EP1652406B1 - System and method for determining a representation of an acoustic field - Google Patents

Description

The present invention relates to a method, a device and a system for determining a representation of an acoustic field in the form of a plurality of acoustic or audiophonic signals, each associated with a predetermined general direction of reproduction defined with respect to a given point of space.

The determination of such a representation is based on the use of acoustic wave acquisition means comprising a plurality of elementary sensors arranged in space and each delivering a measurement signal.

These measurement signals are processed by the application of filtering combinations, representative in particular of structural characteristics of the acquisition means and of the general directions of predetermined restitution, so as to obtain said plurality of acoustic signals.

Such a plurality of signals is commonly designated by the expression “multichannel signal” and corresponds to a plurality of signals, called “channels”, transmitted in parallel or multiplexed with each other. Each of the signals is intended for an element or a group of reproduction elements forming an ideal source arranged in a predefined general direction with respect to a given point in space.

For example, a classic multichannel standard known under the name of "5.1 ITU-R BF 775-1", comprises five channels intended for restitution elements arranged in five predetermined general directions defined by the angles 0 °, + 30 °, - 30 °, + 110 ° and -110 ° in relation to the listening center.

Such an arrangement therefore corresponds to the arrangement: of a loudspeaker or a group of loudspeakers in front of the center, one on each side in front on the left and on the right and one on each side behind on the left and on the right.

The application of the acoustic signals to restitution elements arranged in the appropriate predetermined general directions theoretically allows the restitution of an acoustic field.

Acquisition and processing are key elements in the quality of this restitution.

Certain existing acquisition means are formed from a set of elementary directional sensors where each sensor directly delivers a channel corresponding to one of the predetermined general directions of restitution. In this case, each sensor is substantially oriented in the direction corresponding to its associated channel.

The quality of the representation obtained with such acquisition means is limited by the intrinsic directivity of the sensors, since no processing is carried out, so that the representation is not a high quality representation.

Other techniques, such as the techniques grouped under the term "ambisonic" are based on a modeling of the acquisition means in the form of a specific set of elementary and directional sensors, so as to consider only the directions of origin. sounds with respect to the center of the acquisition means.

However, the impossibility of positioning all the elementary sensors at the same point, the absence of elementary sensors with high directivity characteristics as well as the simplicity of the processing operations carried out, such as gain matrices, restrict these technologies to a representation. the quality of which is limited to the level of precision commonly called "order 1" on the basis of spherical harmonics.

Finally, the system described in the article entitled " Circular microphone array for discrete multichannel audio recording ", presented on March 22, 2003 at the 114th AES convention , uses a circular regular array of 288 cardioid microphones. A complex processing in several stages of all the signals delivered by this network of sensors makes it possible to obtain a representation of the acoustic field of high quality.

It therefore appears that the existing acquisition and processing means require a large quantity of elementary sensors distributed in a regular manner as well as complex processing operations in order to achieve a high quality representation of the acoustic field in a multichannel format.

This significantly reduces the portability of these systems and increases the cost of implementation as well as the computation times.

The document XP002280618 (Laborie, Bruno, Montoya: <<A new comprehensive approach of surround sound recording>>, 119th convention of the audio engineering society, convention paper 5717, March 22, 2003 ) describes how to process measurement signals to obtain a representation
of the sound field as a function of Fourier-Bessel. This document further explains that the field
encoded was listened to using speakers.

The object of the invention is to solve the foregoing problems by providing a system and a method for determining a high quality representation of an acoustic field in a multi-channel format of increased portability and speed and at reduced cost.

To this end, the subject of the invention is a system for determining a representation of an acoustic field according to claim 1.

Other features of the system are set out in claims 2 to 7.

The subject of the invention is also a method for determining a representation of an acoustic field according to claim 8.

Other characteristics of the process of the invention are set out in claims 9 and 10.

• la Fig.1 est une représentation d'un repère sphérique;
• la Fig.2 est un schéma bloc d'un système de restitution selon l'invention ;
• la Fig.3 est un organigramme du procédé de l'invention ; et
• la Fig.4 est une représentation détaillée du traitement réalisé par l'invention.

The invention will be better understood on reading the description which will follow, given solely by way of example and made with reference to the appended drawings, in which:

• the Fig. 1 is a representation of a spherical coordinate system;
• the Fig. 2 is a block diagram of a rendering system according to the invention;
• the Fig. 3 is a flowchart of the method of the invention; and
• the Fig. 4 is a detailed representation of the processing performed by the invention.

On the figure 1 , a conventional spherical frame has been shown, so as to specify the coordinate system to which reference is made in the text.

This frame of reference is an orthonormal frame of reference, of origin O and comprising three axes (OX), ( OY ) and (OZ). In this frame, a position noted x is described by means of its spherical coordinates ( r, θ, φ ) , where r denotes the distance from the origin O , θ the orientation in the vertical plane and φ the orientation in the horizontal plane.

In such a frame, an acoustic field is known if we define at any point at each instant t the acoustic pressure noted p ( r, θ, φ, t ) , whose Fourier transform is noted P (r, θ, φ, f ) where f denotes the frequency.

The method of the invention is based on the use of spatio-temporal functions making it possible to describe any acoustic field in time and in the three dimensions of space.

In the embodiments described, these functions are so-called spherical Fourier-Bessel functions of the first kind, hereinafter called Fourier-Bessel functions.

In a zone void of sources and void of obstacles, the Fourier-Bessel functions correspond to the solutions of the wave equation and constitute a basis which generates all the acoustic fields produced by sources located outside this zone.

Any three-dimensional acoustic field can therefore be expressed by a linear combination of Fourier-Bessel functions, according to the expression of the inverse Fourier-Bessel transform which is expressed: $$P\left(r,\theta ,\varphi ,f\right)=4\pi {\displaystyle \sum _{l=0}^{\infty }{\displaystyle \sum _{m=-l}^l{P}_{l,m}\left(f\right)j^l{j}_l\left(\mathit{kr}\right)y_l^m\left(\theta ,\varphi \right)}}$$

c est la célérité du son dans l'air (340 ms^-1), j_l (kr) est la fonction de Bessel sphérique de première espèce d'ordre l définie par $j_l\left(x\right)=\sqrt{\frac{\pi }{2x}}{J}_{l+1/2}\left(x\right)$

où J _v(x) est la fonction de Bessel de première espèce d'ordre v, et $y_l^m\left(\theta ,\varphi \right)$

est l'harmonique sphérique réelle d'ordre l et de terme m, avec m allant de -l à /, définie par : $$y_l^m\left(\theta ,\varphi \right)=P_l^{\left|m\right|}\left(\cos \theta \right){\mathrm{trg}}_m\left(\varphi \right)$$

avec : $${\mathrm{trg}}_m\left(\varphi \right)=\{\begin{array}{ll}\frac{1}{\sqrt{\pi }}\cos \left(\mathit{m\varphi }\right)& \mathrm{pour}m>0\\ \frac{1}{\sqrt{2\pi }}& \mathrm{pour}m=0\\ \frac{1}{\sqrt{\pi }}\sin \left(\mathit{m\varphi }\right)& \mathrm{pour}m<0\end{array}$$

In this equation, the terms P _{l, m} ( f ) are defined as the Fourier-Bessel coefficients of the field p ( r, θ, φ, t ) , $k=\frac{2\mathit{\pi f}}{\mathrm{vs}},$

c is the speed of sound in air (340 ms ^-1 ), j _l ( kr ) is the spherical Bessel function of the first kind of order l defined by $j_l\left(x\right)=\sqrt{\frac{\pi }{2x}}{J}_{l+1/2}\left(x\right)$

where J _v ( x ) is the Bessel function of the first kind of order v, and $y_l^m\left(\theta ,\varphi \right)$

is the real spherical harmonic of order l and term m, with m ranging from -l to /, defined by: $$y_l^m\left(\theta ,\varphi \right)=P_l^{\left|m\right|}\left(\cos \theta \right){\mathrm{trg}}_m\left(\varphi \right)$$

with: $${\mathrm{trg}}_m\left(\varphi \right)=\{\begin{array}{ll}\frac{1}{\sqrt{\pi }}\cos \left(\mathit{m\varphi }\right)& \mathrm{for}m>0\\ \frac{1}{\sqrt{2\pi }}& \mathrm{for}m=0\\ \frac{1}{\sqrt{\pi }}\sin \left(\mathit{m\varphi }\right)& \mathrm{for}m<0\end{array}$$

sont les fonctions de Legendre associées définies par : $$P_l^m\left(x\right)=\sqrt{\frac{2l+1}{2}}\sqrt{\frac{\left(l-m\right)!}{\left(l+m\right)!}}{\left(1-x^2\right)}^{m/2}\frac{{\mathrm{d}}^m}{\mathrm{d}{x}^m}{P}_l\left(x\right)$$

avec P_l (x) les polynômes de Legendre, définis par :

In this equation, the $P_l^m\left(x\right)$

are the associated Legendre functions defined by: $$P_l^m\left(x\right)=\sqrt{\frac{2l+1}{2}}\sqrt{\frac{\left(l-m\right)!}{\left(l+m\right)!}}{\left(1-x^2\right)}^{m/2}\frac{{\mathrm{d}}^m}{\mathrm{d}{x}^m}{P}_l\left(x\right)$$

with P _l ( x ) the Legendre polynomials, defined by:

The Fourier-Bessel coefficients are also expressed in the time domain by the coefficients p _{l, m} ( t ) corresponding to the inverse temporal Fourier transform of the coefficients P _{l, m} ( f ) .

In other embodiments, the acoustic field is decomposed on a basis of functions, where each of the functions is expressed by a possibly infinite linear combination of Fourier-Bessel functions.

On the figure 2 , there is schematically shown a system according to the invention.

This system comprises acquisition means 1 formed of Q elementary sensors 2 ₁ to 2 _Q delivering measurement signals c ₁ ( t ) to c _Q ( t ) , also denoted c ₁ to c _Q , which are introduced into a device 6 for determining a representation of an acoustic field.

The device 6 comprises processing means 8 suitable for applying to the measurement signals c ₁ to c _Q filtering combinations representative of structural characteristics of the acquisition means 1, to deliver at output a plurality of acoustic signals each associated with a direction predetermined general restitution defined with respect to a given point in space.

The acoustic signals sc ₁ ( t ) to sc _N ( t ) , also denoted sc ₁ to sc _N , delivered by the device 6, are then transmitted to reproduction means 10 comprising N of reproduction elements 12 ₁ to 12 _N arranged in predetermined directions with respect to a given point 14 in space, corresponding to the center of the restitution means 10.

The control of these restitution elements 12 ₁ to 12 _N by the acoustic signals sc ₁ to sc _N , allows the restitution of the acoustic field picked up by the acquisition means 1.

Preferably, the processing means 8 of the device 6 are configured beforehand and are associated in a specific manner with a set of elementary sensors 2 ₁ to 2 _Q forming the acquisition means 1 and with a set of restitution elements forming the means of restitution 10.

Advantageously, the processing means 8 however comprise a plurality of filtering combinations corresponding to different acquisition means and / or to different output formats and selectable by a user, for example directly by means of a switch or through a control interface.

The device 6 may take the form of electronic equipment dedicated to the implementation of the invention or else of computer software comprising program code instructions intended to be executed by equipment comprising a processing processor and interface means with acquisition means and restitution means.

For example, the device 6 is formed by a computer associated with suitable interface cards.

The elementary sensors 2 ₁ to 2 _Q are arranged at known points in space around a predetermined point 4, designated as the center of the acquisition means 1.

Thus, the position ( r _q , θ _q , φ _q ) of each elementary sensor 2 _{q is} expressed in space in a spherical frame of reference such as the one described with reference to figure 1 , centered on the center 4 of the acquisition means 1.

According to the invention, the elementary sensors 2 ₁ to 2 _Q are distributed in space in a substantially non-regular manner.

For a given configuration, or a network, to be considered as non-regular in space, it is necessary that for all the usual three-dimensional reference frames, either Cartesian, cylindrical or even spherical, for at least one of the coordinates of the reference frame, the values of the coordinates of the positions of all the elementary sensors are neither constant nor distributed at a constant pitch, that is to say they are distributed over distinct values and at a non-constant pitch.

Or again, a configuration is non-regular if for all the usual reference frames, for at least one of the three coordinates of the reference frame, the values of the coordinates of the positions of all the sensors are distributed in an interval or domain of non-zero space and with a variable deviation of the coordinates taken successively.

Thus, configurations in which the sensors are arranged at regular intervals along a line or a circle, at the intersections of a fictitious plane grid or else at the intersections of a fictitious cubic mesh, are regular configurations.

The assessment of such a non-regular distribution must obviously take into account a tolerance resulting from the constraints of physical production and the constraints linked to the sizing of the elementary sensors used.

Therefore, the coordinates of the sensors must be distributed in an interval greater than a tolerance interval and have deviations varying beyond this tolerance interval.

In general, the position of a sensor corresponds to the position of the center of its sensitive part and a tolerance interval in each direction of space is defined around this position.

Advantageously, the tolerance interval for a set of elementary sensors forming the acquisition means corresponds to a distance equivalent to a quarter of the distance between the two closest elementary sensors. For example, such a distance is of the order of 2cm, so that the tolerance interval corresponds approximately to 0.5cm.

In contrast, a configuration is considered to be regular if, in one of the usual reference frames, for the three coordinates of the reference frame, the coordinate values of the positions of all the sensors are constant or distributed at constant pitch.

Or again, a configuration is regular if, in one of the usual reference frames, for all the coordinates of the reference frame, the coordinate values of the positions of all the sensors are distributed in a substantially zero interval or with a substantially constant successive deviation.

Furthermore, sensors with a substantially non-zero physical footprint contiguous to one another, form a point or almost point distribution considered as a regular configuration.

The following method makes it possible to determine whether a given configuration of elementary sensors is regular or not.

The aforementioned configuration is considered with reference to a first of the three usual references, such as the three-dimensional Cartesian reference.

The values of the positions of all the sensors are then checked according to a first coordinate of the reference frame, such as the abscissa. If these values are neither constant nor distributed at regular intervals, considering an interval tolerance, then the configuration is not regular in this reference and we start again with another reference.

If the values of these first coordinates are either constant or distributed at regular intervals, the values of the positions of the sensors are verified according to a second coordinate of the reference frame, such as the ordinate.

If the values of these second coordinates are neither constant nor distributed at regular intervals, the configuration is non-regular in this coordinate system and we start over with another coordinate system.

Conversely, if the values of these coordinates are either constant or distributed at regular intervals, the values of the positions of the sensors are checked according to the third and last coordinate of the reference frame, such as that along a vertical axis called the zenith coordinate.

If the values of these third coordinates are neither constant nor distributed at regular intervals, the configuration is non-regular in this coordinate system and we start over with another coordinate system.

In the opposite case, in this frame, for all the coordinates, the values of the coordinates of the positions of all the sensors are either constant or distributed at regular intervals. Therefore, the configuration is regular in this frame.

At the end of the tests in the three usual benchmarks, if the configuration is regular in one of the three benchmarks, it is said to be regular. Conversely, if the configuration is non-regular in the three reference frames, it is said to be non-regular.

Such a substantially non-regular distribution makes it possible to avoid the redundancy of the information taken by the elementary sensors in the acoustic field, so that a reduced number of sensors is necessary.

Advantageously, the maximum number Q of elementary sensors is less than or equal to five times the number of acoustic signals forming the representation of the acoustic field at the end of the treatment.

Furthermore, the distribution of the elementary sensors 2 _q in space can meet certain rules while meeting the criteria of non-regularity as defined previously.

Advantageously, the acquisition means 1 reproduce the general geometric characteristics of the reproduction means 10, such as an arrangement planar and a certain symmetry, while respecting the criteria of non-regularity.

With reference to figures 3 and 4 , we will now describe the operation of the system of the invention.

Prior to the implementation of the invention, the acquisition means 1 are arranged in space in a substantially non-regular manner.

During a first acquisition step 20, the system of the invention is exposed to an acoustic field P and each sensor 2 _q of the acquisition means 1 delivers a measurement signal c _q ( t ) which corresponds to the measurement made by this sensor in the acoustic field P.

The acquisition means 1 therefore deliver a plurality of signals for measuring the acoustic field c ₁ ( t ) to c _Q ( t ) , which are directly linked to the acquisition capacities of the elementary sensors 2 ₁ to 2 _Q.

The method then comprises a step 30 of processing by applying filtering combinations to the measurement signals c ₁ to c _Q delivered by the acquisition means 1.

As has been indicated previously, these filtering combinations are representative of the structural characteristics of the acquisition means 1 and are adapted to deliver a plurality of acoustic signals sc ₁ to sc _N each associated with a general direction of predetermined restitution and defined by relative to a given point in space.

More particularly, the N channels sc ₁ ( t ) to sc _N ( t ) are obtained from the Q measurement signals c ₁ ( t ) to c _Q ( t ) by means of a single matrix filtering involving N x Q filters varying as a function of the frequency, and denoted T _{n, q} ( f ) . Each output channel sc _n ( t ) is obtained by filtering each of the measurement signals c ₁ ( t ) to c _Q ( t ) and by applying a linear combination to the signals thus filtered.

Each filter T _{n, q} ( f ) is therefore representative of the contribution of the measurement signal c _q ( t ) in the constitution of the channel sc _n ( t ) . The channels are obtained according to the relation: $${\mathit{SC}}_{\mathrm{not}}\left(f\right)={\displaystyle \sum _{q=1}^Q{T}_{\mathrm{not},q}\left(f\right){\mathrm{VS}}_q\left(f\right)}$$

In this relation, SC _n ( f ) is the Fourier transform of sc _n ( t ) and C _q ( f ) is the Fourier transform of c _q ( t ) .

The filters T _{n, q} ( f ) can be organized in a matrix T of size N x Q as follows: $$\mathit{T}=\left[\begin{array}{cccc}{T}_{1.1}\left(f\right)& T_{1.2}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="imgf0002.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1,Q}\left(f\right)\\ T_{2.1}\left(f\right)& T_{2.2}\left(f\right)& \cdots & T_{2,Q}\left(f\right)\\ ⋮& ⋮& & ⋮\\ T_{\mathrm{NOT},1}\left(f\right)& T_{\mathrm{NOT},2}\left(f\right)& \cdots & T_{\mathrm{NOT},Q}\left(f\right)\end{array}\right]$$

In the embodiment described, the matrix T is obtained by means of the following matrix relation: $$\mathit{T}=\mathit{D}\mathit{E}$$

In this equation, E is an encoding matrix representative of the characteristics of the acquisition means 1 and in particular of their spatial configuration. The matrix E makes it possible to obtain a representation in Bessel Fourier coefficients of an acoustic field P̃ corresponding to an estimate of the acoustic field P in which the elementary sensors 2 ₁ to 2 _Q are immersed, from the measurement signals c ₁ ( t ) to c _Q ( t ) . The matrix E is of size ( L +1) ² x Q, the coefficient L corresponding to the order to which the encoding is carried out and to the maximum resolution that the encoding makes it possible to achieve. The matrix E is obtained by means of the relation: $$\mathit{E}=\mu {\mathit{B}}^{\mathrm{T}}{\left(\mu \mathit{B}{\mathit{B}}^{\mathrm{T}}+\left(1-\mu \right){\mathit{I}}_{\mathrm{NOT}}\right)}^{-1}$$

In this equation, the coefficient µ specifies a compromise between the fidelity of representation of the acoustic field P̃ and the minimization of the background noise provided by the elementary sensors 2 ₁ to 2 _Q and can take all the values between 0 and 1. Thus, if µ = 0, the background noise is minimal and if µ = 1, the spatial quality is maximum

Advantageously, the parameters L and µ can vary with the frequency.

In this relation, B is a spatial sampling matrix of size Q x ( L +1) ² whose elements B _{q , l, m} ( f ) are organized as follows: $$\left[\begin{array}{cccccccccc}{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,0.0}\left(f\right)& B_{1.1,-1}\left(\mathrm{<figure-callout\; id="1"\; label="f\; B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>},\right)& B_{}{}_{1,1.0}\left(\mathrm{<figure-callout\; id="1"\; label="f\; B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>},\right)& B_{}{}_{1,1.1}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,L,-L}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,L,0}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,L,L}\left(f\right)\\ B_{2,0.0}\left(f\right)& B_{2.1,-1}\left(f\right)& B_{2,1.0}\left(f\right)& B_{2,1.1}\left(f\right)& \cdots & B_{2,L,-L}\left(f\right)& \cdots & B_{2,L,0}\left(f\right)& \cdots & B_{2,L,L}\left(f\right)\\ ⋮& ⋮& ⋮& ⋮& & ⋮& & ⋮& & ⋮\\ B_{Q,0.0}\left(f\right)& B_{Q,1,-1}\left(f\right)& B_{Q,1.0}\left(f\right)& B_{Q,1.1}\left(f\right)& \cdots & B_{Q,L,-L}\left(f\right)& \cdots & B_{Q,L,0}\left(f\right)& \cdots & B_{Q,L,L}\left(f\right)\end{array}\right]$$

If all the elementary sensors 2 ₁ to 2 _Q are sensors of the omnidirectional type, the term B is expressed as follows: $$B_{q,l,m}\left(f\right)=4{\mathit{\pi j}}^l{j}_l\left({\mathit{kr}}_q\right)y_l^m\left({\theta }_q,{\varphi }_q\right)$$

In this relation, ( r _q , θ _q , φ _q ) is the position of the sensor 2 _q in the spherical coordinate system described with reference to figure 1 .

de sorte que le capteur 2_q présente une sensibilité maximale dans la direction $\left({\theta }_q^{\alpha },{\varphi }_q^{\alpha }\right).$

Dans ce cas les éléments B_q,l,m (f) sont obtenus de la manière suivante : $$B_{n,l,m}\left(f\right)=4\pi j^l\times \left\{\left(1-d_q\right)j_l\left({\mathit{kr}}_q\right)y_l^m\left({\theta }_q,{\varphi }_q\right)-{\mathit{jd}}_q\times \left({j^{\ast }}_l\left({\mathit{kr}}_q\right)y_l^m\left({\theta }_q,{\varphi }_q\right)u_r-\frac{j_l\left({\mathit{kr}}_q\right)}{{\mathit{kr}}_q}{R}_l^{\left|m\right|}\left(\cos {\theta }_q\right){\mathrm{trg}}_m\left({\varphi }_q\right)u_{\theta }+\frac{{\mathit{mj}}_l\left({\mathit{kr}}_q\right)}{{\mathit{kr}}_q\sin {\theta }_q}{y}_l^{-m}\left({\theta }_q,{\varphi }_q\right)u_{\varphi }\right)\right\}$$

où : $${j^{\ast }}_l\left({\mathit{kr}}_q\right)=\frac{l{j}_{l-1}\left({\mathit{kr}}_q\right)-\left(l+1\right)j_{l+1}\left({\mathit{kr}}_q\right)}{2l+1}$$

$$R_l^m\left(\cos {\theta }_q\right)=\{\begin{array}{ll}\sqrt{l\left(l+1\right)}{P}_l^1\left(\cos {\theta }_q\right)& \mathrm{pour}m=0\\ \frac{\sqrt{\left(l-m\right)\left(l+m+1\right)}}{2}{P}_l^{m+1}\left(\cos {\theta }_q\right)-\frac{\sqrt{\left(l+m\right)\left(l-m+1\right)}}{2}{P}_l^{m-1}\left(\cos {\theta }_q\right)& \mathrm{pour}1\le m\le l-1\\ -\sqrt{\frac{l}{2}}{P}_l^{l-1}\left(\cos {\theta }_q\right)& \mathrm{pour}m=l\end{array}$$

et où : $$u_r=\sin {\theta }_q\sin {\theta }_q^{\alpha }\cos \left({\varphi }_q-{\varphi }_q^{\alpha }\right)+\cos {\theta }_q\cos {\theta }_q^{\alpha }$$

$$u_{\theta }=\cos {\theta }_q\sin {\theta }_q^{\alpha }\cos \left({\varphi }_q-{\varphi }_q^{\alpha }\right)-\sin {\theta }_q\cos {\theta }_q^{\alpha }$$

$$u_{\varphi }=\sin {\theta }_q^{\alpha }\sin \left({\varphi }_q^{\alpha }-{\varphi }_q\right)$$

In other embodiments, each sensor 2 _q is placed at the position ( r _q , θ _q , φ _q ), has a directivity composed of a combination of omnidirectional and bidirectional diagrams of proportion d _q and is oriented in the direction $\left({\theta }_q^{\alpha },{\varphi }_q^{\alpha }\right),$

so that the sensor 2 _q has a maximum sensitivity in the direction $\left({\theta }_q^{\alpha },{\varphi }_q^{\alpha }\right).$

In this case the elements B _{q, l, m} ( f ) are obtained as follows: $$B_{\mathrm{not},l,m}\left(f\right)=4\pi j^l\times \left\{\left(1-d_q\right)j_l\left({\mathit{kr}}_q\right)y_l^m\left({\theta }_q,{\varphi }_q\right)-{\mathit{jd}}_q\times \left({j^{\ast }}_l\left({\mathit{kr}}_q\right)y_l^m\left({\theta }_q,{\varphi }_q\right)u_r-\frac{j_l\left({\mathit{kr}}_q\right)}{{\mathit{kr}}_q}{R}_l^{\left|m\right|}\left(\cos {\theta }_q\right){\mathrm{trg}}_m\left({\varphi }_q\right)u_{\theta }+\frac{{\mathit{mj}}_l\left({\mathit{kr}}_q\right)}{{\mathit{kr}}_q\sin {\theta }_q}{y}_l^{-m}\left({\theta }_q,{\varphi }_q\right)u_{\varphi }\right)\right\}$$

or : $${j^{\ast }}_l\left({\mathit{kr}}_q\right)=\frac{l{j}_{l-1}\left({\mathit{kr}}_q\right)-\left(l+1\right)j_{l+1}\left({\mathit{kr}}_q\right)}{2l+1}$$

$$R_l^m\left(\cos {\theta }_q\right)=\{\begin{array}{ll}\sqrt{l\left(l+1\right)}{P}_l^1\left(\cos {\theta }_q\right)& \mathrm{for}m=0\\ \frac{\sqrt{\left(l-m\right)\left(l+m+1\right)}}{2}{P}_l^{m+1}\left(\cos {\theta }_q\right)-\frac{\sqrt{\left(l+m\right)\left(l-m+1\right)}}{2}{P}_l^{m-1}\left(\cos {\theta }_q\right)& \mathrm{for}1\le m\le l-1\\ -\sqrt{\frac{l}{2}}{P}_l^{l-1}\left(\cos {\theta }_q\right)& \mathrm{for}m=l\end{array}$$

and or : $$u_r=\sin {\theta }_q\sin {\theta }_q^{\alpha }\cos \left({\varphi }_q-{\varphi }_q^{\alpha }\right)+\cos {\theta }_q\cos {\theta }_q^{\alpha }$$

$$u_{\theta }=\cos {\theta }_q\sin {\theta }_q^{\alpha }\cos \left({\varphi }_q-{\varphi }_q^{\alpha }\right)-\sin {\theta }_q\cos {\theta }_q^{\alpha }$$

$$u_{\varphi }=\sin {\theta }_q^{\alpha }\sin \left({\varphi }_q^{\alpha }-{\varphi }_q\right)$$

In the case where the acquisition means 1 only include cardioid sensors, the parameter d _q takes the value ½ for the Q sensors.

In general, the matrix denoted E is therefore representative of the position of the elementary sensors 2 ₁ to 2 _Q.

The determination of E does not impose any constraint on the position ( r _q , θ _q , φ _q ) of the sensors and makes it possible in particular to take account of non-regular configurations. Such non-regular configurations are more efficient, because they make it possible to take more information on the initial field P , by being free from the redundancies introduced by the regular configurations.

In the equation expressing T, the filtering matrix D is a decoding matrix representative of the selected predetermined restitution general directions. The matrix D makes it possible to determine the control signals allowing the high precision restitution of the estimated acoustic field P̃ and therefore of the acquired acoustic field P. The matrix D is of size N x ( L +1) ² and is obtained by means of the following matrix relation: $$\mathit{D}={\left({\mathit{M}}^{\mathrm{T}}\mathit{W}\mathit{M}\right)}^{-1}{\mathit{M}}^{\mathrm{T}}\mathit{W}$$

W is a matrix corresponding to a spatial window defining the volume in which the restitution must be made. It is a diagonal matrix of size ( L +1) ² containing weighting coefficients W _l and in which each coefficient W _l is found 2 l +1 times in a row on the diagonal. The matrix W therefore has the following form: $$\mathit{W}=\left[\begin{array}{cccccccc}{W}_0& 0& \cdots & \cdots & \cdots & \cdots & \cdots & 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="imgf0002.png"\; state="\{\{state\}\}">W</figure-callout>}}_1& \ddots & & & & & ⋮\\ ⋮& \ddots & {\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="imgf0002.png"\; state="\{\{state\}\}">W</figure-callout>}}_1& \ddots & & & & ⋮\\ ⋮& & \ddots & {\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="imgf0002.png"\; state="\{\{state\}\}">W</figure-callout>}}_1& \ddots & & & ⋮\\ ⋮& & & \ddots & \ddots & \ddots & & ⋮\\ ⋮& & & & \ddots & W_L& \ddots & ⋮\\ ⋮& & & & & \ddots & \ddots & 0\\ 0& \cdots & \cdots & \cdots & \cdots & \cdots & 0& W_L\end{array}\right]$$

In the embodiment described, the values taken by the coefficients W _l correspond to the values of a function such as a Hamming window of size 2 L +1 evaluated at l , so that the parameter W _l is determined for / ranging from 0 to L.

M is a matrix corresponding to the general predetermined restitution directions, ie to the output multichannel format. It is a matrix of size ( L +1) ² over N, made up of elements M _{l , m, n} , the indices l, m denoting row l ² + l + m and n denoting column n. The matrix M therefore has the following form: $$\left[\begin{array}{cccc}{M}_{0,0.1}& M_{0,0.2}& \cdots \cdots & M_{0.0,\mathrm{NOT}}\\ {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1.1}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1.2}& \cdots \cdots & {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1,\mathrm{<figure-callout\; id="1"\; label="NOT\; M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">NOT</figure-callout>}}& \\ M_{}{}_{1,0.1}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,0.2}& \cdots \cdots & M_{1.0,\mathrm{NOT}}\\ {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,1.1}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0002.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,1.2}& \cdots \cdots & M_{1.1,\mathrm{NOT}}\\ ⋮& ⋮& & ⋮\\ M_{L,-L,1}& M_{L,-L,2}& \cdots \cdots & M_{L,-L,\mathrm{NOT}}\\ ⋮& ⋮& & ⋮\\ M_{L,0.1}& M_{L,0.2}& \cdots \cdots & L_{L,0,\mathrm{NOT}}\\ ⋮& ⋮& & ⋮\\ M_{L,L,1}& M_{L,L,2}& \cdots \cdots & M_{L,L,\mathrm{NOT}}\end{array}\right]$$

où (θ_n ,φ_n ) correspond à la direction générale associée au canal sc_n (t) dans le format multicanal.In the embodiment described, the elements M _{l , m, n are} obtained from the multichannel format according to the relation: $$M_{l,m,\mathrm{not}}=y_l^m\left({\theta }_{\mathrm{not}},{\varphi }_{\mathrm{not}}\right)$$

where ( θ _n , φ _n ) corresponds to the general direction associated with the channel sc _n ( t ) in the multichannel format.

Processing step 30 therefore corresponds to the application to all the measurement signals c ₁ to c _Q of filtering combinations to generate a plurality of processed signals constituting a representation P représentation of the acoustic field P ) substantially independent of the characteristics structural data acquisition means 1, in the form of a finite number of Fourier-Bessel coefficients.

Step 30 also corresponds to the application, to said processed signals, of specific linear combinations to generate the corresponding plurality of acoustic signals sc ₁ to sc _N.

On the figure 4 , there is shown schematically the implementation of the processing step 30 carried out by the means 8 described above.

• le filtrage dans le domaine fréquentiel comme par exemple, des techniques de convolution par bloc ;
• le filtrage dans le domaine temporel par réponse impulsionnelle ; et
• le filtrage dans le domaine temporel au moyen de filtres récursifs à réponse impulsionnelle infinie.

The filters T _{n, q} ( f ) are applied to the measurement signals c ₁ ( t ) to c _N ( t ) by means of the usual filtering methods such as for example:

• filtering in the frequency domain such as, for example, block convolution techniques;
• impulse response time domain filtering; and
• time domain filtering using recursive infinite impulse response filters.

.The N output signals sc ₁ ( t ) to sc _N ( t ) obtained at the end of the processing of the invention are representative of an acoustic field P which is restored by connecting each channel sc _n ( t ) to the corresponding restitution element 12 _n emitting plane waves of direction ( θ _n , φ _n ) according to the specifications of the multichannel format. The simultaneous action of the N restitution elements 12 ₁ to 12 _N respectively controlled by the channels sc ₁ ( t ) to sc _N ( t ) makes it possible to reproduce the acoustic field

.

au format multicanal est proche du champ acoustique P dans lequel sont plongés les capteurs 2_q. Il apparaît que la matrice T est obtenue en manipulant des descriptions de champ acoustique décomposées à un ordre élevé et conduit à une représentation de haute qualité du champ acoustique.Thanks to the processing carried out corresponding to the filtering matrix T, the representation of the acoustic field

in multichannel format is close to the acoustic field P in which the sensors 2 _q are immersed. It appears that the matrix T is obtained by manipulating high order decomposed sound field descriptions and leads to a high quality representation of the sound field.

It therefore appears that the implementation of a substantially non-regular distribution of the elementary sensors makes it possible to single out each of the sensors and to take more spatial information on the acoustic field.

Thanks to the processing of the invention, all this information can be reproduced at best in order to obtain a high quality representation in the multichannel format with a small number of elementary sensors.

In particular, in the case of a reproduction of the so-called 5.1 type as described above, the number of elementary sensors is for example less than 25 and preferably less than 10.

Of course, many embodiments can be envisaged.

In particular, other types of sensors can be used by modifying the equations according to their nature. For example, the elementary sensors can all or in part be omnidirectional and / or cardioid sensors.

Claims (10)

1. System for determining a representation of an acoustic field (P) of the type comprising:

   - acoustic wave acquisition means (1) comprising a plurality of elementary sensors (2₁ to 2_Q) which are distributed in space and which each deliver a measurement signal (c₁ to c_Q); and

   a device for determining a representation of an acoustic field (P) of the type comprising:

   means (8) for processing the measurement signals (c₁ to c_Q) delivered by the acoustic wave acquisition means (1), by applying filtering combinations representative of structural characteristics of the said acquisition means (1) in order to deliver a plurality of acoustic signals (sc₁ to sc_N) each associated with a predetermined general direction of restitution defined with respect to a given point in space (14), said acoustic signals (sc₁ to sc_N) forming a representation of said acoustic field (P), said processing means (8) being adapted to process signals delivered by the acquisition means (1),

   the determining device being configured for transmitting the acoustic signals to restitution means comprising N restitution elements (12₁ to 12_N) arranged according to the predetermined general directions with respect to the given point in space (14), N being a positive integer,

   said elementary sensors (2₁ to 2_Q) being distributed in space in a substantially non-regular manner and said filtering combinations being representative of this distribution;

   the determination system being characterized in that said processing means (8) are adapted to implement a single matrix filtering receiving as input said measurement signals (c₁ to c_Q) and delivering as output said plurality of acoustic signals (sc₁ to sc_N),

   the matrix filtering comprising a matrix T=DE, with E an encoding matrix representative of the acquisition means (1) and D a decoding matrix representative of the selected predetermined general directions of restitution.
2. System according to claim 1, wherein said acquisition means (1) are such that, for all of the usual coordinate systems, for at least one of the coordinates of the coordinate system, the values of the coordinates of the positions of all of the elementary sensors (2₁ to 2_Q) are distributed on distinct values and at a non-constant step.
3. System according to claim 1 or claim 2, wherein said acquisition means (1) comprise at least one omnidirectional elementary sensor.
4. System according to any one of claims 1 to 3, wherein said acquisition means (1) comprise at least one elementary sensor whose directivity is a combination of omnidirectional and bidirectional patterns.
5. System according to any one of claims 1 to 4, wherein said acquisition means (1) comprise a number of elementary sensors (2₁ to 2 _Q ) of one to five times the number of predetermined general directions of restitution.
6. System according to claim 5, wherein said processing means (8) form weighted linear combinations of the measurement signals (c₁ to c_Q) in order to form the acoustic output signals (sc₁ to sc_N).
7. System according to any one of claims 1 to 6, wherein the processing means (8) permit the application of filtering combinations which vary with the frequency of the measurement signals (c₁ to c_Q) processed.
8. Method for determining a representation of an acoustic field (P), comprising:

   - a step (20) of acquiring, at a plurality of points distributed in space in a substantially non-regular manner, the acoustic field (P) by acoustic wave acquisition means (1) in order to deliver a plurality of measurement signals (c₁ to c_N) which are representative at each point, in amplitude and in phase, of the acoustic field (P);

   - a step (30) of processing by applying, to the measurement signals (c₁ to c_Q), filtering combinations representative of structural characteristics of the acquisition means (1) in order to deliver a plurality of acoustic signals (sc₁ to sc_N) which are each associated with a predetermined general direction of restitution defined relative to a given point in space (14), the set of acoustic signals (sc₁ to sc_N) forming a representation of the acoustic field (P),

   the method comprising transmitting the acoustic signals to restitution means comprising N restitution elements (12₁ to 12_N) arranged according to the predetermined general directions with respect to the given point in space (14), N being a positive integer,
   le method being characterized in that it comprises a step of carrying out a single matrix filtering receiving as input said measurement signals (c₁ to c_Q) and delivering as output said plurality of acoustic signals (sc₁ to sc_N),
   the matrix filtering comprising a matrix T=DE, with E an encoding matrix representative of the acquisition means (1) and D a decoding matrix representative of the selected predetermined general directions of restitution.
9. Method according to claim 8, wherein the processing step (30) corresponds to:

   - the application to the measurement signals (c₁ to c_Q) of filtering combinations in order to generate a plurality of processed signals constituting a representation of the acoustic field (P) which is substantially independent of the structural characteristics of the acquisition means (1), in the form of a finite number of Fourier-Bessel coefficients; and

   - the application to the processed signals of specific linear combinations in order to generate the corresponding plurality of acoustic signals (sc₁ to sc_N).
10. Method according to claim 8 or claim 9, wherein said processing step (30) corresponds to the application of filtering combinations in accordance with a technique selected from the group formed:

    - by filtering techniques in the frequency domain;

    - by filtering techniques in the temporal domain by impulse response; and

    - by filtering techniques in the temporal domain by means of infinite impulse response recursive filters.

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