EP1563485B1 - Method for processing audio data and sound acquisition device therefor - Google Patents

Abstract

The digital sound processing method codes sounds from a three dimensional space at a set distance from a reference point representing the components on a spherical harmonic base. The components are then applied to a near field compensation by filtering as a function of a second distance (R) defined by the loudspeaker positions and the distance to the hearing position.

Description

The present invention relates to the processing of sound data.

Techniques relating to the propagation of a sound wave in the three-dimensional space, notably involving specialized simulation and / or sound reproduction, implement methods for processing the audio signal applied to the simulation of acoustic and psychoacoustic phenomena. . Such processing methods provide spatial encoding of the acoustic field, its transmission and spatial reproduction on a set of loudspeakers or on headphones of a stereo headset.

Among the spatialized sound techniques, there are two categories of treatments complementary to one another but which are generally implemented, one and the other, within the same system.

On the one hand, a first category of treatments relates to processes for synthesizing the room effect, or more generally for environmental effects. From a description of one or more sound sources (transmitted signal, position, orientation, directivity, or other) and based on a room effect model (involving a room geometry, or an acoustic perception desired), a set of elementary acoustic phenomena (direct waves, reflected or diffracted), or a macroscopic acoustic phenomenon (reverberated and diffuse field), allowing to translate the spatial effect at the level of a listener located at a selected point of auditory perception, in the three-dimensional space. A set of signals typically associated with reflections ( "secondary" sources , active by re-emission of a received main wave, having a spatial position attribute) and / or associated with a late reverberation (decorrelated signals for a field) are then calculated. diffuse).

On the other hand, a second category of processes relates to the positional or directional rendering of sound sources. These methods are applied to signals determined by a method of the first category described above (involving primary and secondary sources) depending on the spatial description (source position) associated with them. In particular, such methods according to this second category make it possible to obtain signals to be broadcast on loudspeakers or headphones, in order to finally give to a listener the auditory impression of sound sources placed at predetermined respective positions around the auditor. Processes according to this second category are called "creators of three-dimensional sound images", because of the distribution in the three-dimensional space of the feeling of the position of the sources by a listener. Methods according to the second category generally comprise a first stage of spatial encoding of the elementary acoustic events which produces a representation of the sound field in the three-dimensional space. In a second step, this representation is transmitted or stored for a deferred use. In a third decoding step, the decoded signals are delivered on loudspeakers or headphones of a playback device.

The present invention is rather in the second category mentioned above. It concerns in particular the spatial encoding of sound sources and a specification of the three-dimensional sound representation of these sources. It applies as well to an encoding of " virtual " sound sources (applications where sound sources are simulated such as games, a spatialized conference, or others), an "acoustic" encoding of a natural sound field, during sound recording by one or more three-dimensional microphone networks. A similar acoustic encoding method is presented byJ. Chen et al: "Synthesis of 3D virtual auditory space via a spatial feature extraction and regularization model", Proceedings of the virtual reality annual international symposium, Seattle, Sept. 18-22, 1993, IEEE, New York, US, pages 188 -193.

Among the conceivable techniques of spatialization of sound, the "ambisonic" approach is preferred. The ambisonic encoding, which will be described in detail below, consists of representing signals relating to one or more sound waves in a base of spherical harmonics (in spherical coordinates involving in particular an elevation angle and an azimuthal angle, characterizing a direction of the sound or sounds). The components representing these signals and expressed in this basis of spherical harmonics are also a function, for the waves emitted in the near field, of a distance between the sound source emitting this field and a point corresponding to the origin of the harmonic base. spherical. More particularly, this dependence of distance is expressed as a function of the sound frequency, as will be seen below.

• elle traduit, de façon rationnelle, la réalité des phénomènes acoustiques et apporte un rendu auditif spatial réaliste, convaincant et immersif ;
• la représentation des phénomènes acoustiques est scalable : elle offre une résolution spatiale qui peut être adaptée à différentes situations. En effet, cette représentation peut être transmise et exploitée en fonction de contraintes de débit lors de la transmission des signaux encodés et/ou de limitations du dispositif de restitution ;
• la représentation ambisonique est flexible et il est possible simuler une rotation du champ sonore, ou encore, à la restitution, d'adapter le décodage des signaux ambisoniques à tout dispositif de restitution, de géométries diverses.

This ambisonic approach offers a large number of possible functionalities, especially in terms of virtual source simulation, and, in general, has the following advantages:

• it translates, in a rational way, the reality of the acoustic phenomena and brings a realistic, convincing and immersive spatial auditory rendering;
• the representation of acoustic phenomena is scalable: it offers a spatial resolution that can be adapted to different situations. Indeed, this representation can be transmitted and exploited as a function of flow constraints during the transmission of encoded signals and / or limitations of the rendering device;
• the ambisonic representation is flexible and it is possible to simulate a rotation of the sound field, or else, at restitution, to adapt the decoding of the ambisonic signals to any restitution device, of various geometries.

• M.A.GERZON, "General Metatheory of Auditory Localisation", preprint 3306 of the 92^nd AES Convention, 1992, page 52.

Ce phénomène devient particulièrement critique pour des ordres d'harmoniques sphériques élevées impliquant des polynômes de puissance élevée.In the known ambisonic approach, the encoding of virtual sources is essentially directional. The encoding functions return to calculate gains that depend on the incidence of the sound wave expressed by spherical harmonic functions that depend on the elevation angle and the azimuth angle in spherical coordinates. In particular, at decoding, it is assumed that the speakers, at restitution, are far away. he This results in a distortion (or curvature) of the shape of reconstructed wave fronts. Indeed, as indicated above, the components of the sound signal in the base of spherical harmonics, for a near field, in fact also depend on the distance of the source and the sound frequency. More precisely, these components can be expressed mathematically in the form of a polynomial whose variable is inversely proportional to the aforementioned distance and to the sound frequency. Thus, the ambison components, in the sense of their theoretical expression, are divergent in the low frequencies and, in particular, tend towards infinity when the sound frequency decreases towards zero, when they represent a sound in near field emitted by a source located at a finite distance. This mathematical phenomenon is known, in the field of ambisonic representation, already for order 1, by the term "bass boost", in particular by:

• MAGERZON, "General metatheory of Auditory Localization", preprint 3306 of the 92 ^nd AES Convention 1992, page 52.

This phenomenon becomes particularly critical for high spherical harmonic orders involving high power polynomials.

• SONTACCHI et HÔLDRICH, "Further Investigations on 3D Sound Fields using Distance Coding" (Proceedings of the COST G-6 Conference on Digital Audio Effects (DAFX-01), Limerick, Irlande, 6-8 Décembre 2001),
  une technique pour prendre en compte une incurvation des fronts d'ondes au sein d'une représentation proche d'une représentation ambisonique, dont le principe consiste à :
  • appliquer un encodage ambisonique (d'ordre élevé) aux signaux issus d'une prise de son virtuelle (simulée), de type WFS (pour "Wave Field Synthesis") ;
  • et reconstruire le champ acoustique sur une zone d'après ses valeurs sur une frontière de zone, se fondant ainsi sur le principe de HUYGENS-FRESNEL.

We know by:

• SONTACCHI and HOLDRICH, "Further Investigations on 3D Sound Fields Using Distance Coding" , Limerick, Ireland, 6-8 December 2001),
  a technique to take into account a curvature of the wave fronts within a representation close to an ambisonic representation, the principle of which consists in:
  • apply an ambisonic encoding (high order) to the signals coming from a virtual sound recording (simulated), of type WFS (for "Wave Field Synthesis" );
  • and reconstructing the acoustic field over an area according to its values on a zone boundary, thus relying on the principle of HUYGENS-FRESNEL.

• les ressources informatiques nécessaires pour le calcul de toutes les surfaces permettant d'appliquer le principe de HUYGENS-FRESNEL, ainsi que les temps de calcul nécessaires, sont excessifs ;
• des artefacts de traitement dits d'"aliasing spatial" apparaissent à cause de la distance entre les microphones, à moins de choisir un maillage de microphone virtuels serré dans l'espace, ce qui alourdit les traitements ;
• cette technique est difficilement transposable à un cas réel de capteurs à disposer en réseau, en présence d'une source réelle, à l'acquisition ;
• à la restitution, la représentation sonore tridimensionnelle est implicitement assujettie à un rayon figé du dispositif de restitution car le décodage ambisonique doit se faire, ici, sur un réseau de hauts-parleurs de mêmes dimensions que le réseau de microphones initial, ce document ne proposant aucun moyen d'adapter l'encodage ou le décodage à d'autres tailles de dispositifs de restitution.

However, the technique presented in this document, although promising because it uses a high order ambisonic representation, poses a number of problems:

• the computer resources necessary for the calculation of all the surfaces making it possible to apply the HUYGENS-FRESNEL principle, as well as the necessary calculation times, are excessive;
• so-called " spatial aliasing " processing artifacts appear because of the distance between the microphones, unless you choose a tight virtual microphone mesh in the space, which makes the processing more cumbersome;
• this technique is difficult to transpose to a real case of sensors to be networked, in the presence of a real source, acquisition;
• in the restitution, the three-dimensional sound representation is implicitly subject to a frozen ray of the rendering device because the ambisonic decoding must be done here on a network of loudspeakers of the same dimensions as the initial microphone array, this document not proposing no way to adapt encoding or decoding to other sizes of rendering devices.

Above all, this document presents a horizontal network of sensors, which assumes that the acoustic phenomena considered here propagate only in horizontal directions, which excludes any other direction of propagation and which, therefore, does not represent the physical reality of an ordinary acoustic field.

More generally, the current techniques do not make it possible to deal satisfactorily with all types of sound sources, especially in the near field, but rather with distant sound sources (plane waves), which corresponds to a restrictive and artificial situation in many applications. .

An object of the present invention is to provide a method for processing, by encoding, transmission and reproduction, any type of sound field, in particular the effect of a sound source in the near field.

Another object of the present invention is to provide a method for encoding virtual sources, not only in direction, but also in distance, and to define a decoding adaptable to any rendering device.

Another object of the present invention is to provide a robust processing method for sounds of all sound frequencies (including low frequencies), especially for sound recording of natural acoustic fields using three-dimensional microphone networks.

• a) on code des signaux représentatifs d'au moins un son se propageant dans l'espace tridimensionnel et issu d'une source située à une première distance d'un point de référence, pour obtenir une représentation du son par des composantes exprimées dans une base d'harmoniques sphériques, d'origine correspondant audit point de référence, et
• b) on applique auxdites composantes une compensation d'un effet de champ proche par un filtrage qui est fonction d'une seconde distance définissant sensiblement, pour une restitution du son par un dispositif de restitution, une distance entre un point de restitution et un point de perception auditive.

For this purpose, the present invention proposes a sound data processing method, in which:

• a) coding signals representative of at least one sound propagating in the three-dimensional space and coming from a source located at a first distance from a reference point, to obtain a representation of the sound by components expressed in a basis of spherical harmonics, of origin corresponding to said reference point, and
• b) a compensation of a near-field effect is applied to said components by a filtering which is a function of a second distance substantially defining, for a restitution of the sound by a rendering device, a distance between a restitution point and a point of auditory perception.

• on obtient des composantes d'ordres successifs m pour la, représentation du son dans ladite base d'harmoniques sphériques, et
• on applique un filtre dont les coefficients, appliqués chacun à une composante d'ordre m, s'expriment analytiquement sous la forme de l'inverse d'un polynôme de puissance m, dont la variable est inversement proportionnelle à la fréquence sonore et à ladite seconde distance, pour compenser un effet de champ, proche au niveau du dispositif de restitution.

In a first embodiment, said source being distant from the reference point,

• components of successive orders m are obtained for the representation of the sound in said base of spherical harmonics, and
• a filter is applied whose coefficients, each applied to a component of order m, are expressed analytically in the form of the inverse of a power polynomial m, whose variable is inversely proportional to the sound frequency and to said second distance, to compensate for a field effect, close to the rendering device.

• on obtient des composantes d'ordres successifs m pour la représentation du son dans ladite base d'harmoniques sphériques, et
• on applique un filtre global dont les coefficients, appliqués chacun à une composante d'ordre m, s'expriment analytiquement sous la forme d'une fraction, dont :
  • le numérateur est un polynôme de puissance m, dont la variable est inversement proportionnelle à la fréquence sonore et à ladite première distance, pour simuler un effet de champ proche de la source virtuelle, et
  • le dénominateur est un polynôme de puissance m, dont la variable est inversement proportionnelle à la fréquence sonore et à ladite seconde distance, pour compenser l'effet du champ proche de la source virtuelle dans les basses fréquences sonores.

In a second embodiment, said source being a virtual source provided at said first distance,

• we obtain components of successive orders m for the representation of the sound in said base of spherical harmonics, and
• a global filter is applied whose coefficients, each applied to a component of order m, are expressed analytically in the form of a fraction, of which:
  • the numerator is a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said first distance, to simulate a near-field effect of the virtual source, and
  • the denominator is a power polynomial m, the variable of which is inversely proportional to the sound frequency and to said second distance, to compensate for the effect of the near field of the virtual source in the low frequencies of sound.

Preferably, the data encoded and filtered in steps a) and b) are transmitted to the rendering device with a parameter representative of said second distance.

In addition or alternatively, the rendering device comprising means for reading a memory medium, the encoded and filtered data is stored on a memory medium intended to be read by the rendering device. in steps a) and b) with a parameter representative of said second distance.

Advantageously, prior to a sound reproduction by a rendering device comprising a plurality of loudspeakers arranged at a third distance from said auditory perception point, an adaptation filter is applied to the coded and filtered data whose coefficients are a function of said second and third distances.

• le numérateur est un polynôme de puissance m, dont la variable est inversement proportionnelle à la fréquence sonore et à ladite seconde distance,
• et le dénominateur est un polynôme de puissance m, dont la variable est inversement proportionnelle à la fréquence sonore et à ladite troisième distance.

In a particular embodiment, the coefficients of this adaptation filter, each applied to a component of order m, are expressed analytically in the form of a fraction, of which:

• the numerator is a polynomial of power m whose variable is inversely proportional to the sound frequency and to the said second distance,
• and the denominator is a polynomial of power m whose variable is inversely proportional to the sound frequency and to said third distance.

• pour des composantes d'ordre m pair, des filtres audionumériques sous la forme d'une cascade de cellules d'ordre deux ; et
• pour des composantes d'ordre m impair, des filtres audionumériques sous la forme d'une cascade de cellules d'ordre deux et une cellule supplémentaire d'ordre un.

Advantageously, for the implementation of step b), provision is made for:

• for even-order components m, digital audio filters in the form of a cascade of second-order cells; and
• for odd m-order components, digital audio filters in the form of a cascade of second-order cells and an additional order-one cell.

In this embodiment, the coefficients of a digital audio filter, for a component of order m, are defined from the root digital values of said power polynomials m.

In a particular embodiment, the aforementioned polynomials are Bessel polynomials.

To the acquisition of the sound signals, a microphone is advantageously provided comprising an acoustic transducer array arranged substantially on the surface of a sphere whose center corresponds substantially to said reference point, to obtain said signals representative of at least one sound. propagating in three-dimensional space.

In this embodiment, a global filter is applied to step b) in order firstly to compensate for a near-field effect as a function of said second distance and secondly to equalize the signals from the transducers to compensate for a difference. directivity weighting of said transducers.

Preferably, there is provided a number of transducers function of a selected total number of components to represent the sound in said base of spherical harmonics.

According to an advantageous characteristic, a total number of components in the base of spherical harmonics to obtain, at the restitution, a region of the space around the point of perception in which the sound reproduction is faithful and whose dimensions are increasing with the total number of components.

Preferably, there is further provided a playback device having a number of speakers at least equal to said total number of components.

• on prévoit un dispositif de restitution comportant au moins un premier et un second haut-parleur disposés à une distance choisie d'un auditeur,
• on obtient, pour cet auditeur, une information de ressenti attendu de la position dans l'espace de sources sonores situées à une distance de référence prédéterminée de l'auditeur pour l'application d'une technique dite de "synthèse binaurale" ou "transaurale", et
• on applique la compensation de l'étape b) avec ladite distance de référence sensiblement en tant que seconde distance.

As a variant, in the context of a restitution with binaural or transaural synthesis:

• there is provided a rendering device comprising at least a first and a second loudspeaker arranged at a selected distance from a listener,
• for this listener, an expected feeling information is obtained of the position in the space of sound sources located at a predetermined reference distance from the listener for the application of a so-called " binaural synthesis" or " transaural " technique. ", and
• the compensation of step b) is applied with said reference distance substantially as a second distance.

• on prévoit un dispositif de restitution comportant au moins un premier et un second haut-parleur disposés à une distance choisie d'un auditeur,
• on obtient, pour cet auditeur, une information de ressenti de la position dans l'espace de sources sonores situées à une distance de référence prédéterminée de l'auditeur, et
• préalablement à une restitution sonore par le dispositif de restitution, on applique aux données codées et filtrées aux étapes a) et b) un filtre d'adaptation dont les coefficients sont fonction de la seconde distance et sensiblement de la distance de référence.

In a variant where one introduces an adaptation to the playback device with two earphones:

• there is provided a rendering device comprising at least a first and a second loudspeaker arranged at a selected distance from a listener,
• we get, for this listener, a feeling information of the position in the space of sound sources located at a predetermined reference distance from the listener, and
• prior to sound reproduction by the rendering device, an adaptation filter whose coefficients are a function of the second distance and substantially of the reference distance is applied to the data coded and filtered in steps a) and b).

• le dispositif de restitution comporte un casque à deux écouteurs pour les oreilles respectives de l'auditeur,
• et préférentiellement, séparément pour chaque écouteur, on applique le codage et le filtrage des étapes a) et b) pour des signaux respectifs destinés à alimenter chaque écouteur, avec, en tant que première distance, respectivement une distance séparant chaque oreille d'une position d'une source à restituer dans l'espace de restitution.

In particular, in the context of a binaural synthesis restitution:

• the rendering device comprises a headset with two earphones for the respective ears of the listener,
• and preferably, separately for each earphone, the coding and filtering of steps a) and b) are applied for respective signals intended to feed each earphone, with, as first distance, respectively a distance separating each ear from a position a source to restore in the restitution space.

• une matrice comportant lesdites composantes dans la base des harmoniques sphériques, et
• une matrice diagonale dont les coefficients correspondent à des coefficients de filtrage de l'étape b),

et on multiplie lesdites matrices pour obtenir une matrice résultat de composantes compensées.Preferably, in steps a) and b), a matrix system comprising at least:

• a matrix comprising said components in the base of the spherical harmonics, and
• a diagonal matrix whose coefficients correspond to filter coefficients of step b),

and multiplying said matrices to obtain a result matrix of compensated components.

• le dispositif de restitution comporte une pluralité de haut-parleurs disposés sensiblement à une même distance du point de perception auditive, et
• pour décoder lesdites données codées et filtrées aux étapes a) et b) et former des signaux adaptés pour alimenter lesdits haut-parleurs :
  • * on forme un système matriciel comportant ladite matrice résultat de composantes compensées et une matrice de décodage prédéterminée, propre au dispositif de restitution, et
  • * on obtient une matrice comportant des coefficients représentatifs des signaux d'alimentation des hauts-parleurs par multiplication de la matrice résultat par ladite matrice de décodage.

Preferably, at restitution:

• the rendering device comprises a plurality of loudspeakers disposed substantially at the same distance from the auditory perception point, and
• for decoding said coded and filtered data in steps a) and b) and forming appropriate signals to power said loudspeakers:
  • a matrix system is formed comprising said compensated component result matrix and a predetermined decoding matrix specific to the rendering device, and
  • a matrix is obtained comprising coefficients representative of the signals for supplying the loudspeakers by multiplication of the result matrix by said decoding matrix.

• recevoir des signaux émanant chacun d'un transducteur,
• appliquer auxdits signaux un codage pour obtenir une représentation du son par des composantes exprimées dans une base d'harmoniques sphériques, d'origine correspondant au centre de ladite sphère,
• et appliquer auxdites composantes un filtrage qui est fonction, d'une part, d'une distance correspondant au rayon de la sphère et, d'autre part, d'une distance de référence.

The present invention also relates to a sound acquisition device comprising a microphone provided with a network of acoustic transducers disposed substantially on the surface of a sphere. According to the invention the device further comprises a processing unit arranged for:

• receive signals from each of a transducer,
• applying to said signals a coding to obtain a representation of the sound by components expressed in a base of spherical harmonics, of origin corresponding to the center of said sphere,
• and applying to said components a filtering which is a function, on the one hand, of a distance corresponding to the radius of the sphere and, on the other hand, a reference distance.

Preferably, the filtering performed by the processing unit consists, on the one hand, of equalizing, as a function of the radius of the sphere, the signals coming from the transducers to compensate for a directivity weighting of said transducers and, on the other hand, to compensating a near-field effect according to said reference distance.

• la figure 1 illustre schématiquement un système d'acquisition et création, par simulation de sources virtuelles, de signaux sonores, avec encodage, transmission, décodage et restitution par un dispositif de restitution spatialisé,
• la figure 2 représente plus précisément un encodage de signaux définis à la fois en intensité et par rapport à la position d'une source dont ils sont issus,
• la figure 3 illustre les paramètres en jeu dans la représentation ambisonique, en coordonnées sphériques ;
• la figure 4 illustre une représentation par une métrique tridimensionnelle dans un repère de coordonnées sphériques, d'harmoniques sphériques ${\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}$
  
  de différents ordres ;
• la figure 5 est un diagramme des variations du module de fonctions radiales j _m (kr), qui sont des fonctions de Bessel sphériques, pour des valeurs d'ordre m successives, ces fonctions radiales intervenant dans la représentation ambisonique d'un champ de pression acoustique ;
• la figure 6 représente l'amplification due à l'effet de champ proche pour différents ordres successifs m, en particulier dans les basses fréquences ;
• la figure 7 représente schématiquement un dispositif de restitution comportant une pluralité de hauts-parleurs HP_i , avec le point (référencé P) de perception auditive précité, la première distance précitée (référencée ρ) et la seconde distance précitée (référencée R) ;
• la figure 8 représente schématiquement les paramètres mis en jeu dans l'encodage ambisonique, avec un encodage directionnel, ainsi qu'un encodage de distance selon l'invention ;
• la figure 9 représente des spectres d'énergie des filtres de compensation et de champ proche simulés pour une première distance d'une source virtuelle p = 1 m et une pré-compensation de hauts-parleurs situés à une seconde distance R = 1,5 m ;
• la figure 10 représente des spectres d'énergie des filtres de compensation et de champ proche simulés pour une première distance de la source virtuelle p = 3 m et une pré-compensation de hauts-parleurs situés à une distance R = 1,5 m ;
• la figure 11A représente une reconstruction du champ proche avec compensation, au sens de la présente invention, pour une onde sphérique dans le plan horizontal ;
• la figure 11B, à comparer avec la figure 11A, représente le front d'onde initial, issu d'une source S ;
• la figure 12 représente schématiquement un module de filtrage pour adapter les composantes ambisoniques reçues et pré-compensées à l'encodage pour une distance de référence R en tant que seconde distance, à un dispositif de restitution comportant une pluralité de hauts-parleurs disposés à une troisième distance R₂ d'un point de perception auditive ;
• la figure 13A représente schématiquement la disposition d'une source sonore M, à la restitution, pour un auditeur utilisant un dispositif de restitution appliquant une synthèse binaurale, avec une source émettant en champ proche ;
• la figure 13B représente schématiquement les étapes d'encodage et de décodage avec effet de champ proche dans le cadre de la synthèse binaurale de la figure 13A à laquelle est combiné un encodage/décodage ambisonique ;
• la figure 14 représente schématiquement le traitement des signaux issus d'un microphone comportant une pluralité de capteurs de pression agencés sur une sphère, à titre illustratif, par encodage ambisonique, égalisation et compensation de champ proche au sens de l'invention.

Other advantages and characteristics of the invention will become apparent on reading the detailed description below and on examining the figures which accompany it, in which:

• FIG. 1 schematically illustrates a system for acquiring and creating, by simulation of virtual sources, sound signals, with encoding, transmission, decoding and restitution by a spatialized reproduction device,
• FIG. 2 more precisely represents an encoding of signals defined both in intensity and with respect to the position of a source from which they are derived,
• FIG. 3 illustrates the parameters involved in the ambisonic representation, in spherical coordinates;
• FIG. 4 illustrates a representation by a three-dimensional metric in a coordinate system of spherical coordinates, of spherical harmonics ${\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}$
  
  different orders;
• FIG. 5 is a diagram of the variations of the radial function module j _m (kr), which are spherical Bessel functions, for successive order values m, these radial functions occurring in the ambisonic representation of a pressure field acoustic ;
• FIG. 6 represents the amplification due to the near-field effect for different successive orders m, in particular in the low frequencies;
• FIG. 7 schematically represents a reproduction device comprising a plurality of loudspeakers HP _i , with the aforementioned point (referenced P) of auditory perception, the first aforementioned distance (referenced ρ) and the second aforementioned distance (referenced R);
• FIG. 8 schematically represents the parameters involved in the ambisonic encoding, with a directional encoding, as well as a distance encoding according to the invention;
• FIG. 9 represents energy spectra of the simulated compensation and near field filters for a first distance of a virtual source p = 1 m and a pre-compensation of loudspeakers situated at a second distance R = 1.5 m;
• FIG. 10 represents energy spectra of the simulated compensation and near field filters for a first distance from the virtual source p = 3 m and a pre-compensation of loudspeakers located at a distance R = 1.5 m;
• FIG. 11A represents a near field reconstruction with compensation, within the meaning of the present invention, for a spherical wave in the horizontal plane;
• FIG. 11B, to be compared with FIG. 11A, represents the initial wavefront, originating from a source S;
• FIG. 12 schematically represents a filtering module for adapting the received and pre-compensated ambisonic components to the encoding for a distance of reference R as a second distance, to a rendering device having a plurality of loudspeakers arranged at a third distance R ₂ from a point of auditory perception;
• FIG. 13A schematically represents the arrangement of a sound source M, at restitution, for a listener using a rendering device applying a binaural synthesis, with a source emitting in the near field;
• Fig. 13B schematically illustrates the near field effect encoding and decoding steps in the context of the binaural synthesis of Fig. 13A to which ambisonic encoding / decoding is combined;
• FIG. 14 diagrammatically represents the processing of signals from a microphone comprising a plurality of pressure sensors arranged on a sphere, by way of illustration, by ambisonic encoding, equalization and near-field compensation in the sense of the invention.

Reference is firstly made to FIG. 1, which represents by way of illustration a global system of sound spatialization. A simulation module of a virtual scene defines a sound object as a virtual source of a signal, for example monophonic, of position chosen in the three-dimensional space and which defines a direction of sound. In addition, specifications of the geometry of a virtual room can be provided to simulate reverberation of the sound. A processing module 11 applies a management of one or more of these sources with respect to a listener (definition of a virtual position of the sources with respect to this listener). It implements a room effect processor for simulating reverberations or the like by applying delays and / or routine filtering. The signals thus constructed are transmitted to a spatial encoding module 2a of the elementary contributions of the sources.

In parallel, a natural sound recording can be performed as part of a sound recording by one or more microphones arranged in a chosen manner with respect to real sources (module 1b). The signals picked up by the microphones are encoded by a module 2b. The acquired and encoded signals can be transformed according to an intermediate representation format (module 3b), before being mixed by the module 3 to the signals generated by the module 1a and encoded by the module 2a (from the virtual sources). The mixed signals are then transmitted or stored on a medium, for later retrieval (arrow TR). They are then applied to a decoding module 5, for the purpose of rendering on a reproduction device 6 comprising loudspeakers. If necessary, the decoding step 5 may be preceded by a step of manipulation of the sound field, for example by rotation, by means of a processing module 4 provided upstream of the decoding module 5.

The reproduction device may be in the form of a multiplicity of loudspeakers, arranged for example on the surface of a sphere in a three-dimensional configuration (periphery) to ensure, in the restitution, in particular a sense of direction sound in three-dimensional space. For this purpose, an auditor place generally in the center of the sphere formed by the network of speakers, this center corresponding to the auditory perception point cited above. Alternatively, the speakers of the playback device can be arranged in a plane (two-dimensional panoramic configuration), the speakers being arranged in particular on a circle and the listener usually placed in the center of this circle. In another variant, the rendering device may be in the form of a "surround" type device (5.1). Finally, in an advantageous variant, the rendering device can be in the form of a headset with two earphones for a binaural synthesis of the sound reproduced, which allows the listener to feel a direction of the sources in the three-dimensional space, as will be discussed in more detail below. Such a two-speaker reproduction device, for a feeling in the three-dimensional space, can also be in the form of a transaural restitution device, with two loudspeakers arranged at a selected distance from a listener.

Reference is now made to FIG. 2 to describe a spatial encoding and a decoding for a three-dimensional sound reproduction of elementary sound sources. A signal from a source 1 to N is transmitted to a spatial encoding module 2, as well as its position (real or virtual). Its position can be as well defined in terms of incidence (direction of the source as seen by the listener) and in terms of distance between this source and a listener. The plurality of signals thus encoded allows to obtain a multi-channel representation of a global sound field. The encoded signals are transmitted (arrow TR) to a sound reproduction device 6, for a sound reproduction in the three-dimensional space, as indicated above with reference to FIG.

dès l'origine O à un point de la sphère est décrit par un azimut θ_r, une élévation δ_r et un rayon r (correspondant à la distance à l'origine O).Reference is now made to FIG. 3 to describe hereinafter the ambisonic representation by spherical harmonics in the three-dimensional space of an acoustic field. An area around an origin O (sphere of radius R) devoid of acoustic source is considered. We adopt a system of spherical coordinates in which each vector $\overrightarrow{\mathit{r}}$

from the origin O at a point of the sphere is described by an azimuth θ _r , an elevation δ _r and a radius r (corresponding to the distance to the origin O).

à l'intérieur de cette sphère (r < R où R est le rayon de la sphère) peut s'écrire dans le domaine fréquentiel comme une série dont les termes sont les produits pondérés de fonctions angulaires ${\mathit{y}}_{\mathit{mn}}^{\mathit{\sigma }}(\mathrm{\theta },\mathrm{\delta })$

et de fonction radiale j_m(kr) qui dépendent ainsi d'un terme de propagation où k=2πf/c, où f est la fréquence sonore et c est la vitesse du son dans le milieu de propagation.The pressure field $\mathit{p}\left(\overrightarrow{\mathit{r}}\right)$

inside this sphere (r <R where R is the radius of the sphere) can be written in the frequency domain as a series whose terms are the weighted products of angular functions ${\mathit{there}}_{\mathit{mn}}^{\mathit{\sigma }}(\mathrm{\theta },\mathrm{\delta })$

and of radial function j _m (kr) which thus depend on a propagation term where k = 2πf / c, where f is the sound frequency and c is the speed of sound in the propagation medium.

The pressure field is expressed by: $$p\left(\overrightarrow{\mathit{r}}\right)={\displaystyle \underset{m=0}{\overset{\infty }{\Sigma }}{j}^m{j}_m\left(kr\right)}{\displaystyle \underset{0\le \mathrm{not}\le m,\sigma =\pm 1}{<figure-callout\; id="0"\; label="\Sigma "\; filenames="imgf0004.png,imgf0007.png"\; state="\{\{state\}\}">\Sigma </figure-callout>}{B}_{m\mathrm{not}}^{\sigma }{Y}_{m\mathrm{not}}^{\sigma \left(\mathrm{NOT}3D\right)}\left({\theta }_r,{\delta }_r\right)}$$

qui sont implicitement fonction de la fréquence, décrivent ainsi le champ de pression dans la zone considérée. Pour cette raison, ces facteurs sont appelés "composantes harmoniques sphériques" et représentent une expression fréquentielle du son (ou du champ de pression) dans la base des harmoniques sphériques ${\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}\mathrm{.}$

The set of weighting factors ${\mathit{B}}_{\mathit{mn}}^{\mathit{\sigma }}\mathit{,}$

which are implicitly a function of the frequency, thus describe the pressure field in the zone considered. For this reason, these factors are called "spherical harmonic components" and represent a frequency expression of sound (or pressure field) in the spherical harmonics basis ${\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}\mathrm{.}$

où P _mn (sinδ) dont des fonctions de Legendre de degré m et d'ordre n ;
δ_p,q est le symbole de Krönecker (égal à 1 si p=q et 0, sinon)The angular functions are called "spherical harmonics" and are defined by: $$Y_{m\mathrm{not}}^{\sigma }\left(\theta ,\delta \right)=\sqrt{\mathrm{two}m+1}\sqrt{\left(\mathrm{two}-{\mathrm{<figure-callout\; id="0"\; label="\delta "\; filenames="imgf0004.png,imgf0007.png"\; state="\{\{state\}\}">\delta </figure-callout>}}_{0;\mathrm{not}}\right)\frac{\left(m-\mathrm{not}\right)!}{\left(m+\mathrm{not}\right)!}}{P}_{m\mathrm{not}}\left(\sin \delta \right)\times \{\begin{array}{l}\cos \mathrm{}\mathit{}\mathit{}\mathit{not}\mathrm{\theta \; if\; \sigma }=+1\\ \sin \mathrm{}\mathit{}\mathit{}\mathit{not}\theta \mathrm{if}\sigma =-1\end{array}$$

where P _mn (sinδ) whose functions of Legendre of degree m and of order n;
δ _{p, q} is the Krönecker symbol (equal to 1 if p = q and 0 otherwise)

$${F|G}_{4\pi }=\frac{1}{4\pi }{\displaystyle ∯F\left(\theta ,\delta \right)G\left(\theta ,\delta \right),d\Omega \left(\theta ,\delta \right)}$$

The spherical harmonics form an orthonormal basis where the scalar products between harmonic components and, generally between two functions F and G, are respectively defined by: $${<Y_{m\mathrm{not}}^{\sigma }|Y_{m^{\text{'}}{\mathrm{not}}^{\text{'}}}^{{\sigma }^{\text{'}}}>}_{4\pi }={\mathrm{\delta }}_{\mathit{mm}\text{'}}{\mathrm{\delta }}_{\mathit{nn}\text{'}}{\mathrm{\delta }}_{\mathrm{\sigma \sigma }\text{'}}\mathrm{.}$$

$${F|\mathrm{<figure-callout\; id="4"\; label="BOY\; WUT"\; filenames="imgf0004.png,imgf0008.png"\; state="\{\{state\}\}">BOY\; WUT</figure-callout>}}_{4\pi }=\frac{1}{4\pi }{\displaystyle ∯F\left(\theta ,\delta \right)\mathrm{BOY\; WUT}\left(\theta ,\delta \right),d\Omega \left(\theta ,\delta \right)}$$

Spherical harmonics are bounded real functions, as shown in Figure 4, as a function of the order m and the indices n and σ. The dark and light parts correspond respectively to the positive and negative values of spherical harmonic functions. The higher the order m, the higher the angular frequency (and hence the discrimination between functions). The radial functions j _m (kr) are spherical Bessel functions, the module of which is illustrated for some values of the order m in FIG.

An interpretation of the ambisonic representation can be given by a base of spherical harmonics as follows. The ambisonic components of the same order m finally express "derivatives" or "moments" of order m of the pressure field in the vicinity of the origin O (center of the sphere shown in FIG. 3).

décrit la grandeur scalaire de la pression, tandis que ${\mathit{B}}_{11}^{+1}=\mathit{X},\mathrm{\hspace{1em}}{\mathit{B}}_{11}^{-1}=\mathit{Y},\mathrm{\hspace{1em}}{\mathit{B}}_{10}^{+1}=\mathit{Z}$

sont liés aux gradients de pression (ou encore à la vélocité particulaire), à l'origine O. Ces quatre premières composantes W, X, Y et Z sont obtenues lors d'une prise de son naturelle à l'aide de microphones omnidirectifs (pour la composante W d'ordre 0) et bidirectifs (pour les trois autres composantes suivantes). En utilisant un plus grand nombre de transducteurs acoustiques, un traitement approprié, notamment par égalisation, permet d'obtenir d'avantage de composantes ambisoniques (ordres m plus élevés supérieurs à 1).In particular, ${\mathit{<figure-callout\; id="00"\; label="B"\; filenames="imgf0011.png"\; state="\{\{state\}\}">B</figure-callout>}}_{00}^{+1}=\mathit{W}$

describes the scalar magnitude of the pressure, while ${\mathit{<figure-callout\; id="11"\; label="B"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">B</figure-callout>}}_{11}^{+1}=\mathit{X},\mathrm{}{\mathit{B}}_{11}^{-1}=\mathit{Y},\mathrm{}{\mathit{<figure-callout\; id="10"\; label="B"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">B</figure-callout>}}_{10}^{+1}=\mathit{Z}$

are related to the pressure gradients (or particle velocity), at the origin O. These four first components W, X, Y and Z are obtained during a natural sound recording using omnidirectional microphones ( for the W component of order 0) and bidirectional (for the other three components below). By using a larger number of acoustic transducers, a treatment appropriate, in particular by equalization, makes it possible to obtain more ambisonic components (orders m higher than 1).

By taking into account additional components of higher order (greater than 1), thus increasing the angular resolution of the ambisonic description, an approximation of the pressure field is obtained on a wider neighborhood with respect to the length of the wave of the sound wave, around the origin O. It will thus be understood that there is a close relationship between the angular resolution (order of spherical harmonics) and the radial range (radius r) that can be represented. In short, when one deviates spatially from the point of origin O of FIG. 3, the higher the number of ambisonic components (high order M) and the better the representation of the sound by all these ambisonic components. . It will also be understood that the ambisonic representation of the sound is however less satisfactory as one moves away from the origin O. This effect becomes critical especially for high sound frequencies (of short wavelength). . It is therefore advantageous to obtain a maximum number of ambisonic components, which makes it possible to create a region of the space around the point of perception, in which the reproduction of the sound is faithful and whose dimensions are increasing with the total number of components.

An application with an encoding / transmission / reproduction system of a spatialized sound is described below.

In practice, an ambisonic system takes into account a subset of spherical harmonic components, as described above. We speak of a system of order M when this one takes into account ambisonic components of subscript m <M. When it is a restitution by a rendering device with loudspeakers, it will be understood that if these loudspeakers are arranged in a horizontal plane, only the harmonics of index m = n are exploited. On the other hand, when the rendering device comprises loudspeakers disposed on the surface of a sphere (" periphery "), it is possible in principle to use as many harmonics as there are loudspeakers.

The reference S designates the pressure signal carried by a plane wave and picked up at the point O corresponding to the center of the sphere of FIG. 3 (origin of the base in spherical coordinates). The incidence of the wave is described by the azimuth θ and the elevation δ. The expression of the components of the field associated with this plane wave is given by the relation: $$B_{m\mathrm{not}}^{\sigma }=S.Y_{m\mathrm{not}}^{\sigma }\left(\theta ,\delta \right)$$

pour "incurver" la forme des fronts d'onde, en considérant qu'un champ proche émet, en première approximation, une onde sphérique. Les composantes encodées du champ deviennent : $$B_{mn}^{\sigma }=S.F_m^{\left(\rho /c\right)}\left(\omega \right)Y_{mn}^{\sigma }\left(\theta ,\delta \right)$$

et l'expression du filtre précité ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{c})}$

est donnée par la relation : $$F_m^{\left(\rho /c\right)}\left(\omega \right)={\displaystyle \sum _{n=0}^m\frac{\left(m+n\right)!}{\left(m-n\right)!n!}{\left(2j\omega \rho /c\right)}^{-n}}$$

où ω = 2πf est la pulsation de l'onde, f étant la fréquence du son.To encode (simulate) a near-field source at a distance p from the origin O, a filter is applied ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{vs})}$

to "bend" the shape of the wave fronts, considering that a near field emits, as a first approximation, a spherical wave. The encoded components of the field become: $$B_{m\mathrm{not}}^{\sigma }=S.F_m^{\left(\rho /\mathrm{vs}\right)}\left(\omega \right)Y_{m\mathrm{not}}^{\sigma }\left(\theta ,\delta \right)$$

and the expression of the aforementioned filter ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{vs})}$

is given by the relation: $$F_m^{\left(\rho /\mathrm{vs}\right)}\left(\omega \right)={\displaystyle \underset{\mathrm{not}=0}{\overset{m}{\Sigma }}\frac{\left(m+\mathrm{not}\right)!}{\left(m-\mathrm{not}\right)!\mathrm{not}!}{\left(\mathrm{two}j\omega \rho /\mathrm{vs}\right)}^{-\mathrm{not}}}$$

where ω = 2πf is the pulsation of the wave, where f is the frequency of the sound.

These last two relations [A4] and [A5] show finally that, for a virtual source (simulated) as for a real source in near field, the components of the sound in the ambisonic representation are expressed mathematically (in particular analytically) in the form of a polynomial, here Bessel, power m and whose variable (c / 2jωρ) is inversely proportional to the sound frequency.

• dans le cas d'une onde plane, l'encodage produit des signaux qui ne diffèrent du signal d'origine que d'un gain réel, fini, ce qui correspond à un encodage purement directionnel (relation [A3]) ;
• dans le cas d'une onde sphérique (source en champ proche), le filtre supplémentaire ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{c})}\left(\mathrm{\omega }\right)$
  
  encode l'information de distance en introduisant, dans l'expression des composantes ambisoniques, des rapports d'amplitudes complexes qui dépendent de la fréquence, comme exprimé dans la relation [A5].

Thus, it will be understood that:

• in the case of a plane wave, the encoding produces signals which differ from the original signal only by a real, finite gain, which corresponds to a purely directional encoding (relation [A3]);
• in the case of a spherical wave (source in the near field), the additional filter ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{vs})}\left(\mathrm{\omega }\right)$
  
  encodes distance information by introducing, in the expression of the ambison components, frequency-dependent complex amplitude ratios as expressed in relation [A5].

It should be noted that this additional filter is of the "integrator" type, with an amplifying effect increasing and diverging (unbounded) as the sound frequencies decrease towards zero. FIG. 6 shows, for each order m, an increase in the gain at low frequencies (here the first distance ρ = 1m). It is therefore unstable and divergent filters when one seeks to apply them to any audio signals. This divergence is all the more critical for high value orders m.

It will be understood in particular, from the relations [A3], [A4], and [A5], that the modeling of a virtual source in the near field presents divergent ambison components at low frequencies, in a particularly critical manner for m orders. As shown in FIG. 6, this divergence in the low frequencies corresponds to the "bass boost" phenomenon stated above. It is also manifested in sound acquisition, for real sources.

For this reason in particular, the ambisonic approach, especially for high orders, has not known, in the state of the art, a concrete application (other than theoretical) in sound processing.

• chaque point où se situe un haut-parleur HP_i correspond à un point de restitution énoncé ci-avant,
• le point P est le point de perception auditive énoncé ci-avant,
• ces points sont séparés de la seconde distance R énoncée ci-avant,

tandis que sur la figure 3 décrite ci-avant :

• le point O correspond au point de référence, énoncé ci-avant, qui forme l'origine de la base des harmoniques sphériques,
• le point M correspond à la position d'une source (réelle ou virtuelle) située à la première distance p, énoncée ci-avant, du point de référence O.

It is understood in particular that a compensation of the near field is necessary to respect, at the restitution, the shape of the wavefronts encoded in the ambisonic representation. Referring to FIG. 7, a rendering device comprises a plurality of loudspeakers HP _i , arranged at the same distance R, in the example described, from a point of auditory perception P. In this FIG.

• each point where an HP _i speaker is located corresponds to a restitution point stated above,
• the point P is the point of auditory perception stated above,
• these points are separated from the second distance R stated above,

while in Figure 3 described above:

• the point O corresponds to the point of reference, stated above, which forms the origin of the base of the spherical harmonics,
• the point M corresponds to the position of a source (real or virtual) situated at the first distance p, stated above, from the reference point O.

et qui s'appliquent aux composantes ambisoniques ${\mathit{B}}_{\mathit{mn}}^{\mathrm{\sigma }}$

précitées.According to the invention, a pre-compensation of the near field is introduced at the very stage of the encoding, this compensation involving filters of the analytical form. $\frac{1}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$

and that apply to ambisonic components ${\mathit{B}}_{\mathit{mn}}^{\mathrm{\sigma }}$

above.

dont l'effet apparaît sur la figure 6 est compensée par l'atténuation du filtre appliqué dès l'encodage $\frac{1}{F_m^{\left(R/c\right)}\left(\omega \right)}.$

En particulier, les coefficients de ce filtre de compensation $\frac{1}{F_m^{\left(R/c\right)}\left(\omega \right)}$

sont croissants avec la fréquence du son et, en particulier, tendent vers zéro, pour les basses fréquences. Avantageusement, cette pré-compensation, effectuée dès l'encodage, assure que les données transmises ne sont pas divergentes pour les basses fréquences.According to one of the advantages provided by the invention, amplification ${\mathit{F}}_{\mathit{m}}^{(\mathrm{\rho }/\mathit{vs})}\left(\mathrm{\omega }\right)$

whose effect appears in FIG. 6 is compensated by attenuation of the filter applied as soon as encoding $\frac{1}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}.$

In particular, the coefficients of this compensation filter $\frac{1}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$

are increasing with the frequency of the sound and, in particular, tend towards zero, for the low frequencies. Advantageously, this pre-compensation, performed as soon as encoding, ensures that the data transmitted are not divergent for low frequencies.

comme indiqué ci-avant, ce qui permet, d'une part, de transmettre des signaux bornés, et, d'autre part, de choisir la distance R, dès l'encodage, pour la restitution du son à partir des hauts-parleurs HP_i, tel que représenté sur la figure 7. En particulier, on comprendra que si l'on a simulé, à l'acquisition, une source virtuelle placée à la distance p de l'origine O, à la restitution (figure 7), un auditeur placé au point P de perception auditive (à une distance R des hauts-parleurs HP_i) ressentira, à l'audition, la présence d'une source sonore S, placée à la distance p du point de perception P et qui correspond à la source virtuelle simulée lors de l'acquisition.To indicate the physical significance of the distance R which occurs in the compensation filter, it is considered, by way of illustration, to consider a real initial plane wave at the acquisition of the sound signals. To simulate a near field effect of this distant source, we apply the first filter of the relation [A5], as indicated in relation [A4]. The distance p then represents a distance between a near virtual source M and the point O representing the origin of the spherical base of FIG. 3. A first near-field simulation filter is thus applied to simulate the presence of a virtual source. at the distance p described above. Nevertheless, on the one hand, as indicated above, the terms of the coefficient of this filter diverge in the low frequencies (FIG. 6) and, on the other hand, the distance p mentioned above will not necessarily represent the distance between the speakers of a rendering device and a point P of perception (Figure 7). According to the invention, a pre-compensation is applied to the encoding, involving a filter of the type $\frac{1}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$

as indicated above, which allows, on the one hand, to transmit bounded signals, and, on the other hand, to choose the distance R, from the encoding, for the restitution of the sound from the loudspeakers HP _i , as shown in FIG. 7. In particular, it will be understood that if a virtual source placed at the distance p of the origin O was simulated at the time of acquisition (FIG. 7) a listener placed at the point P of auditory perception (at a distance R from the loudspeakers HP _i ) will feel, at the hearing, the presence of a sound source S, placed at the distance p from the perception point P and which corresponds to the virtual source simulated during the acquisition.

Le filtre total donné par la relation [A11] est stable et constitue la partie "encodage de distance" dans l'encodage ambisonique spatial selon l'invention, tel que représenté sur la figure 8. Les coefficients de ces filtres correspondent à des fonctions de transfert monotones de la fréquence, qui tendent vers la valeur 1 en hautes fréquences et vers la valeur (R/ρ)^m en basses fréquences. En se référant à la figure 9, les spectres d'énergie des filtres ${\mathit{H}}_{\mathit{m}}^{\mathit{NFC}\mathit{(}\mathit{\rho }\mathit{/}\mathit{c}\mathit{,}\mathit{R}\mathit{/}\mathit{c}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)}$

traduisent l'amplification des composantes encodées, dues à l'effet de champ de la source virtuelle (placée ici à une distance p = 1 m), avec une pré-compensation du champ des hauts-parleurs (placés à une distance R = 1,5 m). L'amplification en décibels est donc positive lorsque p < R (cas de la figure 9) et négative quand p > R (cas de la figure 10 où p = 3 m et R = 1,5 m). Dans un dispositif de restitution spatialisée, la distance R entre un point de perception auditive et les haut-parleurs HP_i est effectivement de l'ordre de un ou quelques mètres.Thus, the pre-compensation of the near field of the loudspeakers (placed at the distance R), at the stage of the encoding, can be combined with a simulated near-field effect of a virtual source placed at a distance p. At encoding, a total filter ultimately comes into play resulting, on the one hand, from the simulation of the near field, and, on the other hand, from the compensation of the near field, the coefficients of this filter being able to express itself. analytically by the relation: $$H_m^{\mathit{NFC}\left(\rho /\mathrm{vs},R/\mathrm{vs}\right)}\left(\omega \right)=\frac{F_m^{\left(\rho /\mathrm{vs}\right)}\left(\omega \right)}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$$

The total filter given by the relation [A11] is stable and constitutes the "distance encoding" part in the spatial ambisonic encoding according to the invention, as represented in FIG. 8. The coefficients of these filters correspond to the functions of FIG. monotonic transfer of the frequency, which tend towards the value 1 in high frequencies and towards the value (R / ρ) ^m in low frequencies. Referring to FIG. 9, the energy spectra of the filters ${\mathit{H}}_{\mathit{m}}^{\mathit{NFC}\mathit{(}\mathit{\rho }\mathit{/}\mathit{vs}\mathit{,}\mathit{R}\mathit{/}\mathit{vs}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)}$

translate the amplification of the encoded components, due to the field effect of the virtual source (placed here at a distance p = 1 m), with a pre-compensation of the field of the loudspeakers (placed at a distance R = 1 , 5 m). The amplification in decibels is therefore positive when p <R (case of FIG. 9) and negative when p> R (case of FIG. 10 where p = 3 m and R = 1.5 m). In a spatialized rendering device, the distance R between an auditory perception point and the speakers HP _i is actually of the order of one or a few meters.

sont conservées pour l'encodage directionnel.Referring again to FIG. 8, it will be understood that, in addition to the usual directional parameters θ and δ, information on the distances involved in the encoding will be transmitted. Thus, the angular functions corresponding to spherical harmonics ${\mathit{Y}}_{\mathit{mn}}^{\mathrm{\sigma }(\mathrm{\theta },\mathrm{\delta })}$

are preserved for directional encoding.

qui sont appliqués aux composantes ambisoniques, en fonction de leur ordre m, pour réaliser l'encodage de la distance, comme représenté sur la figure 8. Un mode de réalisation de ces filtres dans le domaine audionumérique sera décrit en détail plus loin.However, for the purposes of the present invention, it is furthermore possible to provide total filters (near-field compensation and, where appropriate, simulation of a near field) ${\mathit{H}}_{\mathit{m}}^{\mathit{NFC}\mathit{(}\mathit{\rho }\mathit{/}\mathit{vs}\mathit{,}\mathit{R}\mathit{/}\mathit{vs}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)}$

which are applied to the ambison components, according to their order m, to perform the encoding of the distance, as shown in Figure 8. An embodiment of these filters in the digital audio domain will be described in detail below.

It will be noted in particular that these filters can be applied as soon as the distance encoding (r) and even before the direction encoding (θ, δ). It will thus be understood that steps a) and b) above can be brought together in one and the same global step, or even be interchanged (with distance encoding and compensation filtering, followed by direction encoding). The method according to the invention is therefore not limited to a successive implementation over time of steps a) and b).

FIG. 11A represents a visualization (top view) of a near-field reconstruction with compensation, of a spherical wave, in the horizontal plane (with the same distance parameters as those of FIG. 9), for a total order system M = 15 and playback on 32 loudspeakers. FIG. 11B shows the propagation of the initial sound wave from a near-field source situated at a distance p from a point in the acquisition space that corresponds, in the restitution space at point P of Figure 7 of auditory perception. Note in FIG. 11A that the listeners (symbolized by schematized heads) can locate the virtual source in the same geographical location located at the distance p from the perception point P in FIG. 11B.

It is thus well verified that the shape of the encoded wavefront is respected after decoding and playback. However, there is substantially interference to the right of the point P as shown in Figure 11A due to the fact that the number of speakers (therefore ambison components considered) is not sufficient to restore the front perfectly waves in play over the entire area bounded by the speakers.

In what follows, it is described, by way of example, obtaining a digital audio filter for implementing the method within the meaning of the invention.

As indicated above, if one tries to simulate a near field effect, compensated as soon as the encoding is done, one applies to the ambisonic components of the sound a filter of the form: $$H_m^{\mathit{NFC}\left(\rho /\mathrm{vs},R/\mathrm{vs}\right)}\left(\omega \right)=\frac{F_m^{\left(\rho /\mathrm{vs}\right)}\left(\omega \right)}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$$

From the expression of the simulation of a near field given by the relation [A5], it appears that for distant sources (p = ∞), the relation [A11] simply becomes: $$\frac{1}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}=H_m^{\mathit{NFC}\left(\infty ,R/\mathrm{vs}\right)}\left(\omega \right)$$

It thus appears from this last relation [A12] that the case where the source to be simulated emits in far field (source distant) is only a special case of the general expression of the filter formulated in relation [A11].

In the field of digital audio processing, an advantageous method to set a digital filter from the analytical expression of this filter in the analog domain to continuous time is a "bilinear transform."

où τ = ρ/c (c étant la vitesse acoustique dans le milieu, typiquement 340 m/s dans l'air).We first express the relation [A5] in the form of a Laplace transform, which corresponds to: $$F_m^{\left(\tau \right)}\left(p\right)={\displaystyle \underset{\mathrm{not}=0}{\overset{m}{\Sigma }}\frac{\left(m+\mathrm{not}\right)!}{\left(m-\mathrm{not}\right)!\mathrm{not}!}{\left(\mathrm{two}\tau p\right)}^{-\mathrm{not}}}$$

where τ = ρ / c (where c is the acoustic velocity in the medium, typically 340 m / s in air).

si m est impair et $$H_m\left(z\right)={\displaystyle \prod _{q=1}^{m/2}\frac{b_0^q+b_1^q{z}^{-1}+b_2^q{z}^{-2}}{a_0^q+a_1^q{z}^{-1}+a_2^q{z}^{-2}}}$$

si m est pair,
où z est défini par $p=2f_s\frac{1-z^{-1}}{1+z^{-1}}$

par rapport à la relation [A13] précédente,
et avec : $$x_0=1-2\frac{\mathrm{Re}\left(X_{m,q}\right)}{\alpha }+\frac{{\left|X_{m,q}\right|}^2}{{\alpha }^2},\hspace{0.17em}{x}_1=-2\left(1-\frac{{\left|X_{m,q}\right|}^2}{{\alpha }^2}\right)$$

et $$x_2=1+2\frac{\mathrm{Re}\left(X_{m,q}\right)}{\alpha }+\frac{{\left|X_{m,q}\right|}^2}{{\alpha }^2}$$

$$x_0^{\left(m+1\right)/2}=1-\frac{X_{m,q}}{\alpha }\mathrm{\hspace{0.17em}\hspace{1em}\hspace{1em}\hspace{1em}et\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}}{x}_1^{\left(m+1\right)/2}=-\left(1+\frac{X_{m,q}}{\alpha }\right)$$

où α = 4f_s R/c pour x=a
et α = 4f_s ρ/c pour x=bThe bilinear transform consists in presenting, for a sampling frequency f _s , the relation [A11] in the form: $$Hm\left(z\right){\displaystyle \underset{q=1}{\overset{m/\mathrm{two}}{\Pi }}\frac{b_0^q+b_1^q{z}^{-1}+b_{\mathrm{two}}^q{z}^{-\mathrm{two}}}{{\mathrm{at}}_0^q+{\mathrm{at}}_1^q{z}^{-1}+{\mathrm{at}}_{\mathrm{two}}^q{z}^{-\mathrm{two}}}\times \frac{b_0^{\left(m+1\right)/\mathrm{two}}+b_1^{\left(m+1\right)/\mathrm{two}}{z}^{-1}}{{\mathrm{at}}_0^{\left(m+1\right)/\mathrm{two}}+{\mathrm{at}}_1^{\left(m+1\right)/\mathrm{two}}{z}^{-1}}}$$

if m is odd and $$H_m\left(z\right)={\displaystyle \underset{q=1}{\overset{m/\mathrm{two}}{\Pi }}\frac{b_0^q+b_1^q{z}^{-1}+b_{\mathrm{two}}^q{z}^{-\mathrm{two}}}{{\mathrm{at}}_0^q+{\mathrm{at}}_1^q{z}^{-1}+{\mathrm{at}}_{\mathrm{two}}^q{z}^{-\mathrm{two}}}}$$

if m is even,
where z is defined by $p=\mathrm{two}{f}_s\frac{1-z^{-1}}{1+z^{-1}}$

compared to the previous relation [A13],
and with : $$x_0=1-\mathrm{two}\frac{\mathrm{Re}\left(X_{m,q}\right)}{\alpha }+\frac{{\left|X_{m,q}\right|}^{\mathrm{two}}}{{\alpha }^{\mathrm{two}}},x_1=-\mathrm{two}\left(1-\frac{{\left|X_{m,q}\right|}^{\mathrm{two}}}{{\alpha }^{\mathrm{two}}}\right)$$

and $$x_{\mathrm{two}}=1+\mathrm{two}\frac{\mathrm{Re}\left(X_{m,q}\right)}{\alpha }+\frac{{\left|X_{m,q}\right|}^{\mathrm{two}}}{{\alpha }^{\mathrm{two}}}$$

$$x_0^{\left(m+1\right)/\mathrm{two}}=1-\frac{X_{m,q}}{\alpha }\mathrm{and}{x}_1^{\left(m+1\right)/\mathrm{two}}=-\left(1+\frac{X_{m,q}}{\alpha }\right)$$

where α = 4f _s R / c for x = a
and α = 4f _s ρ / c for x = b

et sont exprimées dans le tableau 1 ci-après, pour différents ordres m, sous les formes respectives de leur partie réelle, leur module (séparés par une virgule) et leur valeur (réelle) lorsque m est impair. Tableau 1 : valeurs R _e [X _m,q ], |X _m,q | (et R _e [X _m,m ] lorsque m est impair) d'un polynôme de Bessel calculées à l'aide du logiciel de calcul MATLAB©. m=1 -2.0000000000 m=2 -3.0000000000, 3.4641016151 m=3 -3.6778146454, 5.0830828022 ; -4.6443707093 m=4 -4.2075787944, 6.7787315854 ; -5.7924212056, 6.0465298776 m=5 -4.6493486064, 8.5220456027 ; -6.7039127983, 7.5557873219 ; -7.2934771907 m=6 -5.0318644956, 10.2983543043 -7.4714167127, 9.1329783045 -8.4967187917, 8.6720541026 m=7 -5.3713537579, 12.0990553610; -8.1402783273, 10.7585400670 ; -9.5165810563, 10.1324122997 ; -9.9435737171 m=8 -5.6779678978, 13.9186233016 ; -8.7365784344, 12.4208298072 ; -10.4096815813, 11.6507064310 ; -11.1757720865, 11.3096817388 m=9 -5.9585215964, 15.7532774523 ; -9.2768797744, 14.1121936859 ; -11.2088436390, 13.2131216226 ; -12.2587358086, 12.7419414392 ; -12.5940383634 m=10 -6.2178324673, 17.6003068759 ; -9.7724391337, 15.8272658299 ; -11.9350566572, 14.8106929213 ; -13.2305819310, 14.2242555605 ; -13.8440898109, 13.9524261065 m=11 -6.4594441798, 19.4576958063 ; -10.2312965678, 17.5621095176 ; -12.6026749098, 16.4371594915 ; -14.1157847751, 15.7463731900 ; -14.9684597220, 15.3663558234 ; -15.2446796908 m=12 -6.6860466156, 21.3239012076 ; -10.6594171817, 19.3137363168 ; -13.2220085001, 18.0879209819 ; -14.9311424804, 17.3012295772 ; -15.9945411996, 16.8242165032 ; -16.5068440226, 16.5978151615 m=13 -6.8997344413, 23.1977134580 ; -11.0613619668, 21.0798161546 ; -13.8007456514, 19.7594692366 ; -15.6887605582, 18.8836767359 ; -16.9411835315, 18.3181073534 ; -17.6605041890, 17.9988179873 ; -17.8954193236 m=14 -7.1021737668, 25.0781652657 ; -11.4407047669, 22.8584924996 ; -14.3447919297, 21.4490520815 ; -16.3976939224, 20.4898067617 ; -17.8220011429, 19.8423306934 ; -18.7262916698, 19.4389130000 ; -19.1663428016, 19.2447495545 m=15 -7.2947137247, 26.9644699653 ; -11.8003034312, 24.6482592959 ; -14.8587939669, 23.1544615283 ; -17.0649181370, 22.1165594535 ; -18.6471986915, 21.3925954403 ; -19.7191341042, 20.9118275261 ; -20.3418287818, 20.6361378957 ; -20.5462183256 m=16 -7.4784635949, 28.8559784487 ;-12.1424827551, 26.4478760957 ; -15.3464816324, 24.8738935490 ; -17.6959363478, 23.7614799683 ; -19.4246523327, 22.9655586516 ; -20.6502404436, 22.4128776078 ; -21.4379698156, 22.0627133056 ; -21.8237730778, 21.8926662470 m=17 -7.6543475694, 30.7521483222 ; -12.4691619784, 28.2563077987 ; -15.8108990691, 26.6058519104 ; -18.2951775164, 25.4225585034 ; -20.1605894729, 24.5585534450 ; -21.5282660840, 23.9384287933 ; -22.4668764601, 23.5193877036 ; -23.0161527444, 23.2766166711 ; -23.1970582109 m=18 -7.8231445835, 32.6525213363 ; -12.7819455282, 30.0726807554 ; -16.2545681590, 28.3490792784 ; -18.8662638563, 27.0981271991 ; -20.8600257104, 26.1693913642 ; -22.3600808236, 25.4856138632 ; -23.4378933084, 25.0022244227 ; -24.1362741870, 24.6925542646 ; -24.4798038436, 24.5412441597 m=19 -7.9855178345, 34.5567065132 ; -13.0821901901, 31.8962504142 ; -16.6796008200, 30.1025072510 ; -19.4122071436, 28.7867778706 ; -21.5270719955, 27.7962699865 ; -23.1512112785, 27.0520753105 ; -24.3584393996, 26.5081174988 ; -25.1941793616, 26.1363057951 ; -25.6855663388, 25.9191817486 ; -25.8480312755 X _{m, q} are the q successive roots of the Bessel polynomial: $$\begin{array}{l}{F}_m\left(x\right)={\displaystyle \underset{\mathrm{not}=0}{\overset{m}{\Sigma }}\frac{\left(m+\mathrm{not}\right)!}{\left(m-\mathrm{not}\right)!\mathrm{not}!}{X}^{m-\mathrm{not}}}\\ ={\displaystyle \underset{q=1}{\overset{m}{\Pi }}\left(X-X_{m,q}\right)}\end{array}$$

and are expressed in Table 1 below, for different orders m, in the respective forms of their real part, their module (separated by a comma) and their (real) value when m is odd. Table 1: values <i> R </ i>_{<i> e </ i>}[<i> X </ i><sub><i> m, q </ i>< / sub>], | <i> X </ i>_{<i> m, q </ i>} | (and <i> R </ i>_{<i> e </ i>}[<i> X </ i><sub><i> m, m </ i></ sub >] when m is odd) of a Bessel polynomial calculated using the MATLAB © calculation software. m = 1 -2.0000000000 m = 2 -3.0000000000, 3.4641016151 m = 3 -3.6778146454, 5.0830828022; -4.6443707093 m = 4 -4.2075787944, 6.7787315854; -5.7924212056, 6.0465298776 m = 5 -4.6493486064, 8.5220456027; -6.7039127983, 7.5557873219; -7.2934771907 m = 6 -5.0318644956, 10.2983543043 -7.4714167127, 9.1329783045 -8.4967187917, 8.6720541026 m = 7 -5.3713537579, 12.0990553610; -8.1402783273, 10.7585400670; -9.5165810563, 10.1324122997; -9.9435737171 m = 8 -5.6779678978, 13.9186233016; -8.7365784344, 12.4208298072; -10.4096815813, 11.6507064310; -11.1757720865, 11.3096817388 m = 9 -5.9585215964, 15.7532774523; -9.2768797744, 14.1121936859; -11.2088436390, 13.2131216226; -12.2587358086, 12.7419414392; -12.5940383634 m = 10 -6.2178324673, 17.6003068759; -9.7724391337, 15.8272658299; -11.9350566572, 14.8106929213; -13.2305819310, 14.2242555605; -13.8440898109, 13.9524261065 m = 11 -6.4594441798, 19.4576958063; -10.2312965678, 17.5621095176; -12.6026749098, 16.4371594915; -14.1157847751, 15.7463731900; -14.9684597220, 15.3663558234; -15.2446796908 m = 12 -6.6860466156, 21.3239012076; -10.6594171817, 19.3137363168; -13.2220085001, 18.0879209819; -14.9311424804, 17.3012295772; -15.9945411996, 16.8242165032; -16.5068440226, 16.5978151615 m = 13 -6.8997344413, 23.1977134580; -11.0613619668, 21.0798161546; -13.8007456514, 19.7594692366; -15.6887605582, 18.8836767359; -16.9411835315, 18.3181073534; -17.6605041890, 17.9988179873; -17.8954193236 m = 14 -7.1021737668, 25.0781652657; -11.4407047669, 22.8584924996; -14.3447919297, 21.4490520815; -16.3976939224, 20.4898067617; -17.8220011429, 19.8423306934; -18.7262916698, 19.4389130000; -19.1663428016, 19.2447495545 m = 15 -7.2947137247, 26.9644699653; -11.8003034312, 24.6482592959; -14.8587939669, 23.1544615283; -17.0649181370, 22.1165594535; -18.6471986915, 21.3925954403; -19.7191341042, 20.9118275261; -20.3418287818, 20.6361378957; -20.5462183256 m = 16 -7.4784635949, 28.8559784487; -12.1424827551, 26.4478760957; -15.3464816324, 24.8738935490; -17.6959363478, 23.7614799683; -19.4246523327, 22.9655586516; -20.6502404436, 22.4128776078; -21.4379698156, 22.0627133056; -21.8237730778, 21.8926662470 m = 17 -7.6543475694, 30.7521483222; -12.4691619784, 28.2563077987; -15.8108990691, 26.6058519104; -18.2951775164, 25.4225585034; -20.1605894729, 24.5585534450; -21.5282660840, 23.9384287933; -22.4668764601, 23.5193877036; -23.0161527444, 23.2766166711; -23.1970582109 m = 18 -7.8231445835, 32.6525213363; -12.7819455282, 30.0726807554; -16.2545681590, 28.3490792784; -18.8662638563, 27.0981271991; -20.8600257104, 26.1693913642; -22.3600808236, 25.4856138632; -23.4378933084, 25.0022244227; -24.1362741870, 24.6925542646; -24.4798038436, 24.5412441597 m = 19 -7.9855178345, 34.5567065132; -13.0821901901, 31.8962504142; -16.6796008200, 30.1025072510; -19.4122071436, 28.7867778706; -21.5270719955, 27.7962699865; -23.1512112785, 27.0520753105; -24.3584393996, 26.5081174988; -25.1941793616, 26.1363057951; -25.6855663388, 25.9191817486; -25.8480312755

The digital filters are thus implemented from the values of Table 1, by providing cascades of cells of order 2 (for m even), and an additional cell (for odd m), from the relationships [A14] given here. -before.

Digital filters are thus produced in an infinite impulse response form, which is easily parameterizable as shown above. It should be noted that an implementation in a finite impulse response form can be envisaged and consists in calculating the complex spectrum of the transfer function from the analytic formula, then deduce a finite impulse response by inverse Fourier transform. A convolution operation is then applied for filtering.

Thus, by introducing this pre-compensation of the near field to the encoding, a modified ambisonic representation is defined (FIG. 8), adopting as transmissible representation signals expressed in the frequency domain, in the form: $${\stackrel{}{B}}_{m\mathrm{not}}^{\sigma \left(R/\mathrm{vs}\right)}=\frac{1}{F_m^{R/\mathrm{vs}}\left(\omega \right)}{B}_{m\mathrm{not}}^{\sigma }$$

As indicated above, R is a reference distance with which a compensated near-field effect is associated and c is the speed of sound (typically 340 m / s in air). This modified ambisonic representation has the same scalability properties (schematically represented by transmitted data "surrounded" near the arrow TR of FIG. 1) and obeys the same transformations of rotation of the field (module 4 of FIG. usual ambisonic.

The operations to be implemented for the decoding of the received ambisonic signals are indicated below.

tels que décrits plus haut, mais avec des paramètres de distance R et R₂, au lieu de p et R. En particulier, il est à noter que seul le paramètre R/c est à mémoriser (et/ou transmettre) entre l'encodage et le décodage.It is firstly indicated that the decoding operation is adaptable to any rendering device, of radius R ₂ , different from the reference distance R above. For this purpose, filters of the type ${\mathit{H}}_{\mathit{m}}^{\mathit{NFC}\mathit{(}\mathit{\rho }\mathit{/}\mathit{vs}\mathit{,}\mathit{R}\mathit{/}\mathit{vs}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)},$

as described above, but with distance parameters R and R ₂ , instead of p and R. In particular, it should be noted that only the parameter R / c is to be memorized (and / or transmitted) between encoding and decoding.

adapte alors, à la réception des données, la pré-compensation à la distance R₁ pour une restitution à la distance R₂. Bien entendu, comme indiqué ci-avant, le dispositif de restitution reçoit aussi le paramètre R₁/c.Referring to FIG. 12, the filtering module represented therein is provided, for example, in a processing unit of a rendering device. Ambisonic components received were pre-compensated for encoding for a reference distance R ₁ as a second distance. However, the rendering device comprises a plurality of loudspeakers arranged at a third distance R ₂ from an auditory perception point P, this third distance R ₂ being different from the second aforementioned distance R ₁ . The filtering module of FIG. 12, in the form ${\mathit{H}}_{\mathit{m}}^{\mathit{NFC}\mathit{(}{\mathit{<figure-callout\; id="1"\; label="R"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">R</figure-callout>}}_1\mathit{/}\mathit{vs}\mathit{,}{\mathit{R}}_{\mathrm{two}}\mathit{/}\mathit{vs}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)},$

then adapts, upon reception of the data, the pre-compensation at the distance R ₁ for a reproduction at the distance R ₂ . Of course, as indicated above, the rendering device also receives the parameter R ₁ / c.

It should be noted that the invention also makes it possible to mix several ambisonic representations of sound fields (real and / or virtual sources), whose reference distances R are different (where appropriate with infinite reference distances and corresponding to distant sources). Preferably, a pre-compensation of all these sources will be filtered at a smallest reference distance, before mixing the signals ambisic, which allows the restitution to obtain a correct definition of the sound relief.

In the context of a so-called "sound focusing" treatment, with the restitution, a sound enrichment effect for a chosen direction of the space (in the manner of a light projector illuminating in a direction chosen in optics) , involving a sound focusing matrix processing (with weighting of the ambison components), the distance encoding with near-field pre-compensation is advantageously applied in combination with the focus processing.

In what follows, an ambisonic decoding method, with compensation of the near-field of the loudspeakers, is described for the restitution.

et en utilisant des hauts-parleurs d'un dispositif de restitution qui prévoit un emplacement "idéal" d'un auditeur qui correspond au point de restitution P de la figure 7, l'onde émise par chaque haut-parleur est définie par un traitement préalable de "ré-encodage" du champ ambisonique au centre du dispositif de restitution, comme suit.To reconstruct an acoustic field encoded according to the ambisonic formalism, from the components ${\mathit{B}}_{\mathit{mn}}^{\mathit{\sigma }}$

and using loudspeakers of a playback device which provides an "ideal" location for a listener corresponding to the playback point P of FIG. 7, the wave transmitted by each speaker is defined by a processing prior to "re-encoding" the ambisonic field in the center of the rendering device, as follows.

In this context of " re-encoding ", it is initially considered, and for simplification, that the sources emit in the far field.

par sa contribution ${\mathit{S}}_{\mathit{i}}\mathit{.}{\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}\mathit{(}{\mathit{\theta }}_{\mathit{i}}\mathit{,}{\mathit{\delta }}_{\mathit{i}}\mathit{)}\mathit{.}$

Referring again to FIG. 7, the wave emitted by a loudspeaker of index i and incidence (θ _i and δ _i ) is powered by a signal Si. This loudspeaker participates in the reconstruction of the component ${\mathit{B}}_{\mathit{mn}}^{\mathit{\text{'}}}\mathit{,}$

by his contribution ${\mathit{S}}_{\mathit{i}}\mathit{.}{\mathit{Y}}_{\mathit{mn}}^{\mathit{\sigma }}\mathit{(}{\mathit{\theta }}_{\mathit{i}}\mathit{,}{\mathit{\delta }}_{\mathit{i}}\mathit{)}\mathit{.}$

The vector c _i of the encoding coefficients associated with the speakers of index i is expressed by the relation: $${\mathrm{vs}}_i=\left[\begin{array}{l}{\mathrm{<figure-callout\; id="00"\; label="Y"\; filenames="imgf0011.png"\; state="\{\{state\}\}">Y</figure-callout>}}_{00}^{+1}\left({\theta }_i,{\delta }_i\right)\hfill \\ {\mathrm{<figure-callout\; id="11"\; label="Y"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Y</figure-callout>}}_{11}^{+1}\left({\theta }_i,{\delta }_i\right)\hfill \\ Y_{11}^{-1}\left({\theta }_i,{\delta }_i\right)\hfill \\ \cdots \hfill \\ Y_{m\mathrm{not}}^{\delta }\left({\theta }_i,{\delta }_i\right)\hfill \\ \cdots \hfill \end{array}\right]$$

The vector S of the signals emanating from the set of N loudspeakers is given by the expression: $$S=\left[\begin{array}{l}{S}_1\hfill \\ S_{\mathrm{two}}\hfill \\ \cdots \hfill \\ S_{\mathrm{NOT}}\hfill \end{array}\right]$$

où chaque terme c_i représente un vecteur selon la relation [B1] ci-avant.The matrix of encoding of these N loudspeakers (which finally corresponds to a matrix of "re-encoding"), is expressed by the relation: $$\mathrm{VS}=\left[{\mathrm{VS}}_1{\mathrm{VS}}_{\mathrm{two}}...{\mathrm{VS}}_{\mathrm{NOT}}\right]$$

where each term c _i represents a vector according to the relation [B1] above.

Thus, the reconstruction of the ambisonic field B 'is defined by the relation: $$\stackrel{}{B}=\left[\begin{array}{l}{B^{\text{'}}}_{00}^{+1}\hfill \\ {B^{\text{'}}}_{11}^{+1}\hfill \\ {B^{\text{'}}}_{11}^{-1}\hfill \\ \cdots \hfill \\ {B^{\text{'}}}_{m\mathrm{not}}^{\sigma }\hfill \\ \cdots \hfill \end{array}\right]=\mathrm{VS}.S$$

aux signaux ré-encodés B̃, pour définir la relation générale : $${\mathrm{B}}^{\prime }=\mathrm{B}$$

The relation [B4] thus defines a re-encoding operation, prior to the restitution. Finally, the decoding, as such, consists in comparing the original and received ambisonic signals by the rendering device, in the form: $$B=\left[\begin{array}{l}{\mathrm{<figure-callout\; id="00"\; label="B"\; filenames="imgf0011.png"\; state="\{\{state\}\}">B</figure-callout>}}_{00}^{+1}\hfill \\ {\mathrm{<figure-callout\; id="11"\; label="B"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">B</figure-callout>}}_{11}^{+1}\hfill \\ B_{11}^{-1}\hfill \\ \cdots \hfill \\ B_{m\mathrm{not}}^{\sigma }\hfill \\ \cdots \hfill \end{array}\right]$$

to the re-encoded signals B, to define the general relation: $${\mathrm{B}}^{\text{'}}=\mathrm{B}$$

It is, in particular, to determine the coefficients of a decoding matrix D, which verifies the relation: $$\mathrm{S}=\mathrm{D}.\mathrm{B}$$

où la notation C^T correspond à la transposée de la matrice C.Preferably, the number of loudspeakers is greater than or equal to the number of ambison components to be decoded and the decoding matrix D is expressed, as a function of the re-encoding matrix C, in the form: $$D={\mathrm{VS}}^T.{\left(\mathrm{VS}.{\mathrm{VS}}^T\right)}^{-1}$$

where the notation C ^T corresponds to the transpose of the matrix C.

It should be noted that the definition of decoding verifying different criteria by frequency bands is possible, which makes it possible to offer an optimized reproduction according to the listening conditions, in particular with regard to the positioning constraint at the center. O of the sphere of Figure 3, during the restitution. For this purpose, it is advantageous to provide simple filtering, in stepwise frequency equalization, to each ambisonic component.

sur chaque composante ambisonique du type ${\mathit{B}\mathit{\prime }}_{\mathit{mn}}^{\mathit{\sigma }}\mathit{.}$

En introduisant les termes de champ proche sous la forme d'une matrice diagonale, la relation [B4] ci-avant devient : $$B^{\prime }=\mathrm{Diag}\left(\left[\begin{array}{lllllll}1\hfill & F_1^{R/c}\left(\omega \right)\hfill & F_1^{R/c}\left(\omega \right)\hfill & \dots \hfill & F_m^{R/c}\left(\omega \right)\hfill & F_m^{R/c}\left(\omega \right)\hfill & \dots \hfill \end{array}\right]\right).C.S$$

However, to obtain a reconstruction of an originally encoded wave, it is necessary to correct the far-field hypothesis for the loudspeakers, that is to say to express the effect of their near field in the re-encoding matrix. C above and invert this new system to set the decoder. For this purpose, assuming a concentricity of the loudspeakers (arranged at the same distance R from point P of FIG. 7), all the loudspeakers have the same near-field effect ${\mathit{F}}_{\mathit{m}}^{\mathit{(}\mathit{R}\mathit{/}\mathit{vs}\mathit{)}}\mathit{\left(}\mathit{\omega }\mathit{\right)}\mathit{,}$

on each ambisonic component of the type ${\mathit{B}\mathit{\text{'}}}_{\mathit{mn}}^{\mathit{\sigma }}\mathit{.}$

By introducing the near-field terms as a diagonal matrix, the relation [B4] above becomes: $$B^{\text{'}}=\mathrm{Diag}\left(\left[\begin{array}{lllllll}1\hfill & F_1^{R/\mathrm{vs}}\left(\omega \right)\hfill & F_1^{R/\mathrm{vs}}\left(\omega \right)\hfill & ...\hfill & F_m^{R/\mathrm{vs}}\left(\omega \right)\hfill & F_m^{R/\mathrm{vs}}\left(\omega \right)\hfill & ...\hfill \end{array}\right]\right).\mathrm{VS}.S$$

The relation [B7] above becomes: $$S=D.\mathit{Diag}\left(\left[\begin{array}{lllllll}1\hfill & \frac{1}{F_1^{R/\mathrm{vs}}\left(\omega \right)}\hfill & \frac{1}{F_1^{R/\mathrm{vs}}\left(\omega \right)}\hfill & ...\hfill & \frac{1}{F_m^{R/\mathrm{vs}}\left(\omega \right)}\hfill & \frac{1}{F_m^{R/\mathrm{vs}}\left(\omega \right)}\hfill & ...\hfill \end{array}\right]\right).B$$

et qui peut être mise en oeuvre sous forme numérique, comme décrit ci-avant, en référence à la relation [A14].Thus, the mastering operation is preceded by a filtering operation that compensates for the near field on each component. ${\mathit{B}}_{\mathit{mn}}^{\mathit{\sigma }},$

and which can be implemented in digital form, as described above, with reference to relation [A14].

It should be noted that in practice, the matrix C of "re-encoding" is specific to the rendering device. Its coefficients can be determined initially by parameterization and sound characterization of the restitution device reacting to a predetermined excitation. The decoding matrix D is also specific to the rendering device. Its coefficients can be determined by the relation [B8]. By repeating the previous notation where B is the matrix of precompensated ambison components, these latter can be transmitted to the rendering device in matrix form B with: $$\stackrel{}{B}=\mathit{Diag}\left(\left[\begin{array}{lllllll}1\hfill & \frac{1}{F_1^{R/\mathrm{vs}}\left(\omega \right)}\hfill & \frac{1}{F_1^{R/\mathrm{vs}}\left(\omega \right)}\hfill & ...\hfill & \frac{1}{F_m^{R/\mathrm{vs}}\left(\omega \right)}\hfill & \frac{1}{F_m^{R/\mathrm{vs}}\left(\omega \right)}\hfill & ...\hfill \end{array}\right]\right).B$$

The rendering device then decodes the received data in matrix form B (column vector of the transmitted components) by applying the decoding matrix D to the pre-compensated ambisonic components, to form the signals Si intended to feed the speakers HP _i , with : $$S=\left(\begin{array}{l}{S}_1\hfill \\ S_i\hfill \\ S_{\mathrm{NOT}}\hfill \end{array}\right)=D.\stackrel{}{B}$$

pour l'adapter à un dispositif de restitution de rayon R₂. L'opération de décodage proprement dite est effectuée ensuite, comme décrit ci-avant, en référence à la relation [B11].Referring again to FIG. 12, if a decoding operation is to be adapted to a rendering device with a radius R ₂ other than the reference distance R ₁ , an adaptation module prior to the decoding proper and described hereinafter before filtering each ambisonic component ${\tilde{\mathit{B}}}_{\mathit{mn}}^{\mathit{\sigma }},$

to adapt it to a restitution device of radius R ₂ . The actual decoding operation is then performed, as described above, with reference to the relation [B11].

An application of the invention to binaural synthesis is described below.

${\overrightarrow{\mathit{r}}}_{\mathit{R}}$

et ${\overrightarrow{\mathit{r}}}_{\mathit{L}}\mathit{.}$

Referring to Fig. 13A, a listener having a two-headset headset of a binaural synthesis device is shown. The two ears of the listener are arranged at respective points O _L (left ear) and O _R (right ear) of the space. The center of the listener's head is located at point O and the radius of the listener's head is of value a. A sound source must be audibly perceived at a point M in the space, at a distance r from the center of the listener's head (and respectively at distances r _R from the right ear and r _L from the ear left). In addition, the direction of the source at the point M is defined by the vectors $\overrightarrow{\mathit{r}},$

${\overrightarrow{\mathit{r}}}_{\mathit{R}}$

and ${\overrightarrow{\mathit{r}}}_{\mathit{The}}\mathit{.}$

In general, binaural synthesis is defined as follows.

Each listener has an ear shape of its own. The perception of a sound in the space by this listener is done by learning, from birth, according to the form of the ears (in particular the shape of the pavilions and the dimensions of the head) peculiar to this listener. The perception of sound in space is manifested inter alia by the fact that the sound reaches one ear, before the other ear, which results in a delay τ between the signals to be emitted by each earphone of the device. restitution applying binaural synthesis.

The playback device is initially set, for the same listener, by scanning a sound source around his head, at the same distance R from the center of his head. It will be understood that this distance R can be considered as a distance between a "restitution point" as stated above and a point of auditory perception (here the center O of the listener's head).

In what follows, the index L is associated with the signal to be restored by the earpiece attached to the left ear and the index R is associated with the signal to be restored by the earpiece attached to the right ear. Referring to Fig. 13B, a delay for each channel for producing a signal for a separate earphone is applied to the initial signal S. These delays τ _L and τ _R are a function of a maximum delay τ _MAX which corresponds here to the ratio a / c where a, as indicated previously, corresponds to the radius of the listener's head and c to the speed of sound. In particular, these delays are defined as a function of the difference in distance from the point O (center of the head) to the point M (position of the source whose sound is to be restored, in FIG. 13A) and of each ear at this point. M. Advantageously, respective gains g _L and g _R are also applied to each channel, which are a function of a ratio of the distances from the point O to the point M and from each ear to the point M. The respective modules applied to each channel 2 _L and 2 _R encode the signals of each channel, in an ambisonic representation, with near field pre-compensation NFC (for "Near Field Compensation") in the sense of the present invention. It will thus be understood that, by implementing the method within the meaning of the present invention, it is possible to define the signals coming from the source M, not only by their direction (azimuthal angles θ _L and θ _R and elevation angles δ _L and δ _R ), but also as a function of the distance separating each ear r _L and r _R from the source M. The signals thus encoded are transmitted to the reproduction device comprising ambisonic decoding modules, for each channel, 5 _L and 5 _R. Thus, an ambisonic encoding / decoding, with near-field compensation, is applied for each channel (left listener, right listener) in the binaural synthesis restitution (here of type "B-FORMAT"), in split form. The near-field compensation is effected, for each channel, with the first distance p a distance r _L and r _R between each ear and the position M of the sound source to be restored.

An application of the compensation in the sense of the invention, in the context of the sound acquisition in ambisonic representation, is described below.

Referring to FIG. 14, a microphone 141 comprises a plurality of transducer capsules capable of picking up acoustic pressures and reproducing electrical signals S _l , ..., S _N. Caps CAP _i are arranged on a sphere of predetermined radius r (here, a rigid sphere, such as a ping-pong ball for example). The capsules are spaced with a regular pitch on the sphere. In practice, the number N of capsules is chosen according to the desired order M for the ambisonic representation.

In the context of a microphone comprising capsules arranged on a rigid sphere, it is indicated below how to compensate for the near field effect, as soon as encoding in the ambisonic context. It will thus be shown that the pre-compensation of the near field can be applied not only for the virtual source simulation, as indicated above, but also to the acquisition and, more generally, by combining the pre-compensation of field close to all types of treatments involving an ambisonic representation.

In the presence of a rigid sphere (capable of introducing a diffraction of the sound waves received), the relation [A1] given above becomes: $$P_r\left({\overrightarrow{u}}_i\right)={\displaystyle \underset{m=0}{\overset{\infty }{\Sigma }}\frac{j^{m-1}}{{\left(kr\right)}^{\mathrm{two}}{h}_m^{{-}^{\text{'}}}\left(kr\right)}}{\displaystyle \underset{\begin{array}{l}0\le \mathrm{not}\le m\\ \sigma =\pm 1\end{array}}{<figure-callout\; id="0"\; label="\Sigma "\; filenames="imgf0004.png,imgf0007.png"\; state="\{\{state\}\}">\Sigma </figure-callout>}{B}_{m\mathrm{not}}^{\sigma }{Y}_{m\mathrm{not}}^{\sigma }\left({\overrightarrow{u}}_i\right)}$$

Derivatives of Hankel spherical functions h ^- _m obey the law of recurrence: $$\left(\mathrm{two}m+1\right)h_m^{{-}^{\text{'}}}\left(x\right)=m{h}_{m-1}^{-}\left(x\right)-\left(m+1\right)h_{m+1}^{-}\left(x\right)$$

du champ initial à partir du champ de pression à la surface de la sphère, en mettant en oeuvre des opérations de projection et d'égalisation données par la relation : $$B_{mn}^{\sigma }=E{Q}_m<p_r|Y_{mn}^{\sigma }>4\pi$$

We deduce the ambisonic components ${\mathit{B}}_{\mathit{mn}}^{\mathit{\sigma }}$

of the initial field from the pressure field to the surface of the sphere, by implementing projection and equalization operations given by the relation: $$B_{m\mathrm{not}}^{\sigma }=E{Q}_m<p_r|Y_{m\mathrm{not}}^{\sigma }>4\pi$$

In this expression, EQ _m is an equalizer filter that compensates a weighting W _m which is related to the directivity of the capsules and which further includes the diffraction by the rigid sphere.

The expression of this filter EQ _m is given by the following relation: $${\mathrm{EQ}}_m=\frac{1}{W_m}={\left(kr\right)}^{\mathrm{two}}{h}_m^{{-}^{\text{'}}}\left(kr\right)j^{-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m\; </figure-callout>}+1}$$

The coefficients of this equalization filter are not stable and we obtain an infinite gain at very low frequencies. Moreover, it should be noted that the spherical harmonic components, themselves, are not of finite amplitude when the sound field is not limited to propagation of plane waves, that is to say from distant sources, as we saw earlier.

On the other hand, if, instead of providing capsules embedded in a solid sphere, cardioid-type capsules with a far-field directivity given by the expression: $$\mathrm{BOY\; WUT}\left(\theta \right)=\alpha +\left(1-\alpha \right)\cos \theta$$

By considering these capsules mounted on an "acoustically transparent" support , the weighting term to be compensated becomes: $$W_m=j^m\left(\alpha jm\left(kr\right)-j\left(1-\alpha \right)j{m}^{\text{'}}\left(kr\right)\right)$$

It also appears that the coefficients of an equalization filter corresponding to the analytical inverse of this weighting given by the relation [C6] are divergent for very low frequencies.

In general, it is indicated that for any type of sensor directivity, the gain of the filter EQ _m to compensate for the weighting W _m related to the directivity of the sensors is infinite for the low frequencies of sound. Referring to FIG. 14, a near field pre-compensation is advantageously applied in the expression of the equalization filter EQ _m , given by the relation: $${\mathrm{EQ}}_m^{\mathit{NFC}\left(R/\mathrm{vs}\right)}\left(\omega \right)=\frac{{\mathit{EQ}}_m\left(r,\omega \right)}{F_m^{\left(R/\mathrm{vs}\right)}\left(\omega \right)}$$

Thus, the signals S ₁ to S _N are recovered from the microphone 141. If necessary, a pre-equalization of these signals is applied by a processing module 142. The module 143 makes it possible to express these signals in the ambisonic context, under matrix form. The module 144 applies the filter of the relation [C7] to the components ambisonic expressed as a function of the radius r of the sphere of the microphone 141. The near-field compensation is performed for a reference distance R as a second distance. The signals encoded and thus filtered by the module 144 can be transmitted, if necessary, with the parameter representative of the reference distance R / c.

Thus, it appears in the various embodiments respectively related to the creation of a virtual source in the near field, to the acquisition of sound signals from real sources, or even to restitution (to compensate for a near-field effect of loudspeakers), that near-field compensation within the meaning of the present invention can be applied to all types of processing involving an ambisonic representation. This near-field compensation makes it possible to apply the ambisonic representation to a multiplicity of sound contexts where the direction of a source and advantageously its distance must be taken into account. Moreover, the possibility of the representation of sound phenomena of all types (near or far fields) in the ambisonic context is ensured by this pre-compensation, because of the limitation to finite real values of the ambison components.

Of course, the present invention is not limited to the embodiment described above by way of example; it extends to other variants.

(figure 4). On peut alors construire les diverses composantes harmoniques sphériques (avec un ordre M choisi) en appliquant une correction de gain pour chaque composante ambisonique et on applique une compensation de champ proche des hauts-parleurs (avec une distance de référence R séparant les haut-parleurs du point de perception auditive comme représenté sur la figure 7).Thus, it will be understood that the near-field pre-compensation can be integrated, at the encoding, as much for a near source as for a distant source. In the latter case (distant source and plane wave reception), the distance p expressed above will be considered infinite, without substantially modifying the expression of the filters H _m given above. Thus, processing using room effect processors that typically provide decorrelated signals that can be used to model the late diffuse field (late reverberation) can be combined with near field pre-compensation. We can consider that these signals are of the same energy and correspond to a part of diffuse field corresponding to the omnidirectional component $\mathit{W}={\mathit{<figure-callout\; id="00"\; label="B"\; filenames="imgf0011.png"\; state="\{\{state\}\}">B</figure-callout>}}_{00}^{+1}$

(Figure 4). The various spherical harmonic components (with a chosen order M) can then be constructed by applying a gain correction for each ambisonic component and a field compensation close to the loudspeakers (with a reference distance R separating the loudspeakers the point of auditory perception as shown in Figure 7).

Of course, the encoding principle in the sense of the present invention is generalizable to radiation models other than monopolar sources (real or virtual) and / or speakers. Indeed, any form of radiation (including a source spread in space) can be expressed by integration of a continuous distribution of point elementary sources.

In addition, in the context of rendering, it is possible to adapt the near-field compensation to any rendering context. For this purpose, it is possible to calculate transfer functions (re-encoding the spherical harmonic components of the near field for each loudspeaker, taking into account a real propagation in the room where the sound is restored), as well as an inversion of this re-encoding to redefine the decoding.

A decoding method has been described above in which a matrix system involving the ambison components is applied. In a variant, it may be provided a generalized processing by fast Fourier transforms (circular or spherical) to limit the computing time and computing resources (in terms of memory) necessary for the decoding process.

As indicated above with reference to FIGS. 9 and 10, it can be seen that the choice of a reference distance R with respect to the distance p from the near-field source introduces a difference in gain for different values of the sound frequency. It is indicated that the pre-compensation encoding method may be coupled to a digital audio compression for quantizing and adjusting the gain for each frequency subband.

Advantageously, the present invention applies to all types of sound spatialization systems, especially for "virtual reality" type applications (navigation in virtual scenes in three-dimensional space, cat-type conversations on the Internet), interface sonification, audio editing software for recording, mixing and restoring music, but also for acquiring, from use of three-dimensional microphones, for taking musical or cinematic sound, or for the transmission of sound environment on the Internet, for example for "Webcam" sound.

Claims (22)

1. A method of processing sound data, in which:

   a) signals representative of at least one sound propagating in a three-dimensional space and arising from a source situated at a first distance (ρ) from a reference point (O) are coded so as to obtain a representation of the sound by components (B_mn ^σ) expressed in a base of spherical harmonics, of origin corresponding to said reference point (O),

   b) and a compensation of a near field effect is applied to said components (B_mn ^σ) by a filtering which is dependent on a second distance (R) defining substantially, for a playback of the sound by a playback device, a distance between a playback point (HP_i) and a point (P) of auditory perception.
2. The method as claimed in claim 1, in which, said source being far removed from the reference point (O),

   - components of successive orders m are obtained for the representation of the sound in said base of spherical harmonics, and

   - a filter (1/F_m) is applied, the coefficients of which, each applied to a component of order m, are expressed analytically in the form of the inverse of a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said second distance (R), so as to compensate for a near field effect at the level of the playback device.
3. The method as claimed in claim 1, in which, said source being a virtual source envisaged at said first distance (ρ),

   - components of successive orders m are obtained for the representation of the sound in said base of spherical harmonics, and

   - a global filter (H_m) is applied, the coefficients of which, each applied to a component of order m, are expressed analytically in the form of a fraction; in which:

   - the numerator is a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said first distance (p), so as to simulate a near field effect of the virtual source, and

   - the denominator is a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said second distance (R), so as to compensate for the effect of the near field of the virtual source in the low sound frequencies.
4. The method as claimed in one of the preceding claims, in which the data coded and filtered in steps a) and b) are transmitted to the playback device with a parameter representative of said second distance (R/c).
5. The method as claimed in one of claims 1 to 3, in which, the playback device comprising means for reading a memory medium, the data coded and filtered in steps a) and b) are stored with a parameter representative of said second distance (R/c) on a memory medium intended to be read by the playback device.
6. The method as claimed in one of claims 4 and 5, in which, prior to a sound playback by a playback device comprising a plurality of loudspeakers disposed at a third distance (R₂) from said point of auditory perception (P), an adaptation filter (H_m ^{(R1/c, R2/c}) whose coefficients are dependent on said second (R₁) and third distances (R₂) is applied to the coded and filtered data.
7. The method as claimed in claim 6, in which the coefficients of said adaptation filter (H_m ^(R1/c,R2/c)), each applied to a component of order m, are expressed analytically in the form of a fraction, in which:

   - the numerator is a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said second distance (R),

   - and the denominator is a polynomial of power m, whose variable is inversely proportional to the sound frequency and to said third distance (R₂),
8. The method as claimed in one of claims 2, 3 and 7, in which, for the implementation of step b), there is provided:

   - in respect of the components of even order m, audiodigital filters in the form of a cascade of cells of order two; and

   - in respect of the components of odd order m, audiodigital filters in the form of a cascade of cells of order two and an additional cell of order one.
9. The method as claimed in claim 8, in which the coefficients of an audiodigital filter, for a component of order m, are defined from the numerical values of the roots of said polynomials of power m.
10. The method as claimed in one of claims 2, 3, 7, 8 and 9, in which said polynomials are Bessel polynomials.
11. The method as claimed in one of claims 1, 2 and 4 to 10, in which there is provided a microphone comprising an array of acoustic transducers arranged substantially on the surface of a sphere whose center corresponds substantially to said reference point (O), so as to obtain said signals representative of at least one sound propagating in the three-dimensional space.
12. The method as claimed in claim 11, in which a global filter is applied in step b) so as, on the one hand, to compensate for a near field effect as a function of said second distance (R) and, on the other hand, to equalize the signals arising from the transducers so as to compensate for a weighting of directivity of said transducers.
13. The method as claimed in one of claims 11 and 12, in which there is provided a number of transducers that depends on a total number of components chosen to represent the sound in said base of spherical harmonics.
14. The method as claimed in one of the preceding claims, in which in step a) a total number of components is chosen from the base of spherical harmonics so as to obtain, on playback, a region of the space around the point of perception (P) in which the playback of the sound is faithful and whose dimensions are increasing with the total number of components.
15. The method as claimed in claim 14, in which there is provided a playback device comprising a number of loudspeakers at least equal to said total number of components.
16. The method as claimed in one of claims 1 to 5 and 8 to 13, in which:

    - there is provided a playback device comprising at least a first and a second loudspeaker disposed at a chosen distance from a listener,

    - a cue of awareness of the position in space of sound sources situated at a predetermined reference distance (R) from the listener is obtained for this listener, and

    - the compensation of step b) is applied with said reference distance substantially as second distance.
17. The method as claimed in one of claims 1 to 3 and 8 to 13, taken in combination with one of claims 4 and 5, in which:

    - there is provided a playback device comprising at least a first and a second loudspeaker disposed at a chosen distance from a listener,

    - a cue of awareness of the position in space of sound sources situated at a predetermined reference distance (R₂) from the listener is obtained for this listener, and

    - prior to a sound playback by the playback device, an adaptation filter (H_m ^{(R/c, R2/c)}), whose coefficients are dependent on the second distance (R) and substantially on the reference distance (R₂), is applied to the data coded and filtered in steps a) and b).
18. The method as claimed in one of claims 16 and 17, in which:

    - the playback device comprises a headset with two headphones for the respective ears of the listener, and

    - separately for each headphone, the coding and the filtering of steps a) and b) are applied with regard to respective signals intended to be fed to each headphone, with, as first distance (p), respectively a distance (r_R, r_L) separating each ear from a position (M) of a source to be played back.
19. The method as claimed in one of the preceding claims, in which a matrix system is fashioned, in steps a) and b), said system comprising at least:

    - a matrix (B) comprising said components in the base of spherical harmonics, and

    - a diagonal matrix (Diag (1/F_m)) whose coefficients correspond to filtering coefficients of step b), and said matrices are multiplied to obtain a result matrix of compensated components (B̃).
20. The method as claimed in claim 19, in which:

    - the playback device comprises a plurality of loudspeakers disposed substantially at one and the same distance (R) from the point of auditory perception (P), and

    - to decode said data coded and filtered in steps a) and b) and to form signals suitable for feeding said loudspeakers:

    * a matrix system is formed comprising said result matrix (B̃) and a predetermined decoding matrix (D), specific to the playback device, and

    * a matrix (S) is obtained comprising coefficients representative of the loudspeakers feed signals by multiplication of the matrix of the compensated components (B) by said decoding matrix (D).
21. A. sound acquisition device, comprising a microphone furnished with an array of acoustic transducers disposed substantially on the surface of a sphere, characterized in that it furthermore comprises a processing unit arranged so as to:

    - receive signals each emanating from a transducer,

    - apply a coding to said signals so as to obtain a representation of the sound by components (B_mn ^σ) expressed in a base of spherical harmonics, of origin corresponding to the center of said sphere (O),

    - and apply a filtering to said components (B_mn ^σ), which filtering is dependent, on the one hand, on a distance corresponding to the radius of the sphere (r) and, on the other hand, on a reference distance (R).
22. The device as claimed in claim 21, characterized in that said filtering consists, on the one hand, in equalizing, as a function of the radius of the sphere, the signals arising from the transducers so as to compensate for a weighting of directivity of said transducers and, on the other hand, in compensating for a near field effect as a function of a chosen reference distance (R), defining substantially, for a playback of the sound, a distance between a playback point (HP_i) and a point (P) of auditory perception.

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