Method and device for obtaining a filter for a digital audio signal, and method and device using this filter

Abstract

The invention relates to a computer-implemented method for obtaining M filters for digital audio signals that are defined in the time domain, where M is an integer greater than or equal to 1, each filter being associated with a respective acoustic source, referred to as the secondary source, emitting an acoustic pressure field that makes it possible to minimise the reflected acoustic pressure field from a set of acoustic sources, referred to as the primary sources, located in a room, the method comprising: - for each primary and secondary acoustic source, obtaining (S601) N impulse responses for the reflected acoustic pressure at N respective separate locations in the room in which all of the primary and secondary acoustic sources are in the operating position, the N locations being the same for all of the acoustic sources; - determining (S602) the set of M filters by solving an optimisation problem regularised using the set of the impulse responses and formulated in the time domain, the optimisation problem being defined so as to (a) minimise a norm of the sum of the impulse responses at the N locations; and (b) introduce a non-zero action delay for each of the filters; each secondary source being coincident with a primary source, referred to as the associated primary source.

Description

[0001]METHOD AND DEVICE FOR OBTAINING A DIGITAL AUDIO SIGNAL FILTER, METHOD AND DEVICE IMPLEMENTING THIS FILTER Technical field of the invention The present invention relates to a method and a device for obtaining a digital audio signal filter intended to be used in a device producing a signal for an acoustic source. The invention also relates to a signal processing method implementing the filter. The invention is used in the context of reducing the reflections of the acoustic waves produced by this source. Technical background When an acoustic source emits inside a closed space, the acoustic waves, as they propagate, are reflected by the various walls, until the wave is completely attenuated, either via absorption at the walls, or by thermal heating in the air (for the highest frequencies). At low frequencies, the attenuation of an acoustic wave is limited,and the time required for its complete absorption can be long (more than one second), even in the presence of absorbent materials on the walls. This is due to the fact that most of the absorbent materials used dissipate acoustic energy by visco-thermal friction, and that these have an efficiency linked to the thickness of the material with respect to the wavelength considered. As a reminder, the wavelength is equal to the speed of sound in air divided by the frequency. Thus, for low frequencies, the wavelengths are high. For example, the wavelength associated with 50Hz is equal to 6.8m. It is therefore understandable that it is necessary to have very thick absorbent materials so that they can attenuate an acoustic wave in this frequency range, thicknesses which are naturally incompatible with use in a room of average size (less than 100m²). Moreover, at certain particular frequencies,for which the corresponding wavelengths are multiples of one of the dimensions of the room, resonance phenomena appear, characterized by very inhomogeneous pressure fields, with areas having very high acoustic energy (we speak of pressure antinodes), and other areas having very low acoustic energy (we speak of pressure nodes). These resonance phenomena are also called "acoustic modes" or "room modes", and significantly degrade the acoustic quality of a source, compared to the situation where it emits in a free field (for example outside). The degradations linked to acoustic modes are of various types: - spatial: for a given frequency, areas of very high pressure coexist with areas of very low pressure, thus leading to a strong spatial variability of the sound level. - frequency: consequently, for fixed positions,the magnitude of the pressure as a function of frequency, commonly called "frequency response", varies greatly. - temporal: acoustic modes, due to the low attenuation of acoustic energy, result in attenuation times, also called reverberation times, which can be very high. This is commonly referred to as drag. The number of acoustic modes per frequency band, also called "modal density", depends on the volume of the room. The larger a room, the higher the number of acoustic modes will be, in a given frequency band, compared to a smaller room. However, a low modal density is more problematic, because the modes present tend to be more distinguishable (because they are further apart in the frequency domain), and more energetic. Room modes are therefore particularly problematic in mixing and listening rooms, as well as in small and medium-sized concert halls,where they can strongly alter low frequencies (between 20 Hz and 100-200 Hz). For larger halls, the higher modal density makes the acoustic influence of the hall less problematic. The Schroeder frequency simply quantifies the transition between modal behavior, where the different acoustic modes are clearly identifiable and more energetic, and statistical behavior, where the frequencies of these modes are too close together to be clearly identifiable, and at which the modes are less energetic. This frequency is inversely proportional to the volume of the hall. Thus, for large concert halls, we move to statistical behavior, which is less problematic, at frequencies low enough not to require correction. This control would also be too complex to implement. Some approaches have been proposed to attenuate acoustic modes,by adding so-called "secondary" acoustic sources whose function is to absorb the acoustic wave emitted by so-called "primary" sources. These secondary sources are, for example, placed on a wall opposite the one next to which the primary sources are placed. Among these approaches, we find the so-called "CABS" approach (for "Controlled Acoustic Bass System" or "Controlled Acoustic Bass System" in English) by Adrian Celestinos et al. (see reference 1 in the appendix). Another approach is the so-called "impedance matching" approach, as proposed by the Swiss Federal Institute of Technology in Lausanne. A third approach is described by Franz Heuchel et al. in his article "Active Room Compensation for Sound Reinforcement Using Sound Field Separation Techniques" (reference 2). This approach uses a plane wave decomposition (or PWD for "Plane Wave Decomposition").to establish a model of the incident field and the reflected field. The authors then solve a frequency domain optimization problem aimed at finding the optimal filters for secondary sources to cancel the reflected field. This method requires a calibration step using microphone doublets placed in the room. A fourth approach consists of adding electronic correction using filters, in order to modify the frequency response curve at one or more reference positions in the room. These corrections do not aim to eliminate acoustic modes, but simply to "equalize" the frequency response at certain positions preferentially, by reducing the sound pressure level, at the emission level, at the frequencies corresponding to pressure antinodes,and sometimes by increasing the sound pressure level to those corresponding to the pressure nodes. This fourth approach is not satisfactory, however, because by reducing the sound pressure level at emission, the acoustic wave before reflection, also called "direct field", is also degraded, which loses precision and impact. Document US8660272 describes a technique for reducing the reflections of acoustic waves from a device equipped with a loudspeaker in a room. The signal transmitted to the loudspeaker comprises an audio signal to which the same filtered audio signal is added, the filtering comprising the application of a multi-stage filter, each stage of which comprises a delay and a gain, the characteristics of each stage being obtained iteratively. It is desirable to have a solution for reducing the reflections of acoustic waves produced by one or more acoustic sources in a room,requiring few resources during a calibration phase. Summary of the invention A first aspect relates to a computer-implemented method for obtaining M digital audio signal filters defined in the time domain, with M being an integer greater than or equal to 1, each filter being associated with a respective acoustic source, called a secondary source, emitting an acoustic pressure field allowing the minimization of the reflected acoustic pressure field of a set of acoustic sources, called primary sources, located in a room, the method comprising: - for each primary and secondary acoustic source, obtaining N impulse responses of the reflected acoustic pressure at N respective distinct locations in the room in which all the primary and secondary acoustic sources are placed in the operating position,the N locations being the same for all the acoustic sources; - the determination of the set of M filters by solving a regularized optimization problem which is a function of all of said impulse responses and formulated in the time domain, the optimization problem being defined to (a) minimize a norm of the sum of the impulse responses at the N locations; and (b) introduce a non-zero action delay for each of the filters; each secondary source being confused with a primary source,said associated primary source. Each filter is intended to be applied to a signal obtained from an input audio signal of the respective acoustic source associated with the filter; the respective acoustic source being configured to diffuse the sum of the input audio signal and the filtered signal. The input audio signals of the acoustic sources are identical. This results in a reduction of the reflections of the acoustic waves produced. According to one or more embodiments, M is greater than or equal to 2. According to one or more embodiments, obtaining an impulse response of the reflected acoustic pressure, at a given location among the N locations, for a given secondary acoustic source merged with its associated primary source, comprises: - the emission, by the given secondary acoustic source merged with its associated primary source,of acoustic waves in response to an excitation signal; - obtaining a signal representative of the acoustic pressure resulting from the excitation signal at said location; - determining the impulse response of the reflected acoustic pressure as a function of the signal representative of the acoustic pressure obtained. According to one or more embodiments, the signal representative of the acoustic pressure is obtained using a microphone placed at the given location, the determination of the impulse response comprising the application of a time window to the signal representative of the acoustic pressure in order to suppress the direct acoustic waves received from the given secondary acoustic source merged with its associated primary source, while retaining the reflected acoustic waves. According to one or more embodiments,the signal representative of the acoustic pressure is obtained using a doublet of microphones placed around the given location, and the determination of the impulse response comprises the determination of the pressure and the speed of the acoustic waves in order to separate the direct acoustic waves received from the acoustic source from the reflected acoustic waves. According to one or more embodiments, the action delay is substantially equal to the average propagation time of acoustic waves generated by the sources, between the sources and the walls of the room. According to one or more embodiments, the method comprises the determination of a regularization parameter for the regularization of the optimization problem,the determination taking into account a maximum amplitude threshold of the filters. A second aspect relates to a data processing device comprising means for implementing one of the above methods. A third aspect relates to an audio signal processing device, comprising: - an input configured to receive a first audio signal (x(t)); - 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; - an adder for adding the first and second audio signals to obtain a third audio signal for controlling the acoustic source associated with the first filter. According to one or more embodiments,the audio signal processing device comprises a low-pass filter for filtering the first audio signal and the output of which is connected to the input of the first filter. According to one or more embodiments, the audio signal processing device comprises a downsampling circuit for downsampling the audio signal after the low-pass filter and before supplying to the first filter; and an upsampling circuit for upsampling the audio signal after filtering by the first impulse response filter and before supplying to the adder. According to one or more embodiments,the audio signal processing device comprises one of: an adjustable attenuator for applying a gain between 0 and 100% to the second audio signal; and a switch configured to connect or disconnect the second signal from the input of the adder. A fourth aspect relates to an audio signal processing method implemented by a device comprising a processor, a memory and software code, the method comprising - receiving a first audio signal; - filtering the audio signal by a finite impulse response filter obtained by applying one of the above filter obtaining methods; - summing the first audio signal and the signal filtered by the finite impulse response filter to form a signal suitable for being supplied to the acoustic source associated with the finite impulse response filter. According to one or more exemplary embodiments,the audio signal processing method comprises low-pass filtering the first audio signal before filtering by the impulse response filter. According to one or more exemplary embodiments, the audio signal processing method comprises downsampling the audio signal after low-pass filtering and before filtering by the impulse response filter and upsampling the audio signal after filtering by the impulse response filter and before summing. One or more embodiments relate to a recording medium readable by a device having a processor, said medium comprising instructions which, when the program is executed by a processor of a device,lead the device to implement at least one of the methods described. The recording medium may in particular be non-transient. Brief description of the figures Other characteristics and advantages of the invention will appear during the reading of the detailed description which follows for the understanding of which reference will be made to the appended drawings in which: – figure 1 is a functional block diagram of a device according to one or more embodiments – figure 2 is a functional block diagram of a set of devices such as that of figure 1, receiving the same audio signal as input; [– figure 3 is a schematic illustration of a room comprising several primary acoustic sources and several secondary acoustic sources intended to reduce the reflections of the waves produced by the primary sources,according to one or more exemplary embodiments; – Figure 4 is a curve representing the magnitude of filters as a function of the norm of the correction error for different lambda regularization parameters of the optimization problem; – Figure 5 is a schematic illustration of a room comprising several primary and secondary acoustic sources combined, according to one or more exemplary embodiments; – Figure 6 is a flowchart of a method for determining one or more filters according to one or more embodiments; – Figure 7 is a block diagram of an exemplary device for determining filters according to one or more exemplary embodiments. Detailed description of the invention In the following description, identical, similar or analogous elements will be designated by the same reference numbers. The block diagrams, flowcharts and message sequence diagrams in the figures illustrate the architecture,the functionalities and operation of systems, devices, methods and computer program products according to one or more exemplary embodiments. Each block of a block diagram or each phase of an algorithm may represent a module or a portion of software code comprising instructions for implementing one or more functions. According to certain implementations, the order of the blocks or phases may be changed, or the corresponding functions may be implemented in parallel. The process blocks or phases may be implemented using circuits, software or a combination of circuits and software, in a centralized manner, or in a distributed manner, for all or part of the blocks or phases. The systems, devices, methods and methods described may be modified, added to and / or deleted while remaining within the scope of the present description. For example,The components of a device or system may be integrated or separate. Also, the described functions may be implemented using more or fewer components or phases, or with other components or through other phases. Any suitable data processing system may be used for the implementation. A suitable data processing system or device includes, for example, a combination of software code and circuitry, such as a processor, controller, or other circuitry suitable for executing the software code. When the software code is executed,the processor or controller causes the system or device to implement all or part of the functionalities of the blocks and / or phases of the methods or processes according to the exemplary embodiments. The software code may be stored in a memory or a readable medium accessible directly or through another module by the processor or controller. One embodiment relates to an audio signal processing device intended to be broadcast by an acoustic source, which is typically an electroacoustic transducer transforming an electrical signal into an acoustic signal. The transducer is for example a loudspeaker, but other transducers may be implemented. The terms acoustic source, transducer and loudspeaker will be used equivalently in the following. Schematically, according to one or more exemplary embodiments, the signal produced by the audio signal processing device comprises the input audio signal,said reference signal, for example musical content, and a control signal that allows to attenuate the reflected waves in the room in which the transducer diffuses. More precisely, the control signal corresponds to the delayed and filtered input audio signal. Thus, when the transducer is fed with the input audio signal, the processed audio signal propagates in the room and is reflected against the walls. When the wave is reflected and propagates in the room, it undergoes an alteration that is similar to filtering. After a certain delay compared to the reference audio signal, the transducer emits a copy of the reflected and filtered signal, in phase opposition. The reflected wave is then canceled and the resonance can no longer be established. Depending on the desired implementation, a signal processing device is adapted to produce signals either for a,either for several transducers. A processing device may be combined into a device with one or more transducers or be in a separate device. Figure 1 is a schematic diagram showing, in the form of functional blocks, the processing carried out on the reference signal and the transducer fed by the processed signal. A device 100 comprises an input 101 of the reference audio signal x(t). This audio signal is intended to be broadcast by a loudspeaker 103 which, in the present example, is external to the device 100. It is assumed for the purposes of the present description that the reference signal is a digital signal – if this is not the case,the person skilled in the art will provide circuits for digitizing the reference signal in a known manner. The reference audio signal input is connected to a first input of an adder 104 whose output is connected to the loudspeaker 103. A branch path of the reference signal connected on the one hand to the signal input 101 and on the other hand to a second input of the adder 104 comprises a digital filter w 105 intended to filter the signal at its input to produce the control signal. According to one embodiment, the digital filter advantageously implements both the delay and the filtering of the signal at its input. The filter 105 will also be called a 'control filter' in the following, in relation to its role in generating the control signal. According to an alternative embodiment, the delay and the filtering are introduced by separate units. According to the present embodiment, before being subjected to the filter 105,the input audio signal is subjected to a low-pass filter 106 whose role is to ensure that the filter 105 is only applied to the frequency range for which reflection compensation is necessary or desired. This low-pass filter can be achieved by sub-sampling the audio signal. The sub-sampling is carried out at a frequency much lower than that of the original audio signal and the filtering is carried out at this new sampling frequency. This sub-sampling makes it possible in particular, for a given computing resource, to increase the efficiency of the filter - this is also referred to as increasing the order of the filter. Before summing by the adder 104, the filtered signal is over-sampled to be at a sampling frequency identical to that of the reference signal. According to one or more exemplary embodiments,the low-pass filter is optional. This is the case, for example, when the reference signal is already in the desired frequency band. Reference 102 designates the block bringing together the signal processing functions and integrating in particular adder 104, filter 105 and low-pass filter 106. Device 100 may include other circuits, in particular power amplifiers. Block 102 may be a suitable signal processor implementing the functions shown in Figure 1. In a non-limiting manner and for purely illustrative purposes, for certain applications, the sub-sampling frequency may for example be 500 Hz. According to a particular embodiment,the filter w(t) 105 is a finite impulse response filter. This filter performs a convolution operation on the signal received at its input. Figure 1 illustrates the main signal processing operations carried out and the basic concepts applied. Other components or functions may be present, and additional signal processing may be carried out. Furthermore, an actual implementation may obviously differ from that of Figure 1 – in particular the signal processing block 102 itself may be partially or entirely implemented using an appropriate signal processor. Figure 2 shows a set of several processing devices 100_i, each processing device comprising the elements of Figure 1. In the example of Figure 2, all the processing devices receive the same reference audio signal x(t) as input. The filters w, _i(t) can be differentiated from one processing device 100_i to another. i is an integer between 1 and M, where M is the number of processing devices. In the following, the general case of Figure 2 will be considered, noting that 'i' can be taken equal to 1. For reasons of clarity, not all the elements of the device 100 of Figure 1 are repeated in Figure 2. According to a particular embodiment, in the case of the broadcasting of distinct reference audio signals on as many channels ('multichannel' context), the device of Figure 2 is reproduced for each of the reference audio signals. The delay and the filtering to be applied for the creation of the control signal are fixed in time, and are specific to each transducer or loudspeaker, for a given placement of the loudspeaker in a given room.According to an alternative embodiment, the delay and filtering are not fixed in time – they are for example re-evaluated at regular intervals or punctually depending on one or more parameters among: changes in temperature, occupancy of the room, change in the arrangement or orientation of the transducer… 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 and involving the impulse responses between each loudspeaker and a set of N so-called 'control' microphones positioned in the room. The impulse responses between each loudspeaker and a set of microphones positioned in the room can be obtained either by a measurement step, or by a simulation step.The measurement phase followed by the calibration phase makes it possible to obtain the delays and characteristics of the filters which will be used to parameterize the respective signal processing device(s). The optimization problem consists, according to one embodiment, in searching for the set of M filters which make it possible to minimize the L2 norm of the reflected field. The formulation of the optimization problem in the time domain makes it possible to impose an individual action delay for each filter which avoids obtaining filters which cancel the reference signal in the low frequencies upon emission, such as: [MATH 1] ^. ^ (^) = −1 for n = 1 and ^ ^(^) = 0 for any other ^. According to an alternative embodiment, the action delay is identical for all filters. We will then take a minimal action delay that is suitable for all filters. The optimization problem is an ill-conditioned linear inverse problem. It is therefore necessary to regularize its solution. This regularization is obtained according to the Tikhonov method formulated in the time domain. Regularization makes it possible to obtain filters whose amplitude can be controlled and limited. According to a particular embodiment, in the case where the implementation of the signal processing is carried out by a signal processing processor, the latency of this processor is taken into account in the optimization problem.Indeed, in addition to avoiding obtaining the solution described by equation 1 above, the possibility of imposing an action delay for the filters makes it possible to take this latency into account and thus avoid truncations of the first samples of the filter linked to the real-time digital implementation. General case We will first describe the position of the optimization problem for obtaining the filters w_i in a general case, in which secondary sources – distinct from the primary sources – are used to compensate for the reflections due to the signals of these primary sources and in which control microphones are used during a calibration phase allowing the obtaining of the filters applied to the reference audio signal to obtain the acoustic signals diffused by the secondary sources. In a second step, we will describe the advantageous case in which the primary and secondary sources are combined.Figure 3 is a schematic representation of a room comprising acoustic sources. This non-limiting schematic illustration will serve to explain the position of the optimization problem in the general case. Figure 3 shows: - primary sources 301 capable of diffusing a reference audio signal; - secondary sources 302, positioned near a reflective wall 303 and on which the acoustic waves emitted by the primary sources are reflected; - a row of microphones, called 'control' microphones 304; - evaluation microphones 305 arranged in the room. The optimization problem that we seek to solve with a view to controlling the waves reflected by the secondary sources is as follows: We consider ^. ^ primary sources and ^ ^secondary sources, the latter being initially taken as separate from the former. It is desired that the acoustic field created by the secondary sources cancels the field emitted by the primary sources, once it has been reflected by the wall 303. The measurements made by the row of control microphones 304 are sent to the optimizer to obtain the electronic filters. The evaluation microphones 305 can optionally be used to control the quality of the cancellation. The optimizer can be implemented using any device comprising one or more processors capable of processing the data with a view to solving the optimization problem and obtaining the filters.Figure 7 is a block diagram which illustrates an example of such a device 700, comprising a processor 701, a working memory 702, a long-term storage memory 703 comprising software code, a communication interface 704 and a communication bus 705 connecting the different components. The communication interface makes it possible to receive the data relating to the impulse responses, to provide the filters to the processing devices 100_i and, if necessary, to control the necessary devices. The processor causes the device 700, when the software code is executed, to implement at least one method for obtaining the filters as described. It should be noted that the device 700 may comprise other components, depending on the implementation (user interface, display, etc.).Formulation of the problem in the frequency domain We seek to determine the appropriate filters to apply to the secondary sources so that the sum of the primary and secondary fields, created respectively by the primary and secondary sources, minimizes the reflected pressure, ^. ^ , for all pairs of monitoring microphones. Finding these filters involves solving an optimization problem that considers the signals from all monitoring microphones. For clarity of presentation, the pressure measured by all monitoring microphones is presented in vector form such that ^ ^ ⋯ ^ ^ ^ where ^ ^ is the pressure evaluated for the jth pair of microphones, N is the total number of microphones and [ . ] ^ represents the transpose of a matrix. We also introduce the vector of filters ^, such that ^ = [^ ^ ^ ^ ⋯ ^ ^]^ , where M is the total number of secondary sources. The complete pressure field can be expressed as the sum of the primary field and the secondary field, such that: [MATH 2] ^ = ^ ^ + ^ ^ where ^ ^ represents the pressure transfer function between the sum of the primary sources and the control microphones, and: [MATH 3] ^ ^ ^ = ^ ^ ^ where ^ ^ ^ is the pressure transfer function between each secondary source and the control microphones, and ^ the filters of the secondary sources to be estimated. Several methods will be detailed later, allowing the extraction of the reflected pressure from the measurement of the impulse responses at the control microphones. In the general case, we assume that the reflected pressure is a linear function of the electronic filters, so that the pressure ^ ^ can be expressed as follows: [MATH 4] ^ ^= ^^ + ^ We then seek to determine the electronic filters to be applied to the secondary sources so that the reflected pressure field is minimized. This involves the expression of a cost function expressed as follows: This is a least-squares optimization problem, the solution of which is a linear inversion: Formulation in the time domain According to the present exemplary embodiment, the formulation of the optimization problem is carried out in the time domain. The filters obtained by solving this problem are therefore filters also applied in the time domain. The formulation in the time domain has the following advantages in particular: - It makes it possible to take into account constraints linked to the firmware of the signal processing device. - An implementation of an additional delay (compared to the action delay mentioned above) linked to the application becomes easy. For example, it is possible to force the output of the filter generating the control signal to zero for as many samples as necessary to introduce the desired delay.- Non-causal components due to the inverse Fourier transform of a bandwidth-limited frequency filter are avoided, as part of the impulse response energy is present at the end of the filter. As is well known, a difference between a frequency-domain formulation and a time-domain formulation is that a multiplication in the frequency domain corresponds to a convolution in the time domain. Taking the example of a frequency transfer function ^. ( ^ ) multiplied by a filter ^ ( ^ ) to give pressure ^ ( ^ ) , we can write: [MATH 8] ^(^) = ^(^)^(^) The equivalent in the continuous time domain is then: [MATH 9] ^(^) = ℎ(^) ∗ ^(^) For application to discrete numerical values, this can be written as follows in the discrete time domain: where I is the length of the filter. If J is taken to be the length of h, the pressure can be calculated by a single operation of multiplying a matrix by a vector as follows: or, in condensed form: [MATH 12] ^ = ^^ where ^ is the pressure vector of dimension (^ + ^ − 1) and ^ is the convolution matrix of dimensions (^ + ^ − 1) ∗ ^. The expressions for the different variables are rewritten in the time domain. Thus, ^ ^ becomes : where ^ ^ ^^ is the vector representing the impulse response in terms of pressure between the sum of the primary sources and the microphone of index ^. ^ is the concatenation of all the filter vectors of length I of the secondary sources in the time domain: [MATH 14] ^ = ^^ ^ ^ ^ ^ ^ ^ ⋯ ^ ^ ⋯ where ^ is the filter of the j-th source. Lastly, ^ ^is the matrix representing the impulse response in terms of pressure between each secondary source and the control microphones, and containing the convolution operator: where ^ ^ ^^ ^ ^ is a matrix of dimensions (^ + ^ − 1) ^ ^, and where ^ is the length of the impulse response ℎ ^ ^^ ^ ^ . The temporal problem thus posed in matrix form, the expression of the cost function previously established remains valid: Estimation of the reflected pressure field by plane wave decomposition The separation of incident and reflected waves can be based on the principle of plane wave decomposition. This model assumes that the acoustic field is, at each location, composed of two plane waves moving in opposite directions, namely the incident and reflected components ^ ^ and ^ ^ , such as: where ^ and ^ ^represent the pressure and normal particle velocity of the total field, ^ is the air density and ^ is the speed of sound in air. A usual microphone can only pick up pressure information – a double array of microphones is used to obtain velocity information as well. ^ ^^^^^ and ^ ^^^^è^^ denote the pressure at the first microphone and the second microphone of a pair of microphones, respectively, the front microphone being the one in the row furthest from the reflecting wall, as illustrated in Figure 3. The pressure and the normal velocity can then be estimated at a virtual point between the two microphones of a pair separated by a distance d by setting: [MATH 19] The normal velocity ^ ^is here estimated by a finite difference approximation of the Euler equation. We then seek the appropriate filters to apply to the secondary sources so that the sum of the primary and secondary fields, created respectively by the primary and secondary sources, minimizes the reflected pressure, ^ ^ , for all pairs of monitoring microphones. Finding these filters involves solving an optimization problem that considers the signals from all monitoring microphones. For clarity of presentation, pressure and velocity of all monitoring microphones are presented in respective vector forms ^ And ^^ , such as ^ ^ ^ = ^^ ^^ ⋯ ^ ^^ ⋯ ^ ^^ ^ where ^ ^^ is the speed evaluated for the ith pair of ^ microphones, and ^ = ⋯ ^^ ⋯ ^^ ^ where ^ ^is the pressure evaluated for the jth pair of microphones, N is the total number of microphones and [ . ] ^ represents the transpose of a matrix. We also introduce the vector of filters ^, such that ^ = [ ^ ^ ^ ^ ⋯ ^ ^ ] ^ , where M is the total number of secondary sources. For both pressure and velocity, the complete field can be expressed as the sum of the primary and secondary fields, such that: [MATH 20] ^ = ^ ^ + ^ ^ and ^ ^ = ^ ^ + ^ ^ where ^ ^ and ^ ^ represent the respective pressure and velocity transfer functions between the primary sources and the control microphones, with: [MATH 21] ^ ^ ^ ^ = ^ ^ ^ and ^ ^ = ^ ^ ^ where ^ ^ ^ are the pressure and velocity transfer functions between each secondary source and each control microphone, and ^ the secondary source filters to be estimated. Using equations 20 to 23, it is possible to establish a model of the reflected pressure including the different transfer functions and the filters sought: We therefore find the expression of the reflected pressure field using a linear operator following equation 5 with Windowing of the total pressure field According to an alternative embodiment, the direct field and the reflected field can also be separated by applying a time window to the pressure signals measured by the control microphones, and thus not using velocity estimates. A simple windowing can consist of removing the first moments of the pressure signals from the primary sources, identified as being part of the direct field. This then leaves only the reflected field. Thus the total pressure of the primary and secondary sources that we seek to minimize is written: [MATH 24] ^ = ^ ^ ^ ^ +^ ^ ^ with [MATH 25] where ^^ ^ ^^ is a windowed version of ^ ^ ^^ , see equation 13, where the first L samples are replaced by zeros, L being defined as the time strictly necessary for the direct field to be measured. Thus the estimator of the reflected pressure field remains in the form [MATH 26] ^ ^= ^^ + ^ with this time, [MATH 27] ^ = ^ ^ ^ and ^ = ^ ^The solution can be obtained as previously by solving equation 7. In practice, the associated time (L x the signal sampling frequency) is chosen so that it is of the order of the propagation time between the primary sources and the walls of the room – after this propagation delay, only the reflections remain. Special case where the primary sources can also be secondary sources According to one or more embodiments, the secondary sources and the primary sources are combined, in the sense that a physical source diffuses both a reference signal (as a primary source) and a control signal (as a secondary source) resulting from the delay and filtering of the reference signal. The sources therefore carry out their own control, or even self-control.In other words, a 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 of the first. The sum of the two signals thus reduces the intensity of the reflected pressure field. Being able to apply a delay to the control filter allows this delay to be implemented – the control filter is forced to provide an output only after the delay time. This avoids a trivial solution to the optimization problem, where the source emits at the same time the reference signal and, in the form of the controlled signal, the opposite of the reference signal – indeed, if the source wants to cancel the reflected pressure field, one way is to suppress the total pressure field directly at the source. Without a delay imposed on the filters, the optimization problem has the following trivial solution:. ^ where −^^ is the filter vector of the j-th source, whose first element is -1 and all other elements are zero. In such a case, the control signal is the reference signal in phase opposition and no sound is emitted by the source. In mathematical terms, to impose a delay during which the filters do not act, one or more of the first components of each filter are forced to zero. This can be done for example by removing from the optimization problem the components that one seeks to set to zero. In the expression of the convolution matrix, this amounts to removing a number of left columns equal to the number of samples for which one seeks to impose a starting delay. For example, for a delay equivalent to one sample, the following convolution matrix: Similarly, we remove as many first components in each source filter ^ ^ in the filter vector ^ defined by: [MATH 31] ^ = ^^ ^ ^ ^^ ^ ^ ^ ⋯ ^ ^ ⋯ ^ ^ ^ In a second step, after solving the optimization problem, we add at the beginning of each filter as many zero components as those which were initially removed. Regularization The optimization problem consisting of finding the optimal filters is an ill-conditioned linear optimization problem. Consequently, depending on the measurement noise present and the underdetermined nature of the problem, the amplitude of the filters obtained can be much higher than necessary to control the field. According to an alternative embodiment, to control the amplitude, we integrate a regularization term into the optimization problem. For example: [MATH 32] where ^ is a regularization parameter. This can be expressed as follows: where I is the identity matrix. The function of this regularization parameter, as a coefficient for multiplying the filter norm, is to compensate for the effort of minimizing the reflected pressure field by adding another variable to minimize, namely the filter norm. This forces the method to find a compromise between minimizing the reflected pressure field and using large amplitude filters to achieve this. It is desirable to limit the amplitude of the filters – indeed, if the amplitude of the control signals is too large, it could be affected by the limiters of the amplifiers in the enclosures. The regularization parameter can for example be determined via the so-called 'L-curve' method. An example of the use of such a curve is given in reference 3 indicated in the appendix.This method is based on the observation that the larger the filter norm, the smaller the error, and vice versa. In the present embodiment, the error is defined as the resulting residual reflected pressure field, the norm of which is intended to be set equal to zero. The method consists of plotting the filter norm log-log against the correction error norm for different values ​​of the regularization parameter ^ – Figure 4 shows such a curve, where the filter norm is given on the ordinate and the error norm on the abscissa. The larger ^, the more the filter norm is minimized, as opposed to the reflected pressure field norm. The converse is also true. A suitable choice for λ is its value at the inflection point (circled on the graph in Figure 4).According to reference [3] in the appendix, the best compromise is achieved between minimizing the error of the cost function and minimizing the norm of the control filters. Other methods for determining the regularization parameter can be implemented. According to an alternative embodiment, a maximum limit is imposed on the amplitude of the filters in the choice of the regularization parameter. Figure 5 is a schematic illustration of a room or hall showing four speakers 501a to 501d similar to those of figures 1 or 2 positioned along a wall to diffuse towards the interior of the room. Measurement locations are indicated for illustrative purposes in three rows of eight locations (reference 502). Figure 6 is a diagram representing a method for determining the control filter of one or more acoustic sources according to one embodiment.In a first step, the impulse responses of the reflected sound pressure are determined (S601) for each source for a plurality of monitoring microphone positions in the room. The sources are arranged in their position for subsequent use. A source emits an excitation signal and the response for this source is measured and recorded for the plurality of microphone positions. The process is repeated for all sources. In general, the signal measurements required for determining the impulse responses can be carried out using a single microphone that is moved to different locations in the room for each measurement or using several microphones in parallel to obtain several measurements for several locations in the room at the same time.The filters are then determined (S602) by solving a regularized optimization problem that is a function of all of said impulse responses and formulated in the time domain, the optimization problem being defined to (a) minimize a norm of the sum of the impulse responses of the acoustic pressure reflected at the N locations and (b) introduce a non-zero action delay for each of the filters, the delay making it possible to reduce the impact of the control signal on the direct field. According to an alternative embodiment, the control signal path can be disconnected. To do this, the device 100 of FIG. 1 comprises an element 107 to which a control signal 108 is applied. The element is for example a switch that connects or disconnects the control signal from the input of the adder 104.Under the control of the control signal, the device 100 then operates either solely as a primary source (switch open), or as both a primary and secondary source (switch closed). This makes it easy to configure the device 100 as part of a system comprising several speakers and for which flexibility in functionality is sought to adapt to specific needs. This also allows a user to easily disconnect the correction. According to another alternative embodiment, the effects of the control signal can be attenuated. The element 107 is then an attenuator ('fader' in English) capable of varying the level of the control signal between 0 and 100%. The attenuation level is for example controllable via a user interface and makes it possible to dose the control carried out according to the preferences of a user.According to another embodiment that can be combined with the embodiments already presented, the reference signal path can be disconnected – the signal at the output of the block is then only the control signal. Advantages One or more embodiments described above have one or more of the following advantages: - Since an acoustic source behaves as both a primary source and a secondary source, it is not necessary, according to the exemplary embodiments, to add, for example, loudspeakers dedicated solely to controlling resonances in the low frequencies. This results in a greatly reduced cost. - The fact that each source can be both a primary source and a secondary source allows for flexibility to adapt to many situations.Thus, for a given physical configuration of sources, one can decide that the primary sources will be concentrated in the center, for reasons of temporal quality of the direct field, and that all available sources (including the primary sources as well as any other available sources) are secondary sources. One can also use all sources as both primary and secondary sources, in order to have better control of the direct field directivity, without the need to add or move sources. In addition, it is no longer necessary to try to optimally position the secondary sources, which can be a long and difficult step. - The calculation of the individual filter(s) for each source is carried out in a single step, by solving an optimization problem involving all the measured impulse responses.In other words, all sources and all measurements are considered simultaneously in the optimization problem. - Using only the same sources to play the reference musical signal and the control signal also improves the sensation of source localization. Indeed, when secondary sources are used that are spatially distinct from the primary sources, they can emit, in addition to the control signal, unwanted sounds potentially due to the non-linearities of the loudspeakers, or vibrate elements of the decor located in their near field (for example, false ceilings). These unwanted noises can be particularly noticeable because they come from a different direction and time compared to the speaker playing the musical signal.With the approach presented in this description, since the parasitic noises are emitted in the same area as the musical signal, these noises are generally masked by the musical signal. Furthermore, the reference musical signal played by the loudspeaker is not modified, the direct field perceived by the listener is therefore not altered: the impact, precision and timbre are preserved. - Also, the control of resonances is greatly improved. By acting on the physical cause of resonances, namely the reflections, after the passage of the direct field, it is not necessary to make a compromise between alteration of the direct field and control of resonances, which is for example the case when trying to act on the modes at specific positions in the room, by modifying the frequency response by equalization at the source. References 1. “A. Celestinos and SBNielsen, “Controlled acoustic bass system (CABS) - A method to achieve uniform sound field distribution at low frequencies in rectangular rooms,” J. Audio Eng. Soc.56(11), 915–931 (2008) 2. Heuchel et al., “Active room compensation for sound reinforcement using sound field separation techniques”, The Journal of the Acoustical Society of America 143, 1346 (2018) 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 199314:6, 1487–1503.

Claims

CLAIMS 1. A computer-implemented method for obtaining M digital audio signal filters defined in the time domain, with M being an integer greater than or equal to 1, each filter being associated with a respective acoustic source, called a secondary source, emitting an acoustic pressure field enabling the minimization of the reflected acoustic pressure field of a set of acoustic sources, called primary sources, located in a room, the method comprising: - for each primary and secondary acoustic source, obtaining (S601) N impulse responses of the reflected acoustic pressure at N respective distinct locations in the room in which all of the primary and secondary acoustic sources are placed in the operating position, the N locations being the same for all of the acoustic sources;- determining (S602) the set of M filters by solving a regularized optimization problem which is a function of the set of said impulse responses and formulated in the time domain, the optimization problem being defined to (a) minimize a norm of the sum of the impulse responses at the N locations; and (b) introduce a non-zero action delay for each of the filters;each secondary source being merged with a primary source, called the associated primary source.

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

3. Method according to one of claims 1 or 2, in which obtaining an impulse response of the reflected acoustic pressure, at a given location among the N locations, for a given secondary acoustic source merged with its associated primary source, comprises: - the emission, by the given secondary acoustic source merged with its associated primary source, of acoustic waves in response to an excitation signal; - obtaining a signal representative of the acoustic pressure resulting from the excitation signal at said location; - determining the impulse response of the reflected acoustic pressure as a function of the signal representative of the acoustic pressure obtained.

4. Method according to claim 3, in which the signal representative of the acoustic pressure is obtained using a microphone placed at the given location, the determination of the impulse response comprising the application of a time window to the signal representative of the acoustic pressure in order to suppress the direct acoustic waves received from the given secondary acoustic source merged with its associated primary source, while retaining the reflected acoustic waves. 5.Method according to claim 3, in which: - the signal representative of the acoustic pressure is obtained using a doublet of microphones placed around the given location; - the determination of the impulse response comprising the determination of the pressure and the speed of the acoustic waves in order to separate the direct acoustic waves received from the acoustic source from the reflected acoustic waves.

6. Method according to one of claims 1 to 5, in which the action delay is substantially equal to the average propagation time of acoustic waves generated by the sources, between the sources and the walls of the room.

7. Method according to one of claims 1 to 6, comprising the determination of a regularization parameter for the regularization of the optimization problem, the determination taking into account a maximum amplitude threshold of the filters. 8.Data processing device (700) comprising means for implementing a method according to one of claims 1 to 7.

9. Audio signal processing device (100), comprising: - an input (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 and second audio signals to obtain a third audio signal for controlling the acoustic source associated with the first filter.

10. Device according to claim 9, comprising a low-pass filter (105) for filtering the first audio signal and the output of which is connected to the input of the first filter.

11. Device according to claim 10, comprising: a sub-sampling circuit for sub-sampling the audio signal after the low-pass filter (105) and before supplying it to the first filter (106); and an over-sampling circuit for over-sampling the audio signal after filtering by the first impulse response filter and before supplying it to the adder. 12.Device according to one of claims 9 to 11, comprising one of: - 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 from the input of the adder.

13. Audio signal processing method 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 by 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 supplied to the acoustic source associated with the finite impulse response filter.

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

15. The method of claim 14, comprising down-sampling the audio signal after low-pass filtering and before filtering by the impulse response filter and up-sampling the audio signal after filtering by the impulse response filter and before summing.

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