transducer provided by the processed signal. Device 100 includes an input 101 for a reference audio signal x(t). This audio signal is intended to be broadcast by a speaker 103, which in this example is external to device 100. For the purposes of this description, it is assumed that the reference signal is digital; if this is not the case, circuitry for digitizing the reference signal is well known to those skilled in the art. The reference audio signal input is connected to a first input of an adder 104, the output of which is connected to speaker 103. A reference signal bypass path, connected on one hand to signal input 101 and on the other hand to a second input of adder 104, includes a digital filter w105, which is designed to filter the signal at its input to generate a control signal. According to one embodiment, the digital filter advantageously implements both signal delay and filtering at its input. Due to its role in generating the control signal, filter 105 will be referred to as the "control filter" hereinafter.

[0069] According to one embodiment, delay and filtering are introduced by separate units.

[0070] According to this embodiment, before the input audio signal passes through the filter 105, the input audio signal passes through a low-pass filter 106. The function of this low-pass filter is to ensure that the filter 105 is only applied to the frequency range where reflection compensation is required or desired. This low-pass filter can be implemented by downsampling the audio signal. Downsampling is performed at a frequency much lower than the frequency of the original audio signal, and filtering is performed at this new sampling frequency. For a given computing resource, this downsampling improves the efficiency of the filter, also known as increasing the order of the filter. Before being summed by the adder 104, the filtered signal is oversampled to a sampling frequency identical to the sampling frequency of the reference signal.

[0071] According to one or more embodiments, the low-pass filter is optional. This is the case, for example, when the reference signal is already in the desired frequency band.

[0072] Reference 102 refers to a signal processing block including adder 104, filter 105, and low pass filter 106. The device 100 may include other circuits such as a power amplifier. Block 102 may be implemented Figure 1 The functionality of the adaptive signal processor is shown.

[0073] By way of example, for some applications the downsampling frequency may be 500 Hz.

[0074] In a particular embodiment, the filter w(t) 105 is a finite impulse response filter. The filter performs a convolution operation on the signal received at its input.

[0075] Figure 1 The main signal processing operations performed and the basic concepts applied are shown. Other components or functions may be present and additional signal processing may be performed. Moreover, the actual specific implementation may of course vary from Figure 1 The illustrated implementation, in particular, the signal processing block 102 itself may be partially or fully implemented using a suitable signal processor.

[0076] Figure 2 A set of several processing devices 100_i is shown, each of which includes Figure 1 The components shown. Figure 2 In the example shown, all processing devices receive the same reference audio signal x(t) as input. The filter w _i (t) There may be differences between one processing device 100_i and another processing device. i is an integer between 1 and M, where M is the number of processing devices. In the following, we will consider Figure 2 For the general case, note that the value of "i" can be equal to 1. For clarity, Figure 2 Not shown Figure 1All elements of apparatus 100 are shown.

[0077] According to a particular embodiment, in case separate reference audio signals are broadcast on many channels ("multi-channel" scenario), for each of the reference audio signals a Figure 2 Device shown.

[0078] For a given loudspeaker placement in a given room, the delays and filtering to be applied to create the control signal are fixed in time and specific to each transducer or loudspeaker.

[0079] According to one embodiment, delays and filtering are not fixed in time, e.g., they are re-evaluated at regular intervals or on a punctual basis based on one or more of the following parameters: temperature changes, room occupancy, changes in transducer layout or orientation, etc.

[0080] The optimal individual filters and delays to be applied are obtained during a preliminary calibration phase by a single optimization calculation for all the loudspeakers in the loudspeaker system, involving the impulse responses between each loudspeaker and a set of N "control" microphones located in the room. The impulse responses between each loudspeaker and the set of microphones located in the room can be obtained by a measurement step or by a simulation step. The measurement phase is followed by a calibration phase, which provides the delays and filter characteristics for parameterizing the corresponding signal processing devices. According to one embodiment, the optimization problem consists of finding a set of M filters that minimizes the norm L2 of the reflection field. The formulation of the optimization problem in the time domain makes it possible to apply a separate action delay to each filter, which avoids obtaining a filter that cancels the low-frequency reference signal immediately after it is transmitted, such as:

[0081] [Mathematical formula 1]

[0082] w N (n) = -1 for n = 1 and w N (n) = 0 for any other n.

[0083] According to an alternative embodiment, the action time is the same for all filters.The minimum action time suitable for all filters will then be taken.

[0084] The optimization problem is an ill-posed linear inversion problem. Therefore, it is necessary to regularize its solution. This regularization is achieved using the Tikhonov time-domain method. Regularization provides a filter whose amplitude can be controlled and limited.

[0085] In a particular embodiment, if the signal processing is implemented by a signal processor, the latency of this processor is taken into account in the optimization problem. In fact, in addition to avoiding the solution described by equation 1 above, the possibility of applying an action delay to the filter makes it possible to take this latency into account and avoid the truncation of the first filter samples associated with real-time digital implementations.

[0086] General

[0087] First, the position of the optimization problem for obtaining the w_i filters in the general case will be described, wherein secondary sources different from the primary sources are used to compensate for reflections due to the signals from these primary sources, and wherein control microphones are used during a calibration phase to obtain filters applied to a reference audio signal, thereby obtaining the acoustic signal broadcast by the secondary source. Secondly, an advantageous case is described in which the primary and secondary sources are combined.

[0088] Figure 3 is a schematic representation of a room with a sound source. This non-limiting schematic will be used to explain the location of the optimization problem in general. Figure 3 It shows:

[0089] - a primary source 301 capable of broadcasting a reference audio signal;

[0090] a secondary source 302 positioned close to a reflecting wall 303 on which the sound waves emitted by the primary source are reflected;

[0091] - a row of control microphones 304;

[0092] - Evaluation microphones 305 arranged around the room.

[0093] The optimization problem to be solved in order to control the waves reflected by the secondary source is as follows:

[0094] Consider n p primary sources and n s 303. A secondary source is initially considered to be separated from the primary source. It is hoped that the sound field generated by the secondary source, once reflected by the wall 303, will cancel the field emitted by the primary source. The measurements taken by the control microphone array 304 are transmitted to the optimizer to obtain the electronic filter. The evaluation microphone 305 can optionally be used to check the cancellation quality.

[0095] The optimizer may be implemented using any device having one or more processors capable of processing data to solve the optimization problem and obtain the filter. Figure 77 is a block diagram illustrating an example of such a device 700, which includes a processor 701, a working memory 702, a long-term storage memory 703 containing software code, a communication interface 704, and a communication bus 705 connecting the various components. The communication interface allows impulse response data to be received, filters to be provided to the processing device 100_i, and any necessary devices to be controlled. When the software code is executed, the processor causes the device 700 to implement at least one filtering method as described. It should be noted that the device 700 may include other components, depending on the specific implementation (user interface, display, etc.).

[0096] Formulation of the problem in the frequency domain

[0097] The goal is to determine the appropriate filters to be applied to the secondary sources so that the sum of the primary and secondary fields produced by the primary and secondary sources, respectively, causes the reflected pressure p for all control microphone pairs to be r Minimize. Finding these filters involves solving an optimization problem that takes into account the signals from all control microphones.

[0098] For clarity, the pressures measured by all control microphones are presented in vector form p, such that p = [p1 ... p j … P N ] T , where p j is the pressure evaluated for the jth pair of microphones, N is the total number of microphones, and [...] T is the transpose of the matrix. A filter vector w is also introduced, such that w=[w1 w2 … w M ] T , where M is the total number of secondary sources.

[0099] The complete pressure field can be expressed as the sum of the primary and secondary fields such that:

[0100] [Mathematical formula 2]

[0101] p=p P +p S

[0102] where p P represents the pressure transfer function between the sum of the primary sources and the control microphone, and:

[0103] [Mathematical formula 3]

[0104]

[0105] in is the pressure transfer function between each secondary source and the control microphone, and w is the filter of the secondary source to be estimated.

[0106] Several methods for extracting the reflected pressure from the measurement of the impulse response at the control microphone are described in detail below. In the general case, the reflected pressure is assumed to be a linear function of the electronic filter, so that the pressure p r It can be expressed as follows:

[0107] [Formula 4]

[0108] p r =Aw+B

[0109] The goal is then to determine the electronic filter to be applied to the secondary source so that the reflected pressure field is minimized. This involves expressing the cost function as follows:

[0110] [Formula 5]

[0111]

[0112] Therefore, using Equation 4, Equation 5 can be expressed as follows:

[0113] [Formula 6]

[0114]

[0115] This is a least squares optimization problem whose solution is the linear inversion:

[0116] [Formula 7]

[0117] w opt =-(A + A) -1 A + B

[0118] Formulation in the time domain

[0119] According to this exemplary embodiment, the optimization problem is formulated in the time domain. Therefore, the filter obtained by solving the problem is a filter that is also applied in the time domain.

[0120] The time-domain formulation specifically offers the following advantages:

[0121] - This makes it possible to take into account the constraints associated with the firmware of the signal processing device.

[0122] - It becomes easy to implement an additional delay linked to the application (compared to the above-mentioned action delay). For example, the output of the filter generating the control signal can be forced to zero for as many samples as is necessary to introduce the desired delay.

[0123] - Non-causal components due to the inverse Fourier transform of a bandwidth-limited frequency filter are avoided, since part of the impulse response energy is present at the end of the filter.

[0124] As is well known, one difference between frequency domain formulation and time domain formulation is that multiplication in the frequency domain corresponds to convolution in the time domain. Taking the frequency transfer function H(f) multiplied by the filter W(f) to give the pressure P(f) as an example, this can be expressed as:

[0125] [Formula 8]

[0126] P(f)=H(f)W(f)

[0127] The equivalent form in the continuous time domain is:

[0128] [Formula 9]

[0129] p(t)=h(t)*w(t)

[0130] For discrete-valued applications, this can be expressed in the discrete time domain as follows:

[0131] [Formula 10]

[0132]

[0133] where I is the filter length. If J is taken to be of length h, then the pressure can be calculated as follows by a single operation of multiplying the matrix by the vector:

[0134] [Formula 11]

[0135]

[0136] Or, in concise form:

[0137] [Mathematical formula 12]

[0138] p=Hw

[0139] Where p is the pressure vector of dimension (J+I-1), and H is the convolution matrix of dimension (J+I-1)*I.

[0140] Rewrite the expressions for various variables in the time domain. Thus, p P become:

[0141] [Mathematical formula 13]

[0142]

[0143] in is a vector representing the impulse response of the pressure between the microphone of index j and the sum of the primary sources. w is the concatenation of all filter vectors of length I for the secondary sources in the time domain:

[0144] [Mathematical formula 14]

[0145]

[0146] where w j is the filter for the jth source. Finally, is a matrix representing the impulse response according to the pressure between each secondary source and the control microphone, and contains the convolution operator:

[0147] [Mathematical formula 15]

[0148]

[0149] [Mathematical formula 16]

[0150]

[0151] in is a matrix of dimension (J+I-1)xI, and where J is the impulse response length.

[0152] For this time problem posed in matrix form, the cost function expression established previously remains valid:

[0153] [Mathematical formula 17]

[0154] where p r =Aw+B

[0155] Estimation of reflected pressure field by plane wave decomposition

[0156] The separation of incident and reflected waves can be based on the principle of plane wave decomposition. This model assumes that the sound field at each position consists of two plane waves moving in opposite directions, namely the incident component and the reflected component p i and p r , such that:

[0157] [Mathematical formula 18]

[0158] and

[0159] where p and u n are the pressure and particle velocity perpendicular to the total field, ρ is the air density, and c is the speed of sound in air.

[0160] Conventional microphones can only pick up pressure information, and dual-row microphones are also used to obtain velocity information. 前 and p 后 represents the pressure at the first and second microphones in a pair of microphones, where the front microphone is the microphone in the row farthest from the reflecting wall, e.g. Figure 3 shown.

[0161] The pressure and normal velocity at a virtual point between two microphones in a pair of microphones separated by a distance d can then be estimated by defining the following mathematical formulas:

[0162] [Mathematical formula 19]

[0163] and

[0164] Normal velocity u n Here it is estimated by the finite difference approximation of the Euler equation.

[0165] Then, appropriate filters are sought to be applied to the secondary sources so that the sum of the primary and secondary fields generated by the primary and secondary sources, respectively, makes the reflected pressure p for all control microphone pairs r Minimize. Finding these filters involves solving an optimization problem that takes into account the signals from all control microphones.

[0166] For clarity, all control microphone pressures and velocities are expressed as vectors p and u, respectively. n present, make in is the velocity evaluated for the i-th microphone pair, and p = [p1 ... p j … p N ] T , where p j is the pressure evaluated for the jth pair of microphones, N is the total number of microphones, and [...] T is the transpose of the matrix. A filter vector w is also introduced, such that w=[w1 w2 … w M ] T , where M is the total number of secondary sources.

[0167] For both pressure and velocity, the complete field can be expressed as the sum of the primary and secondary fields such that:

[0168] [Mathematical formula 20]

[0169] p=p P +p S And u n =u P +u S

[0170] where p P and u P Denote the corresponding pressure transfer function and velocity transfer function between the primary source and the control microphone, satisfying:

[0171] [Mathematical formula 21]

[0172] and

[0173] in and is the pressure transfer function and velocity transfer function between each secondary source and each control microphone, and w is the filter of the secondary source to be estimated. Using equations 20 to 23, it is possible to build a model of the reflected pressure that includes various transfer functions and the desired filter:

[0174] [Mathematical formula 22]

[0175]

[0176] Therefore, using the linear operator according to Equation 5 to find an expression for the reflected pressure field,

[0177] [Mathematical formula 23]

[0178] And B=p P -ρcu P

[0179] Total pressure field windowing

[0180] According to an alternative embodiment, the use of velocity estimates can be avoided by separating the direct and reflected fields by applying time windowing to the pressure signal measured by the control microphone.

[0181] Simple windowing can consist of removing the first moment of the pressure signal from the primary source, which is identified as part of the direct field. What remains is the reflected field. Therefore, the total pressure of the primary and secondary sources to be minimized is written as:

[0182] [Mathematical formula 24]

[0183]

[0184] satisfy

[0185] [Mathematical formula 25]

[0186]

[0187] in yes is a windowed version of , see Equation 13, where the first L samples are replaced by zeros, and L is defined as the time required to measure the direct field exactly. Thus, the reflected pressure field estimator remains in the form

[0188] [Mathematical formula 26]

[0189] p r =Aw+B

[0190] This time satisfied

[0191] [Mathematical formula 27]

[0192] and

[0193] As before, the solution is obtained by solving equation 7. In practice, the associated time (L x signal sampling frequency) is chosen to be of the order of the propagation time between the primary source and the room walls, after which propagation delay only the reflections remain.

[0194] Special case where a primary source can also be a secondary source

[0195] According to one or more embodiments, the secondary and primary sources are combined in the sense that a physical source broadcasts both a reference signal (as a primary source) and a control signal (as a secondary source) generated by delaying and filtering the reference signal. Thus, the sources perform their own checks, or check themselves. In other words, the source emits a first wave (due to the reference signal) and delays before emitting a second wave (due to the control signal) to reduce reflections from the first wave. Thus, the sum of the two signals reduces the intensity of the reflected pressure field.

[0196] The ability to apply a delay to the control filter makes it possible to implement this delay—the control filter is forced to provide an output only after the delay time. This avoids trivial solutions to optimization problems where the source simultaneously transmits a reference signal and the inverse of the reference signal in the form of a control signal—in fact, if the source wants to cancel the reflected pressure field, one way is to suppress the total pressure field directly at the source.

[0197] Without applying a delay to the filter, the optimization problem has the following trivial solution:

[0198] [Mathematical formula 28]

[0199]

[0200] in is the filter vector for the jth source, whose first element is -1 and whose all other elements are zero. In this case, the control signal is the inverted reference signal and the source emits no sound.

[0201] In mathematical terms, in order to impose a delay during periods of filter inactivity, one or more of the first components of each filter are forced to zero.

[0202] This can be done, for example, by removing the components that we wish to set to zero from the optimization problem. In the expression for the convolution matrix, this is equivalent to deleting a number of left-hand columns equal to the number of samples to which we wish to apply the starting delay. For example, for a delay equal to one sample, the following convolution matrix:

[0203] [Mathematical formula 29]

[0204]

[0205] become

[0206] [Mathematical formula 30]

[0207]

[0208] Similarly, in the filter vector w defined by the following equation, the same number of first components w in each source filter are deleted j :

[0209] [Mathematical formula 31]

[0210]

[0211] In a second step, after the optimization problem has been solved, as many zero components are added to the beginning of each filter as were initially removed.

[0212] Regularization

[0213] The optimization problem involving finding the optimal filter is an ill-posed linear optimization problem. Therefore, depending on the presence of measurement noise and the underdetermined nature of the problem, the amplitude of the filter obtained may be much higher than what is required to control the field.

[0214] According to an alternative embodiment, the magnitude is controlled by integrating a regularization term into the optimization problem. For example:

[0215] [Mathematical formula 32]

[0216]

[0217] where λ is the regularization parameter. This can be expressed as follows:

[0218] [Mathematical formula 33]

[0219] w opt =-(A + A-λI) -1 A + B

[0220] where I is the identity matrix.

[0221] The function of this regularization parameter (which is a multiplication factor of the filter norm) compensates for minimizing the reflected pressure field by adding another variable to be minimized (i.e., the filter norm). This forces the method to find a compromise between minimizing the reflected pressure field and using a large-amplitude filter to achieve this. It is a good idea to limit the amplitude of the filter—in fact, if the amplitude of the control signal is too high, it may be affected by the limiter of the amplifier in the speaker.

[0222] The regularization parameter can be determined, for example, using the "L-curve" method. An example of using such a curve is given in Reference 3 in the Appendix. This method is based on the observation that the larger the filter norm, the smaller the error, and vice versa. In this embodiment, the error is defined as the residual reflected pressure field obtained, the norm of which is sought to be equal to zero. The method consists in plotting the double logarithmic norm of the filter against the norm of the corrected error for different values ​​of the regularization parameter λ - Figure 4 Such a curve is shown in FIG, where the filter norm is on the ordinate and the error norm is on the abscissa. The larger λ is, the smaller the filter norm is compared to the norm of the reflected pressure field. And vice versa. A suitable choice of λ is its value at the inflection point (at Figure 4 According to reference [3] in the appendix, an optimal trade-off is achieved between minimizing the error in the cost function and minimizing the norm of the control filter. Other methods for determining the regularization parameter can also be implemented.

[0223] According to an alternative embodiment, when choosing the regularization parameter, a maximum limit is imposed on the filter amplitude.

[0224] Figure 5 A room or hall is schematically shown in which four loudspeakers 501a to 501d are shown, similar to Figure 1 or Figure 2 The speakers are placed along the walls to broadcast into the room. For illustration purposes, the measurement locations are shown in three rows of eight locations each (reference 502).

[0225] Figure 6 is a diagram illustrating a method for determining a control filter for one or more sound sources according to one embodiment. First, the reflected sound pressure impulse response of each source is determined (S601) for multiple control microphone positions in a room. To this end, the sources are positioned where they will be used later. The source broadcasts an excitation signal, and the source's response is measured and recorded for multiple microphone positions. This process is repeated for all sources.

[0226] Typically, the signal measurements required to determine the impulse response can be performed using a single microphone, which is moved to a different location in the room for each measurement, or using several microphones in parallel to obtain multiple measurements at several locations in the room simultaneously.

[0227] The filters are then determined (S602) by solving a regularized optimization problem based on the set of impulse responses and formulated in the time domain, the optimization problem being defined as (a) minimizing the norm of the sum of the impulse responses of the reflected sound pressure at N positions; and (b) introducing a non-zero action delay for each filter such that the influence of the control signal on the direct field is reduced.

[0228] According to one embodiment, the control signal path can be disconnected. To this end, Figure 1 The device 100 shown includes an element 107 to which a control signal 108 is applied. This element is, for example, a switch that connects or disconnects the control signal to the input of the adder 104. Under the control of the control signal, the device 100 can then operate as a primary source only (switch open) or as both a primary source and a secondary source (switch closed). This makes it easy to configure the device 100 as part of a multi-speaker system, where functional flexibility is required to suit specific needs. This also allows the user to easily disconnect the calibration.

[0229] According to another alternative embodiment, the effect of the control signal can be attenuated. Element 107 is then an attenuator that can vary the level of the control signal between 0 and 100%. For example, the attenuation level can be controlled via a user interface, enabling the control to be customized according to the user's preferences.

[0230] According to a further embodiment, which can be combined with the embodiments already described, the reference signal path can be disconnected, and the output signal of the block is then only the control signal.

[0231] advantage

[0232] One or more of the above embodiments may have one or more of the following advantages:

[0233] Since the sound source behaves both as a primary and a secondary source, according to the example shown, it is not necessary to add a loudspeaker dedicated only to controlling low frequency resonances. The result is a significant reduction in cost of ownership.

[0234] The fact that each source can be both a primary and a secondary source allows for flexibility in adapting to various situations. Thus, for a given physical configuration of sources, and with regard to the temporal quality of the direct field, it may be decided that the primary sources will be concentrated in the center, and all available sources (including the primary sources as well as any other available sources) will be secondary sources. Alternatively, all sources can be used as both primary and secondary sources for greater directional control in the direct field without the need to add or reposition sources. Additionally, there is no longer a need to try and optimally position the secondary sources, which can be a lengthy and difficult process.

[0235] The calculation of a separate filter for each source is performed in a single operation by solving an optimization problem involving the impulse responses of all measurements. In other words, all sources and measurements are considered simultaneously in the optimization problem.

[0236] Using only the same source to play both the reference music signal and the control signal also improves the ability to perceive source localization. Indeed, when using secondary sources that are spatially distinct from the primary source, these sources, in addition to the control signal, may also emit spurious sounds due to loudspeaker nonlinearities or vibrate decorative elements (e.g., false ceilings) located in their near field. This noise can be particularly noticeable because it comes from a different direction and at a different time than the loudspeakers playing the music signal. With the approach outlined in this specification, the unwanted noise is often masked by the music signal, as it is emitted in the same area as the music signal.

[0237] Furthermore, the reference music signal played by the loudspeakers is not modified, so the direct field perceived by the listener is not altered: impact, precision and timbre are preserved.

[0238] Resonance control is also greatly improved. By targeting the physical causes of resonances, i.e. reflections after the direct field has passed, there is no need to compromise between modifying the direct field and controlling resonances, as is the case, for example, when trying to modify the frequency response by equalization at the source in order to target modes at specific locations in the room.

[0239] References

[0240] 1. A. Celestinos and S.B. Nielsen, “Controlled acoustic bass system (CABS)—A method to achieve uniform sound field distribution at low frequencies inrectangular rooms,” Audio Engineering Society Journal 56(11), 915–931 (2008)

[0241] 2. Hauchel et al., “Active room compensation for sound reinforcement using sound field separation techniques,” Journal of the Acoustical Society of America 143, 1346 (2018)

[0242] 3. Christian Hansen and Dianne Prost O'Leary, "The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems," SIAM Journal on Scientific Computing, 1993, 14:6, 1487-1503.

Claims

1. A computer-implemented method for obtaining M filters of a digital audio signal defined in the time domain, wherein M is an integer greater than or equal to 1, each filter being associated with a respective sound source, referred to as a secondary source, emitting a sound pressure field that minimizes the reflected sound pressure field of a set of sound sources, referred to as primary sources, located in a room, the method comprising: - for each primary sound source and secondary sound source, obtaining (S601) an impulse response of the reflected sound pressure at N corresponding different positions in the room, wherein all the primary sound sources and the secondary sound sources are placed in an operating position, the N positions being the same for all the sound sources; - determining (S602) a set of M filters by solving a regularized optimization problem based on the set of impulse responses and formulated in the time domain, the optimization problem being defined as (a) minimizing the norm of the sum of the impulse responses at the N positions; and (b) introducing non-zero action delay for each filter; Each secondary source is combined with a primary source called an associated primary source.

2. The method according to claim 1, characterized in that M is greater than or equal to 2.

3. The method according to claim 1 , wherein, for a given secondary sound source combined with its associated primary source, obtaining an impulse response of the reflected sound pressure at a given one of N positions comprises: - emission of sound waves by said given secondary sound source in combination with its associated primary source in response to an excitation signal; - obtaining a signal representing the sound pressure generated by the excitation signal at the position; - determining said impulse response of said reflected sound pressure based on the obtained signal representing said sound pressure.

4. The method of claim 3 , wherein the signal representing the sound pressure is obtained using a microphone placed at the given position, the determining of the impulse response comprising applying time windowing to the signal representing the sound pressure so as to suppress direct sound waves received from the given secondary sound source in combination with its associated primary source while retaining the reflected sound waves.

5. The method according to claim 3, wherein: - said signal representative of said sound pressure is obtained using a pair of microphones placed around said given position; - determining the impulse response by determining the pressure and velocity of the sound waves in order to separate the direct sound waves received from the sound source from the reflected sound waves.

6. Method according to one of claims 1 to 5, wherein the motion delay is substantially equal to the average propagation time of a sound wave generated by the source between the source and a wall of the room. 7 . The method according to claim 1 , comprising determining a regularization parameter for regularizing the optimization problem, the determination taking into account a maximum amplitude threshold of the filter.

8. A data processing device (700) comprising means for implementing the method according to one of claims 1 to 7.

9. An audio signal processing device (100), comprising: - an input terminal (101) configured to receive a first audio signal (x(t)); - a first filter (106) for filtering the first signal and obtaining a second audio signal, the first filter being a finite impulse response filter obtained by applying the method according to one of claims 1 to 7; - an adder (104) for adding the first audio signal and the second audio signal to obtain a third audio signal for controlling a sound source associated with the first filter.

10. The device according to claim 9, comprising a low-pass filter (105) for filtering the first audio signal, the output of the low-pass filter being connected to the input of the first filter.

11. The device according to claim 10, comprising: a downsampling circuit for downsampling the audio signal after the low-pass filter (105) and before being supplied to the first filter (106); and An oversampling circuit is configured to oversample the audio signal after filtering by the first impulse response filter and before providing the audio signal to the adder.

12. The device according to one of claims 9 to 11, comprising one of the following: - an adjustable attenuator (107) for applying a gain between 0% and 100% to the second audio signal; and - a switch (107) configured to connect or disconnect the second signal to the adder input.

13. A method for processing an audio signal implemented by a device comprising a processor, a memory, and software code, the method comprising: - receiving a first audio signal (x(t)); - filtering the audio signal using a finite impulse response filter obtained by applying the method according to one of claims 1 to 7; - summing the first audio signal and the signal filtered by the finite impulse response filter to form a signal suitable for being provided to a sound source associated with the finite impulse response filter.

14. The method of claim 13, comprising low-pass filtering the first audio signal prior to filtering by the impulse response filter.

15. The method of claim 14, comprising downsampling the audio signal after low-pass filtering and before impulse response filtering, and oversampling the audio signal after impulse response filtering and before summing.

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