EP1479266B1 - Method and device for control of a unit for reproduction of an acoustic field - Google Patents

Description

The present invention relates to a method and a device for controlling a set of restitution of an acoustic field.

Sound is an undulatory acoustic phenomenon that evolves in time and space. Existing techniques act mainly on the temporal aspect of the sounds, the treatment of the spatial aspect being very incomplete.

Indeed, the existing high quality rendering systems impose de facto a predetermined spatial configuration of the restitution set.

For example, so-called multichannel systems send different and predetermined signals to several speakers whose distribution is fixed and known.

Similarly, so-called "ambisonic" systems, which consider the direction of origin of sounds that reach a listener, require a set of restitution whose configuration must respect certain positioning rules.

In these systems, the sound environment is likened to an angular distribution of sound sources around a point, corresponding to the listening position. The signals correspond to a decomposition of this distribution on the basis of directivity functions called spherical harmonics.

In the current state of development of these systems, a good quality reproduction is only possible with a spherical distribution of the speakers and a substantially regular angular distribution.

Thus, when the existing techniques are implemented with a restitution set whose spatial distribution is arbitrary, the quality of restitution is greatly deteriorated, in particular because of angular distortions. Document is known WO94 / 24835 a method for measuring and restoring an acoustic field using only two-dimensional modeling of the acoustic field.

Recent technical developments make it possible to consider a modeling in time and in three dimensions of the space of an acoustic field rather than the angular distribution of the sound environment.

In particular, the doctoral thesis «Representation of acoustic fields, application to the transmission and reproduction of complex sound scenes in a multimedia context» Paris VI University, Jérôme Daniel, July 11, 2000 , defines functions describing the wave characteristics of an acoustic field and allowing a decomposition on the basis of space and time functions that completely describes a three-dimensional acoustic field.

However, in this document, the theoretical solutions are based on so-called "Ambisonic" systems and a high quality reproduction can only be obtained for the existing regular spherical distributions. No element allows to ensure a high quality reproduction from any spatial configuration of the restitution set.

It therefore appears that no system of the prior art makes it possible to perform quality restitution from any given spatial configuration of the reproduction unit.

The object of the invention is to remedy this problem by providing a method and a device for determining driving signals of a set of reproduction of an acoustic field whose spatial configuration is arbitrary.

The invention relates to a control method as defined in claim 1.

• ladite étape d'établissement d'un nombre fini de coefficients représentatifs de la distribution dudit champ acoustique à restituer comporte :
  • une étape consistant à fournir un signal d'entrée comportant des informations temporelles et spatiales d'un environnement sonore ; et
  • une étape de mise en forme dudit signal d'entrée par décomposition desdites informations sur une base de fonctions spatio-temporelles, cette étape de mise en forme permettant de délivrer une représentation dudit champ acoustique à restituer correspondant audit environnement sonore sous la forme d'une combinaison linéaire desdites fonctions ;
• ladite étape d'établissement d'un nombre fini de coefficients représentatifs de la distribution dudit champ acoustique à restituer comporte :
  • une étape consistant à fournir un signal d'entrée comportant un nombre fini de coefficients représentatifs dudit champ acoustique à restituer sous la forme d'une combinaison linéaire de fonctions spatio-temporelles ;
• lesdites fonctions spatio-temporelles sont des fonctions dites de Fourier-Bessel et/ou des combinaisons linéaires de ces fonctions ;
• ladite sous-étape de prise en compte de caractéristiques au moins spatiales dudit ensemble de restitution est réalisée au moins à partir de paramètres représentatifs, pour chaque élément, des trois coordonnées de sa position par rapport au centre placé dans la zone d'écoute, et/ou de sa réponse spatio-temporelle ;
• ladite sous-étape de prise en compte de caractéristiques au moins spatiales dudit ensemble de restitution est réalisée en outre à partir :
  • de paramètres décrivant, sous forme de coefficients de pondération, une fenêtre spatiale qui spécifie la répartition dans l'espace de contraintes de reconstruction du champ acoustique ; et
  • d'un paramètre décrivant un ordre de fonctionnement limitant le nombre de coefficients à prendre en compte lors de ladite étape de détermination de filtres de reconstruction ;
• ladite sous-étape de prise en compte de caractéristiques au moins spatiales dudit ensemble de restitution est réalisée en outre à partir :
  • de paramètres constituant une liste de fonctions spatio-temporelles dont la reconstruction est imposée ; et
  • d'un paramètre décrivant un ordre de fonctionnement limitant le nombre de coefficients à prendre en compte lors de ladite étape de détermination de filtres de reconstruction ;
• ladite étape de prise en compte de caractéristiques au moins spatiales dudit ensemble de restitution est réalisée en outre au moins à partir d'un des paramètres choisis dans le groupe constitué :
  • de paramètres représentatifs d'au moins une des trois coordonnées de la position de chaque ou certains des éléments, par rapport au centre placé dans la zone d'écoute ;
  • de paramètres représentatifs des réponses spatio-temporelles de chaque ou certains des éléments ;
  • d'un paramètre décrivant un ordre de fonctionnement limitant le nombre de coefficients à prendre en compte lors de ladite étape de détermination de filtres de reconstruction ;
  • de paramètres constituant une liste de fonctions spatio-temporelles dont la reconstruction est imposée ;
  • de paramètres représentatifs des gabarits desdits éléments de restitution ;
  • d'un paramètre représentatif de la capacité d'adaptation locale souhaitée à l'irrégularité spatiale de la configuration dudit ensemble de restitution ;
  • d'un paramètre définissant le modèle de rayonnement desdits éléments de restitution ;
  • de paramètres représentatifs de la réponse en fréquence desdits éléments de restitution ;
  • d'un paramètre représentatif d'une fenêtre spatiale ;
  • de paramètres représentatifs d'une fenêtre spatiale sous forme de coefficients de pondération ; et
  • d'un paramètre représentatif du rayon d'une fenêtre spatiale lorsque celle-ci est une boule ;
• le procédé comporte une étape de calibrage permettant de délivrer tout ou partie des paramètres utilisés dans ladite étape de détermination de filtres de reconstruction ;
• ladite étape de calibrage comporte, pour au moins l'un des éléments de restitution :
  • une sous-étape d'acquisition de signaux représentatifs du rayonnement dudit au moins un élément dans le lieu d'écoute ; et
  • une sous-étape de détermination de paramètres spatiaux et/ou acoustiques dudit au moins un élément ;
• ladite étape de calibrage comporte :
  • une sous-étape d'émission d'un signal spécifique vers ledit au moins un élément dudit ensemble de restitution, ladite sous-étape d'acquisition correspondant à l'acquisition de l'onde sonore émise en réponse par ledit au moins un élément ; et
  • une sous-étape de transformation desdits signaux acquis en un nombre fini de coefficients représentatifs de l'onde sonore émise, afin de permettre la réalisation de ladite sous-étape de détermination de paramètres spatiaux et/ou acoustiques ;
• ladite sous-étape d'acquisition correspond à une sous-étape de réception d'un nombre de coefficients représentatifs du champ acoustique généré par ledit au moins un élément sous la forme d'une combinaison linéaire de fonctions spatio-temporelles, lesquels coefficients sont directement utilisés lors de ladite sous-étape de détermination de paramètres spatiaux et/ou acoustiques dudit au moins un élément ;
• ladite sous-étape de calibrage comporte en outre une sous-étape de détermination de la position dans au moins l'une des trois dimensions de l'espace dudit au moins un élément dudit ensemble de restitution ;
• ladite étape de calibrage comporte en outre une sous-étape de détermination de la réponse spatio-temporelle dudit au moins un élément dudit ensemble de restitution ;
• ladite-étape de calibrage comporte en outre une sous-étape de détermination de la réponse en fréquence dudit au moins un élément dudit ensemble de restitution ;
• le procédé comporte une étape de simulation de tout ou partie des paramètres nécessaires à la réalisation de ladite étape de détermination de filtres de reconstruction ;
• ladite étape de simulation comporte :
  • une sous-étape de détermination des paramètres manquants parmi les paramètres utilisés lors de ladite étape de détermination de filtres de reconstruction ;
  • une pluralité de sous-étapes de calcul permettant de déterminer la ou les valeurs du ou des paramètres manquants tels que définis précédemment en fonction des paramètres reçus, de la fréquence, et de valeurs par défaut prédéterminées ;
• ladite étape de simulation comporte une sous-étape de détermination d'une liste d'éléments de l'ensemble de restitution actifs en fonction de la fréquence, et lesdites sous-étapes de calcul sont réalisées pour les seuls éléments de ladite liste ;
• ladite étape de simulation comporte une sous-étape de calcul d'un paramètre représentatif de l'ordre de fonctionnement limitant le nombre de coefficients à prendre en compte lors de ladite étape de détermination de filtres de reconstruction à partir au moins de la position dans l'espace de tout ou partie des éléments de l'ensemble de restitution ;
• ladite étape de simulation comporte une étape de détermination de paramètres représentatifs d'une fenêtre spatiale sous forme de coefficients de pondération à partir d'un paramètre représentatif de la fenêtre spatiale dans le répère sphérique et/ou d'un paramètre représentatif du rayon de ladite fenêtre spatiale lorsque celle-ci est une boule ;
• ladite étape de simulation comporte une sous-étape de détermination d'une liste de fonctions spatio-temporelles dont la reconstruction est imposée à partir de la position de tout ou partie des éléments de l'ensemble de restitution ;
• le procédé comporte une étape de saisie permettant de déterminer tout ou partie des paramètres utilisés lors de ladite étape de détermination de filtres de reconstruction ;
• ladite étape de détermination de filtres de reconstruction comprend :
  • une pluralité de sous-étapes de calcul réalisées pour un nombre fini de fréquences de fonctionnement et permettant de délivrer une matrice de pondération du champ acoustique, une matrice représentative du rayonnement de l'ensemble de restitution, et une matrice représentative des fonctions spatio-temporelles dont la reconstruction est imposée ; et
  • une sous-étape de calcul d'une matrice de décodage, réalisée pour un nombre fini de fréquences de fonctionnement, à partir de la matrice de pondération du champ acoustique, de la matrice représentative du rayonnement de l'ensemble de restitution, de la matrice représentative des fonctions spatio-temporelles dont la reconstruction est imposée, et d'un paramètre représentatif de la capacité d'adaptation locale souhaitée à l'irrégularité spatiale de l'ensemble de restitution, représentative des filtres de reconstruction ;
• ladite sous-étape de calcul permettant de délivrer une matrice représentative du rayonnement de l'ensemble de restitution, est réalisée à partir de paramètres représentatifs pour chaque élément :
  • des trois coordonnées de sa position par rapport au centre placé dans la zone d'écoute ; et/ou
  • de sa réponse spatio-temporelle ; et
• ladite sous-étape de calcul permettant de délivrer une matrice représentative du rayonnement de l'ensemble de restitution est réalisée en outre à partir de paramètres représentatifs pour chaque élément de sa réponse en fréquence.

According to other characteristics:

• said step of establishing a finite number of coefficients representative of the distribution of said acoustic field to be restored comprises:
  • a step of providing an input signal including temporal and spatial information of a sound environment; and
  • a step of shaping said input signal by decomposing said information on a basis of spatio-temporal functions, this shaping step making it possible to deliver a representation of said acoustic field to be restored corresponding to said sound environment in the form of a linear combination of said functions;
• said step of establishing a finite number of coefficients representative of the distribution of said acoustic field to be restored comprises:
  • a step of providing an input signal having a finite number of coefficients representative of said acoustic field to be rendered as a linear combination of spatio-temporal functions;
• said spatio-temporal functions are Fourier-Bessel functions and / or linear combinations of these functions;
• said sub-step of taking into account at least spatial characteristics of said restitution set is made at least from representative parameters, for each element, of the three coordinates of its position relative to the center placed in the listening area, and / or its spatio-temporal response;
• said substep of taking into account at least spatial characteristics of said restitution set is furthermore made from:
  • parameters describing, in the form of weighting coefficients, a spatial window that specifies the spatial distribution of reconstruction constraints of the acoustic field; and
  • a parameter describing an operating order limiting the number of coefficients to be taken into account during said step of determining reconstruction filters;
• said substep of taking into account at least spatial characteristics of said restitution set is furthermore made from:
  • parameters constituting a list of spatio-temporal functions whose reconstruction is imposed; and
  • a parameter describing an operating order limiting the number of coefficients to be taken into account during said step of determining reconstruction filters;
• said step of taking into account at least spatial characteristics of said restitution assembly is also performed at least from one of the parameters selected from the group consisting of:
  • parameters representative of at least one of the three coordinates of the position of each or some of the elements, relative to the center placed in the listening area;
  • parameters representative of the spatio-temporal responses of each or some of the elements;
  • a parameter describing an operating order limiting the number of coefficients to be taken into account during said step of determining reconstruction filters;
  • parameters constituting a list of spatio-temporal functions whose reconstruction is imposed;
  • representative parameters of the templates of said rendering elements;
  • a parameter representative of the desired local adaptation capacity to the spatial irregularity of the configuration of said restitution set;
  • a parameter defining the radiation pattern of said restitution elements;
  • parameters representative of the frequency response of said rendering elements;
  • a parameter representative of a spatial window;
  • parameters representative of a spatial window in the form of weighting coefficients; and
  • a parameter representative of the radius of a spatial window when it is a ball;
• the method comprises a calibration step for delivering all or part of the parameters used in said step of determining reconstruction filters;
• said calibration step comprises, for at least one of the restitution elements:
  • a sub-step of acquiring signals representative of the radiation of said at least one element in the listening location; and
  • a substep of determining spatial and / or acoustic parameters of said at least one element;
• said calibration step comprises:
  • a sub-step of transmitting a specific signal to said at least one element of said restitution set, said acquisition substep corresponding to the acquisition of the sound wave transmitted in response by said at least one element; and
  • a substep of transforming said acquired signals into a finite number of coefficients representative of the emitted sound wave, in order to allow the realization of said substep of determining spatial and / or acoustic parameters;
• said acquisition sub-step corresponds to a substep of receiving a number of coefficients representative of the acoustic field generated by said at least one element in the form of a linear combination of space-time functions, which coefficients are directly used during said substep of determining spatial and / or acoustic parameters of said at least one element;
• said calibration sub-step further comprises a substep of determining the position in at least one of the three dimensions of the space of said at least one element of said rendering assembly;
• said calibration step further comprises a substep of determining the spatio-temporal response of said at least one element of said restitution set;
• said calibration step further comprises a substep of determining the frequency response of said at least one element of said rendering assembly;
• the method comprises a step of simulating all or part of the parameters necessary for carrying out said step of determining reconstruction filters;
• said simulation step comprises:
  • a substep of determining the missing parameters among the parameters used in said step of determining reconstruction filters;
  • a plurality of computation sub-steps for determining the value or values of the missing parameter (s) as defined previously according to the received parameters, the frequency, and predetermined default values;
• said simulation step comprises a sub-step of determining a list of elements of the active rendering set as a function of the frequency, and said calculation sub-steps are performed for the only elements of said list;
• said simulation step comprises a substep of calculating a parameter representative of the operating order limiting the number of coefficients to be taken into account during said step of determining reconstruction filters from at least the position in the space of all or part of the elements of the restitution set;
• said simulation step comprises a step of determining parameters representative of a spatial window in the form of weighting coefficients from a parameter representative of the spatial window in the spherical reponse and / or of a parameter representative of the radius of said space window when it is a ball;
• said simulation step comprises a substep of determining a list of spatio-temporal functions whose reconstruction is imposed from the position of all or part of the elements of the restitution set;
• the method comprises an input step for determining all or part of the parameters used during said step of determining reconstruction filters;
• said step of determining reconstruction filters comprises:
  • a plurality of calculation sub-steps performed for a finite number of operating frequencies and making it possible to deliver a matrix of weighting of the acoustic field, a representative matrix of the radiation of the restitution ensemble, and a representative matrix of the space-time functions whose reconstruction is imposed; and
  • a sub-step of calculating a decoding matrix, performed for a finite number of operating frequencies, from the weighting matrix of the acoustic field, of the representative matrix of the radiation of the restitution assembly, of the matrix representative of the spatio-temporal functions whose reconstruction is imposed, and of a parameter representative of the desired local adaptation capacity to the spatial irregularity of the restitution set, representative of the reconstruction filters;
• said sub-calculation step for delivering a representative matrix of the radiation of the restitution set is made from representative parameters for each element:
  • three coordinates of its position relative to the center placed in the listening area; and or
  • its spatio-temporal response; and
• said sub-calculation step for delivering a representative matrix of the radiation of the restitution set is further performed from representative parameters for each element of its frequency response.

The invention also relates to a computer program comprising program code instructions for executing the steps of the method, when said program is executed on a computer.

The invention also relates to a removable medium of the type comprising at least one processing processor and a non-volatile memory element, characterized in that said memory comprises a program comprising instructions for the execution of the steps of the method, when said processor executes said program.

The invention also relates to a control device as defined in claim 28.

• le dispositif est associé à des moyens de mise en forme d'un signal d'entrée comportant des informations temporelles et spatiales d'un environnement sonore à restituer, adaptés pour décomposer lesdites informations sur une base de fonctions spatio-temporelles afin de délivrer un signal comportant ledit nombre fini de coefficients représentatifs de la distribution dans le temps et dans les trois dimensions de l'espace dudit champ acoustique à restituer, correspondant audit environnement sonore, sous la forme d'une combinaison linéaire desdites fonctions spatio-temporelles ;
• lesdites fonctions spatio-temporelles sont des fonctions dites de Fourier-Bessel et/ou des combinaisons linéaires de ces fonctions;
• lesdits moyens de détermination de filtres de reconstruction reçoivent en entrée au moins l'un des paramètres parmi les paramètres suivants :
  • des paramètres représentatifs d'au moins une des trois coordonnées de la position de chaque ou certains des éléments, par rapport au centre placé dans la zone d'écoute ;
  • des paramètres représentatifs des réponses spatio-temporelles de chaque ou certains des éléments ;
  • un paramètre décrivant un ordre de fonctionnement limitant le nombre de coefficients à prendre en compte dans les moyens de détermination de filtres de reconstruction ;
  • des paramètres représentatifs des gabarits desdits éléments de restitution ;
  • un paramètre représentatif de la capacité d'adaptation locale souhaitée à l'irrégularité spatiale de la configuration dudit ensemble de restitution ;
  • un paramètre définissant le modèle de rayonnement desdits éléments de restitution ;
  • des paramètres représentatifs de la réponse en fréquence desdits éléments de restitution ;
  • un paramètre représentatif d'une fenêtre spatiale ;
  • des paramètres représentatifs d'une fenêtre spatiale sous forme de coefficients de pondération ;
  • de paramètres représentatifs du rayon d'une fenêtre spatiale lorsque celle-ci est une boule ; et
  • des paramètres représentatifs d'une liste de fonctions spatio-temporelles dont la reconstruction est imposée ;
• chacun desdits paramètres reçus par lesdits moyens de détermination de filtres de reconstruction est véhiculé par l'un des signaux parmi le-groupe de signaux suivants :
  • un signal de définition comportant des informations représentatives des caractéristiques spatiales de l'ensemble de restitution ;
  • un signal supplémentaire comportant des informations représentatives des caractéristiques acoustiques associées aux éléments de l'ensemble de restitution ; et
  • un signal d'optimisation comportant des informations relatives à une stratégie d'optimisation,

afin de délivrer, à l'aide des paramètres contenus dans ces signaux, un signal représentatif desdits filtres de reconstruction représentatifs dudit ensemble de restitution ;

• le dispositif est associé à des moyens de détermination de tout ou partie des paramètres reçus par lesdits moyens de détermination de filtres de reconstruction, lesdits moyens comportant au moins l'un des éléments suivants :
  • des moyens de simulation ;
  • des moyens de calibrage ;
  • des moyens de saisie de paramètres;
• lesdits moyens de détermination de filtres de reconstruction sont adaptés pour déterminer un ensemble de filtres représentatifs de la position dans l'espace des éléments de l'ensemble de restitution ; et
• lesdits moyens de détermination de filtres de reconstruction sont adaptés pour déterminer un ensemble de filtres représentatifs de l'effet de salle induit par la zone d'écoute.

According to other features of the invention:

• the device is associated with means for shaping an input signal comprising temporal and spatial information of a sound environment to be rendered, adapted to decompose said information on the basis of spatio-temporal functions in order to deliver a signal having said finite number of coefficients representative of the time and three-dimensional distribution of the space of said acoustic field to be rendered, corresponding to said sound environment, in the form of a linear combination of said space-time functions;
• said spatio-temporal functions are Fourier-Bessel functions and / or linear combinations of these functions;
• said reconstruction filter determining means receives as input at least one of the following parameters:
  • parameters representative of at least one of the three coordinates of the position of each or some of the elements, with respect to the center placed in the listening area;
  • parameters representative of the spatio-temporal responses of each or some of the elements;
  • a parameter describing an operating order limiting the number of coefficients to be taken into account in the reconstruction filter determination means;
  • parameters representative of the templates of said rendering elements;
  • a parameter representative of the desired local adaptation capacity to the spatial irregularity of the configuration of said restitution set;
  • a parameter defining the radiation pattern of said rendering elements;
  • parameters representative of the frequency response of said rendering elements;
  • a parameter representative of a spatial window;
  • parameters representative of a spatial window in the form of weighting coefficients;
  • parameters representative of the radius of a spatial window when it is a ball; and
  • parameters representing a list of spatio-temporal functions whose reconstruction is imposed;
• each of said parameters received by said reconstruction filter determining means is conveyed by one of the following signal group:
  • a definition signal comprising information representative of the spatial characteristics of the reproduction unit;
  • an additional signal comprising information representative of the acoustic characteristics associated with the elements of the reproduction unit; and
  • an optimization signal comprising information relating to an optimization strategy,

to deliver, using the parameters contained in these signals, a signal representative of said reconstruction filters representative of said restitution set;

• the device is associated with means for determining all or part of the parameters received by said reconstruction filter determining means, said means comprising at least one of the following elements:
  • simulation means;
  • calibration means;
  • means for entering parameters;
• said reconstruction filter determining means are adapted to determine a set of filters representative of the position in the space of the elements of the rendering assembly; and
• said reconstruction filter determining means are adapted to determine a set of filters representative of the room effect induced by the listening area.

• la Fig.1 est une représentation d'un repère sphérique ;
• la Fig.2 est un schéma d'un système de restitution selon l'invention ;
• la Fig.3 est un schéma synoptique du procédé de l'invention ;
• la Fig.4 est un schéma détaillant les moyens de calibrage ;
• la Fig.5 est un schéma détaillant l'étape de calibrage ;
• la Fig.6 est un schéma de l'étape de simulation ;
• la Fig.7 est un schéma des moyens de détermination de filtres de reconstruction;
• la Fig.8 est un schéma de l'étape de détermination de filtres de reconstruction ;
• la Fig.9 est un mode de réalisation de l'étape de mise en forme du signal d'entrée ; et
• la Fig.10 est un mode de réalisation de l'étape de détermination de signaux de pilotage.

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

• the Fig.1 is a representation of a spherical landmark;
• the Fig.2 is a diagram of a rendering system according to the invention;
• the Fig.3 is a block diagram of the method of the invention;
• the Fig.4 is a diagram detailing the means of calibration;
• the Fig.5 is a diagram detailing the calibration step;
• the Fig.6 is a diagram of the simulation stage;
• the Fig.7 is a diagram of the means for determining reconstruction filters;
• the Fig.8 is a schematic of the step of determining reconstruction filters;
• the Fig.9 is an embodiment of the step of shaping the input signal; and
• the Fig.10 is an embodiment of the step of determining driving signals.

On the figure 1 a conventional spherical landmark has been shown to specify the coordinate system referred to in the text.

This reference is an orthonormal reference, of origin O and having three axes ( OX ) , ( OY ) and ( OZ ).

In this reference, a position denoted x is described by means of its spherical coordinates (r, θ, φ), where r denotes the distance from the origin O, θ the orientation in the vertical plane and the orientation φ in the horizontal plane.

In such a mark, a sound field is known if one defines each point at each time t the sound pressure denoted by p (r, θ, φ, t), whose temporal Fourier trans-formed is denoted by P (r , θ, φ, t ) where f is the frequency.

The figure 2 is a representation of a rendering system according to the invention.

This system comprises a decoder 1 controlling a reproduction unit 2 which comprises a plurality of elements 3 ₁ to 3 _N , such as loudspeakers, speakers or any other sound source, arranged in a manner Any one in a place of listening 4. Place arbitrarily in the listening place 4, the origin O of the reference which is called center 5 of the set of restitution.

The set of spatial, acoustic and electrodynamic characteristics is considered as the intrinsic characteristics of restitution.

The system also comprises means 6 for shaping an input signal S1 and means 7 for generating parameters comprising simulation means 8, calibration means 9 and means 10 for entering parameters.

The decoder 1 comprises means 11 for determining control signals and means 12 for determining reconstruction filters.

The decoder 1 receives as input an IF signal _FB comprising information representative of the three-dimensional acoustic field to be reproduced, a definition signal SL comprising information representative of the spatial characteristics of the reproduction assembly 2, an additional signal RP comprising information representative of the acoustic characteristics associated with elements 3 ₁ to 3 _N and an optimization signal OS comprising information relating to an optimization strategy.

The decoder transmits to the attention of each of the elements 3 ₁ to 3 _N of the reproduction assembly 2, a signal SC ₁ to SC _N of specific control.

On the figure 3 schematically shows the main steps of the method implemented in a system according to the invention as described with reference to the figure 2 .

The method comprises a step 20 for entering optimization parameters, a calibration step 30 for measuring certain characteristics of the reproduction assembly 2 and a simulation step 40.

During the parameter input step 20 implemented by the interface means, certain parameters of the operation of the system may be defined manually by an operator or delivered by a suitable device.

In step 30 of calibration, described in more detail with reference to Figures 4 and 5 , the calibration means 9 are connected in turn with each of the elements 3 ₁ to 3 _N of the reproduction assembly 2 in order to measure parameters associated with these elements.

The simulation step 40, implemented by the means 8, makes it possible to simulate the signals of parameters necessary for the operation of the system which are neither entered during step 20 nor measured during step 30.

The means 7 for generating parameters then output the definition signal SL, the additional signal RP and the optimization signal OS.

Thus, steps 20, 30 and 40 make it possible to determine the set of parameters necessary for the implementation of step 50.

Following these steps, the method comprises a step 50 of determining reconstruction filters implemented by the means 12 of the decoder 1 and for delivering a signal FD representative of the reconstruction filters.

This step 50 of determining reconstruction filters makes it possible to take into account the at least spatial characteristics of the restitution set 2 defined during the input, calibration or simulation steps. Step 50 also makes it possible to take into account the acoustic characteristics associated with the elements 3 ₁ to 3 _N of the reproduction assembly 2 and the information relating to an optimization strategy.

The reconstruction filters obtained at the end of step 50 are subsequently stored in the decoder 1 so that the steps 20, 30, 40 and 50 are repeated only if the restitution set is modified. 2 or optimization strategies.

In operation, the signal SI comprising temporal and spatial information of a sound environment to be restored, is provided to the formatting means 6, for example by direct acquisition or by reading a recording or by synthesis using computer software. This signal SI is shaped during a shaping step 60. At the end of this step, the means 6 deliver to the decoder 1 a signal IF _FB comprising a finite number of representative coefficients, on the basis of spatio-temporal functions, of the distribution in time and in the three dimensions of the space, an acoustic field to be restored corresponding to the sound environment to be restored.

As a variant, the signal IF _FB is provided by external means, for example a microcomputer comprising synthesis means.

The invention is based on the use of a family of spatio-temporal functions making it possible to describe the characteristics of any acoustic field.

In the embodiment described, these functions are so-called spherical Fourier-Bessel functions of the first kind, hereinafter referred to as Fourier-Bessel functions.

In an empty zone of sound sources and empty of obstacles, the Fourier-Bessel functions are solutions of the wave equation and constitute a base that generates all acoustic fields produced by sound sources located outside this zone. .

Any three-dimensional acoustic field is thus expressed by a linear combination of the Fourier-Bessel functions, according to the expression of the inverse Fourier-Bessel transform which expresses: $$P\left(r,\theta ,\phi ,f\right)=4\pi {\displaystyle \underset{l=0}{\overset{\infty }{\Sigma }}}{\displaystyle \underset{m=-l}{\overset{l}{\Sigma }}}{P}_{l,m}\left(f\right)j^l{j}_l\left(\mathit{kr}\right){\mathrm{there}}_l^m\left(\theta ,\phi \right)$$

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

où J _v(x) est la fonction de Bessel de première espèce d'ordre v, et y_l ^m (θ,φ) est l'harmonique sphérique réelle d'ordre 1 et de terme m, avec m allant de -l à l, définie par : $$y_l^m\left(\theta ,\phi \right)=\{\begin{array}{ll}\frac{1}{\sqrt{\pi }}{P}_l^{\left|m\right|}\left(\cos \theta \right)\cos \left(\mathit{m\phi }\right)& \mathrm{pour}m>0\\ \frac{1}{\sqrt{2\pi }}{P}_l^0\left(\cos \theta \right)& \mathrm{pour}m=0\\ \frac{1}{\sqrt{\pi }}{P}_l^{\left|m\right|}\left(\cos \theta \right)\sin \left(\mathit{m\phi }\right)& \mathrm{pour}m<0\end{array}$$

In this equation, the terms P _l , _m ( _f ) are, by definition, the Fourier-Bessel coefficients of the field p ( r, θ, φ, t ) , $k=\frac{2\mathit{\pi f}}{\mathrm{vs}},$

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

wherein J _v (x) is the Bessel function of the first kind of order v, and y _l ^m (θ, φ) is the real spherical harmonic of order 1 and term m, with m ranging from - l l , defined by: $${\mathrm{there}}_l^m\left(\theta ,\phi \right)=\{\begin{array}{ll}\frac{1}{\sqrt{\pi }}{P}_l^{\left|m\right|}\left(\cos \theta \right)\cos \left(\mathit{m\phi }\right)& \mathrm{for}m>0\\ \frac{1}{\sqrt{2\mathrm{<figure-callout\; id="0"\; label="\pi \; P\; l"\; filenames="imgf0007.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}}}{P}_l^{}{}_0^{}\left(\cos \theta \right)& \mathrm{for}m=0\\ \frac{1}{\sqrt{\pi }}{P}_l^{\left|m\right|}\left(\cos \theta \right)\sin \left(\mathit{m\phi }\right)& \mathrm{for}m<0\end{array}$$

avec P_l (x) les polynômes de Legendre, définis par : $$P_l\left(x\right)=\frac{1}{2^{l}l!}\frac{{\mathrm{d}}^l}{\mathrm{d}{x}^l}{\left(x^2-1\right)}^l$$

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

with P _l ( x ) the Legendre polynomials, defined by: $$P_l\left(x\right)=\frac{1}{2^{l}l!}\frac{{\mathrm{d}}^l}{\mathrm{d}{x}^l}{\left(x^2-1\right)}^l$$

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

In a variant, the method of the invention uses function bases expressing themselves as linear combinations, possibly infinite, of Fourier-Bessel functions.

During the shaping step 60 performed by the means 6, the input signal SI is decomposed into Fourier-Bessel coefficients p _{l, m} ( t ) so as to establish the coefficients forming the signal IF _FB ,

The decomposition into Fourier-Bessel coefficients is conducted up to a limit order L defined prior to this shaping step 60 during the capture step.

At the end of step 60, the IF signal _FB delivered by the shaping means 6 is introduced into the means 11 for determining the control signals. These means 11 also receive the signal FD representative of the reconstruction filters defined by taking into account in particular the spatial configuration of the reproduction unit 2.

The coefficients of the signal IF _FB , delivered at the end of step 60, are used by the means 11 during a step 70 of determining the control signals SC ₁ to SC _N of the elements of the reproduction unit 2 from the application of the reconstruction filters determined in step 50 to these coefficients.

The signals SC ₁ to SC _N are then delivered in order to be applied to the elements 3 ₁ to 3 _N of the reproduction assembly 2 which reproduce the acoustic field whose characteristics are substantially independent of the intrinsic characteristics of restitution of the set of restitution 2.

Thanks to the method of the invention, the control signals SC ₁ to SC _N are adapted to allow an optimal restitution of the acoustic field which makes the best use of the spatial and / or acoustic characteristics of the reproduction unit 2, in particular the effect of room, and which integrates the chosen optimization strategy.

Thus, due to the quasi-independence between the intrinsic characteristics of restitution of the restitution assembly 2 and the acoustic field restored, it is possible to make the latter substantially identical to the acoustic field corresponding to the sound environment represented by the information temporal and spatial input.

The main steps of the process of the invention will now be described in greater detail.

• x _n, représentatif de la position de l'élément 3 _n par rapport au centre d'écoute 5 ; x _n s'exprime dans le repère sphérique au moyen des coordonnées r_n, θ_n, et φ_n;
• G_n (f), représentatif du gabarit de l'élément 3 _n de l'ensemble de restitution spécifiant la bande de fréquence de fonctionnement de cet élément ;
• N_l , _m . _n (f), représentatif de la réponse spatio-temporelle de l'élément 3 _n correspondant au champ acoustique produit dans le lieu d'écoute 4 par l'élément 3 _n , lorsque celui-ci reçoit en entrée un signal impulsionnel ;
• W(r,f), décrivant pour chaque fréquence f considérée une fenêtre spatiale représentative de la répartition dans l'espace de contraintes de reconstruction du champ acoustique, ces contraintes permettant de spécifier la répartition dans l'espace de l'effort de reconstruction du champ acoustique ;
• W_l (f), décrivant directement sous forme de pondération des coefficients de Fourier-Bessel et pour chaque fréquence f considérée, une fenêtre spatiale représentative de la répartition dans l'espace de contraintes de reconstruction du champ acoustique ;
• R(f), représentatif, pour chaque fréquence f considérée, du rayon de la fenêtre spatiale lorsque celle-ci est une boule ;
• H_n (f), représentatif, pour chaque fréquence f considérée, de la réponse en fréquence de l'élément 3 _n ;
• _µ(f), représentatif, pour chaque fréquence f considérée, de la capacité d'adaptation locale souhaitée à l'irrégularité spatiale de la configuration de l'ensemble de restitution ;
• {(l_k, m_k )}(f), constituant pour chaque fréquence f considérée, une liste de fonctions spatio-temporelles dont la reconstruction est imposée ;
• L(f), imposant, pour chaque fréquence f considérée, l'ordre limite de fonctionnement des moyens 12 de détermination de filtres de reconstruction ;
• RM(f), définissant, pour chaque fréquence f considérée, le modèle de rayonnement des éléments 3₁ à 3 _N de l'ensemble de restitution 2.

During the step 20 of entering parameters an operator or a suitable memory system can specify all or part of the calculation parameters and in particular:

• x _n , representative of the position of the element 3 _n with respect to the listening center 5; x _{n is} expressed in the spherical coordinate system by means of the coordinates r _n , θ _n , and φ _n ;
• G _n ( f ), representative of the template of the element 3 _n of the reproduction unit specifying the operating frequency band of this element;
• N _l , _m . _n ( f ), representative of the spatio-temporal response of the element 3 _n corresponding to the acoustic field produced in the listening location 4 by the element 3 _n , when the latter receives an impulse signal as input;
• W ( r, f ) , describing for each frequency f considered a spatial window representative of the distribution in the space of reconstruction constraints of the acoustic field, these constraints making it possible to specify the spatial distribution of the reconstruction effort of the acoustic field;
• W _l ( f ), describing directly in the form of weighting of the Fourier-Bessel coefficients and for each frequency f considered, a spatial window representative of the spatial distribution of reconstruction constraints of the acoustic field;
• R ( f ), representative, for each frequency f considered, of the radius of the spatial window when the latter is a ball;
• H _n ( f ) , representative, for each frequency f considered, of the frequency response of the element 3 _n ;
• _μ ( f ), representative, for each frequency f considered, of the desired local adaptation capacity to the spatial irregularity of the configuration of the reproduction unit;
• {( l _k , m _k )} ( f ) , constituting for each frequency f considered, a list of spatio-temporal functions whose reconstruction is imposed;
• L ( f ), imposing, for each frequency f considered, the limit order of operation of the means 12 for determining reconstruction filters;
• RM ( f ), defining, for each frequency f considered, the radiation pattern of the elements 3 ₁ to 3 _N of the reproduction assembly 2.

The definition signal SL conveys the parameters x _n , the additional signal RP, the parameters H _n ( f ) and N _{/ , m, n} ( f ) and the optimization signal OS, the parameters G _n ( f ) , μ ( f ), {( 1 _k , m ( _k )} ( f ) , L ( f ) , W ( r, f ) , W _l ( f ) , R ( f ) and RM ( f ) .

The interface means 10 implementing this step 20 are conventional means such as a microcomputer or any other appropriate means.

We will now describe in more detail the calibration step 30 and the means 9 which implement it.

On the figure 4 the detail of the calibration means 9 is shown. They comprise a decomposition module 91, an impulse response determination module 92 and a calibration parameter determination module 93.

The calibration means 9 are adapted to be connected to a sound acquisition device 100 such as a microphone or any other suitable device, and to be connected in turn to each element 3 _n of the reproduction assembly 2 in order to take information on this element.

On the figure 5 , the detail of an embodiment of the calibration step 30 implemented by the calibration means 9 and making it possible to measure characteristics of the reproduction assembly 2 is shown.

In a substep 32, the calibration means 9 emit a specific signal u _n ( t ) such as a pseudo-random sequence MLS (Maximum Length Sequence) for a 3 _n element. The acquisition device 100 receives, during a substep 34, the sound wave emitted by the element 3 _n in response to the reception of the signal u _n ( t ) and transmits signals c _{l, m} ( t ) representative of the wave received at the decomposition module 91.

In a substep 36, the decomposition module 91 decomposes the signals picked up by the acquisition device 100 into a finite number of Fourier-Bessel coefficients q _{/ , m} ( t ) .

$$q_{1,-1}\left(t\right)=\mathit{\rho c}\sqrt{\frac{3}{4\pi }}{c}_{1,-1}\left(t\right)\mathrm{avec}{c}_{1,-1}\left(t\right)=v_Y\left(t\right)$$

$$q_{1,0}\left(t\right)=-\mathit{\rho c}\sqrt{\frac{3}{4\pi }}{c}_{1,0}\left(t\right)\mathrm{avec}{c}_{1,0}\left(t\right)=v_Z\left(t\right)$$

$$q_{1,1}\left(t\right)=-\mathit{\rho c}\sqrt{\frac{3}{4\pi }}{c}_{1,1}\left(t\right)\mathrm{avec}{c}_{1,1}\left(t\right)=v_X\left(t\right)$$

For example, the device 100 delivers pressure information p ( t ) and velocity v (t) to the center 5 of the reproduction unit. In this case, the coefficients q _0.0 ( t ) to q _1.1 ( t ) representative of the acoustic field are deduced from the signals c _0.0 ( t ) to c _1.1 ( t ) according to the following relations: $${\mathrm{<figure-callout\; id="0"\; label="q"\; filenames="imgf0007.png"\; state="\{\{state\}\}">q</figure-callout>}}_{0,0}\left(t\right)=\frac{1}{\sqrt{4\pi }}{\mathrm{vs}}_{0,0}\left(t\right)\mathrm{with}{\mathrm{vs}}_{0,0}\left(t\right)=\mathrm{<figure-callout\; id="1"\; label="p\; t\; q"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">p\; </figure-callout>}\left(t\right)$$

$$q_{}$$$${}_{1,-1}\left(t\right)=\mathit{<figure-callout\; id="3"\; label="\rho c"\; filenames="imgf0004.png,imgf0008.png"\; state="\{\{state\}\}">\rho c</figure-callout>}\sqrt{\frac{3}{4\pi }}{\mathrm{vs}}_{1,-1}\left(t\right)\mathrm{with}{\mathrm{vs}}_{1,-1}\left(t\right)=v_{\mathrm{<figure-callout\; id="1"\; label="Y\; t\; q"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">Y\; </figure-callout>}}\left(t\right)$$

$$q_{}$$$${}_{1,0}\left(t\right)=-\mathit{<figure-callout\; id="3"\; label="\rho c"\; filenames="imgf0004.png,imgf0008.png"\; state="\{\{state\}\}">\rho c</figure-callout>}\sqrt{\frac{3}{4\pi }}{\mathrm{vs}}_{1,0}\left(t\right)\mathrm{with}{\mathrm{vs}}_{1,0}\left(t\right)=v_{\mathrm{<figure-callout\; id="1"\; label="Z\; t\; q"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">Z\; </figure-callout>}}\left(t\right)$$

$$q_{}$$$${}_{1,1}\left(t\right)=-\mathit{<figure-callout\; id="3"\; label="\rho c"\; filenames="imgf0004.png,imgf0008.png"\; state="\{\{state\}\}">\rho c</figure-callout>}\sqrt{\frac{3}{4\pi }}{\mathrm{vs}}_{1,1}\left(t\right)\mathrm{with}{\mathrm{vs}}_{1,1}\left(t\right)=v_X\left(t\right)$$

In these equations, v _X ( t ) , v _y ( t ) and v _z ( t ) denote the components of the velocity vector v ( t ) in the orthonormal reference frame considered and ρ denotes the density of the air.

When these coefficients are defined by the module 91, they are addressed to the response determination module 92.

In a substep 38, the response determination module 92 determines the impulse responses hp1 _{, m} ( t ) which connect the Fourier-Bessel coefficients q ,, ", (t) and the transmitted signal u _n ( t ).

The impulse response delivered by the response determination module 92 is addressed to the parameter determination module 93.

In a substep 39, the module 93 derives information on elements of the reproduction set.

In the embodiment described, the parameter determination module 93 determines the distance r _n between the element 3 _n and the center 5 from its response hp _0,0 ( t ) and the measurement of the time put by the it is propagated from the element 3 _n to the acquisition device 100, by delay estimation methods on the response hp _0,0 ( t ).

In the embodiment described, the acquisition device 100 is able to unambiguously encode the orientation of a source in space. Thus, it appears for each instant t of trigonometrical relationships between the 3 Responses hp _{1, -1} (t), _{1 hp, 0} (t) and _1.1 hp (t) involving the coordinates θ _n and φ _n.

The module 93 determines the values hp _{1, -1} , hp _1.0 and hp ₁ , ₁ corresponding to the values taken by the responses hp 1, -1 ( t ) , hp _1.0 ( t ) and hp _1.1 ( t ) at an instant t chosen arbitrarily such as for example the moment for which hp _{0 , 0} ( t ) reaches its maximum.

$$-\mathrm{pour}{\mathit{hp}}_{1,0}<0:{\theta }_n=\pi -\arctan \left(\frac{\sqrt{h{p}_{1,-1}^2+h{p}_{1,1}^2}}{\left|{\mathit{hp}}_{1,0}\right|}\right)$$

$$-\mathrm{pour}{\mathit{hp}}_{1,1}>0:{\phi }_n=-\arctan \left(\frac{{\mathit{hp}}_{1,-1}}{{\mathit{hp}}_{1,1}}\right)$$

$$-\mathrm{pour}{\mathit{hp}}_{1,1}<0:{\phi }_n=\pi -\arctan \left(\frac{{\mathit{hp}}_{1,-1}}{{\mathit{hp}}_{1,1}}\right)$$

Subsequently, the module 93 estimates coordinates θ _n and φ _n from the values hp _{1, -1} , hp _1.0 and hp _{1 , 1} by means of the following trigonometric relations: $$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}>0:{\theta }_{\mathrm{not}}=\arctan \left(\frac{\sqrt{h{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">p</figure-callout>}}_{1,-1}^2+\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="h\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">h\; </figure-callout></figure-callout>}{p}_{}^{}{}_{}^{}{}_{1,1}^2}}{\left|{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,0}\right|}\right)$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}<0:{\theta }_{\mathrm{not}}=\pi -\arctan \left(\frac{\sqrt{h{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">p</figure-callout>}}_{1,-1}^2+\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="h\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">h\; </figure-callout></figure-callout>}{p}_{}^{}{}_{}^{}{}_{1,1}^2}}{\left|{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,0}\right|}\right)$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}>0:{\phi }_{\mathrm{not}}=-\mathrm{<figure-callout\; id="1"\; label="arctan\; hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">arctan\; </figure-callout>}\left(\frac{{\mathit{hp}}_{}}{}\right)\left(\frac{{\mathit{}}_{1,-1}}{{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,1}}\right)$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}<0:{\phi }_{\mathrm{not}}=\pi -\arctan \left(\frac{{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}}{{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}}\right)$$

$$-\mathrm{pour}{\mathit{hp}}_{1,1}=0\mathrm{et}{\mathit{hp}}_{1,-1}=0\mathrm{et}{\mathit{hp}}_{1,0}=0:{\theta }_n\mathrm{et}{\phi }_n\mathrm{sont\; indéfinis}$$

$$-\mathrm{pour}{\mathit{hp}}_{1,1}=0\mathrm{et}{\mathit{hp}}_{1,-1}\ne 0\mathrm{et}{\mathit{hp}}_{1,0}=0:{\theta }_n=\frac{\pi }{2}\mathrm{et}{\phi }_n=-\mathrm{signe}\left({\mathit{hp}}_{1,-1}\right)\frac{\pi }{2}$$

$$-\mathrm{pour}{\mathit{hp}}_{1,1}=0\mathrm{et}{\mathit{hp}}_{1,-1}\ne 0\mathrm{et}{\mathit{hp}}_{1,0}=0:{\phi }_n=-\mathrm{signe}\left({\mathit{hp}}_{1,-1}\right)\frac{\pi }{2}$$

These relationships admit the following special cases: $$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}=0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}\ne 0:{\theta }_{\mathrm{not}}=\frac{\pi }{2}$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}=0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}=0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}=0:{\theta }_{\mathrm{not}}\mathrm{and}{\phi }_{\mathrm{not}}\mathrm{are\; undefined}$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}=0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}\ne 0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}=0:{\theta }_{\mathrm{not}}=\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}\mathrm{and}{\phi }_{\mathrm{not}}=-\mathrm{sign}\left({\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}\right)\frac{\pi }{2}$$

$$-\mathrm{for}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,1}=0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}\ne 0\mathrm{and}{\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="hp"\; filenames="imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout></figure-callout>}}_{1,0}=0:{\phi }_{\mathrm{not}}=-\mathrm{sign}\left({\mathit{<figure-callout\; id="1"\; label="hp"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">hp</figure-callout>}}_{1,-1}\right)\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}$$

Advantageously, the coordinates θ _n and φ _n are estimated over several times. The final determination of the coordinates θ _n and φ _n is obtained by means of averaging techniques between the different estimations.

As a variant, the coordinates θ _n and φ _n are estimated from other responses among the hp _{l, m} ( t ) available or are estimated in the frequency domain from the responses HP _{l, m} ( f ).

Thus defined, the parameters r _n , θ _n , and φ _n are transmitted to the decoder 1 by the definition signal SL.

In the embodiment described, the module 93 also delivers the transfer function H _n ( f ) of each element 3 _n , from the responses hp _{l, m} ( t ) from the response determination module 92.

One solution consists in constructing the response hp ' _0,0 ( t ) corresponding to the selection of the part of the response hp _0,0 ( t ) which comprises a non-zero signal and devoid of the reflections introduced by the listening site 4 The frequency response H _n ( f ) is deduced by Fourier transform from the response hp ' _{0 , 0} ( t ) previously windowed. The window can be chosen from conventional smoothing windows, such as for example rectangular, Hamming, Hanning, and Blackman.

The parameters H _n ( f ) thus defined are transmitted to the decoder 1 by the supplementary signal RP.

In the embodiment described, the module 93 also delivers the spatio-temporal response N / _{, m, n} ( f ) of each element 3 _n of the reproduction set 2, deduced by applying a gain adjustment and a temporal alignment. impulse responses hp _{l, m} ( t ) from the measurement of the distance r _n of the element 3 _n as follows: $${\eta }_{l,m,\mathrm{not}}\left(t\right)=r_{\mathrm{not}}h{p}_{l,m}\left(t+r_{\mathrm{not}}/\mathrm{vs}\right)$$

The spatio-temporal response η _{/ , m, n} ( t ) contains a large amount of information characterizing the element 3 _n , in particular its position and its frequency response. It is also representative of the directivity of the element 3 _n , its non-punctuality, as well as the room effect resulting from the radiation of the element 3 _n in the listening area 4.

The module 93 applies temporal windowing to the response η _{l, m, n} ( t ) to adjust the duration of taking into account the room effect. The spatio-temporal response expressed in the frequency domain N _{l, m, n} ( f ) is obtained by Fourier transform of the response η _{/ , m, n} ( t ) . The spatio-temporal response N _{/ , m, n} ( f ) is then frequency-windowed in order to adjust the frequency band on which the room effect is taken into account. The module 93 then delivers the parameters N _{1, m, n} ( f ) thus shaped which are supplied to the decoder 1 by the supplementary signal RP.

Sub-steps 32 to 39 are repeated for all the elements 3 ₁ to 3 _N of the reproduction assembly 2.

Alternatively, the calibration means 9 are adapted to receive other types of information referring to the element 3 _n . For example, this information is introduced in the form of a finite number of Fourier-Bessel coefficients representative of the acoustic field produced by the element 3 _n in the listening location 4.

Such coefficients can in particular be delivered by acoustic simulation means implementing a geometric modeling of the listening location 4 to determine the position of the image sources induced by the reflections due to the position of the element 3 _n and to the geometry the listening place 4.

The acoustic simulation means receive as input the signal u _n ( t ) emitted by the module 92 and deliver, using the signal c _{l, m} ( t ) , the coefficients of Fourier-Bessel determined by superposition of the acoustic field emitted by the element 3 _n and acoustic fields emitted by the image sources when the element 3 _n receives the signal u _n ( t ). In this case the decomposition module 91 only transmits the signal c _{l, m} ( t ) to the module 92.

In a variant, the calibration means 9 comprise other information acquisition means referenced to the elements 3 ₁ to 3 _N , such as laser position measuring means, signal processing means using techniques channel training or any other appropriate means.

The means 9 implementing the calibration step 30 consist for example of an electronic card or a computer program or any other appropriate means.

We will now describe the details of step 40 of parameter simulation and the means 8 which implement it. This step is performed for each operating frequency f .

The described embodiments require to know for each element 3 _n its complete position described by the parameters r _n , θ _n and φ _n and / or its spatio-temporal response described by the parameters N _{/ , m, n} ( f ).

In a first embodiment, described with reference to the figure 6 Parameters that are not entered by an operator or by external means or measured are simulated.

Step 40 begins with a substep 41 of determining the missing parameters in the received signals RP, SL and OS.

In a substep 42, the parameter H _n ( f ) representative of the response of the elements of the reproduction set 2 takes the default value 1.

During a sub-step 43, the parameter G _n ( f ) representative of the templates of the elements of the reproduction set 2 is determined by thresholding on the parameter H _n ( f ) in the case where the latter is measured, defined by the user, or provided by external means, otherwise, G _n ( f ) takes the default value 1.

Step 40 then comprises a substep 44 for determining the active elements at the frequency f considered.

During this sub-step, a list { n *} ( f ) of elements of the restitution set active at the frequency f is determined, these elements being those whose template G _n ( f ) is non-zero for this frequency. The list { n *} ( f ) comprises N _f elements and is transmitted to the decoder 1 by the optimization signal OS. She is used to select the parameters corresponding to the active elements at each frequency f among the set of parameters. The index parameters n * correspond to the n ^th active element at the frequency f.

• les moyens de simulation 8 calculent le plus petit angle a_min formé par une paire d'éléments de l'ensemble de restitution au moyen d'une relation trigonométrique, telle que par exemple : $$a_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}1*,\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}2*}=\mathrm{acos}\left(\sin {\theta }_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}1*}\sin {\theta }_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}2*}\cos \left({\phi }_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}1*}-{\mathrm{<figure-callout\; id="2"\; label="\phi \; n"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_n\right)+\cos {\theta }_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}1*}\cos {\theta }_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}2*}\right)$$
  
  $$a_{\mathit{min}}=\min \left({\mathit{a}}_{\mathit{<figure-callout\; id="1"\; label="n"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}\mathit{1}*,\mathit{<figure-callout\; id="2"\; label="n"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">n</figure-callout>}\mathit{2}*}\right)$$
  
  parmi l'ensemble des couples (n1*, n2*) tels que n1* ≠ n2* ;
• les moyens 9 de simulation déterminent l'ordre maximum L(f) qui est le plus grand entier respectant la relation $$L\left(f\right)<\mathrm{\pi }/a_{\mathit{min}}\mathrm{.}$$
  

In a substep 45, the parameter L ( f ) representative of the operating order of the module for determining filters at the current frequency f , is determined as follows:

• the simulation means 8 calculate the smallest angle _min formed by a pair of elements of the restitution assembly by means of a trigonometric relation, such as for example: $${\mathrm{at}}_{\mathrm{not}1*,\mathrm{not}2*}=\mathrm{acos}\left(\sin {\theta }_{\mathrm{not}1*}\sin {\theta }_{\mathrm{not}2*}\cos \left({\phi }_{\mathrm{not}1*}-{\phi }_{\mathrm{not}2*}\right)+\cos {\theta }_{\mathrm{not}1*}\cos {\theta }_{\mathrm{not}2*}\right)$$
  
  $${\mathrm{at}}_{\mathit{min}}=\min \left({\mathit{at}}_{\mathit{not}\mathit{1}*,\mathit{not}\mathit{2}*}\right)$$
  
  among the set of pairs ( n1 *, n2 *) such that n1 * ≠ n2 * ;
• the simulation means 9 determines the maximum order L ( f ) which is the largest integer respecting the relation $$\mathrm{The}\left(f\right)<\mathrm{\pi }/{\mathrm{at}}_{\mathit{min}}\mathrm{.}$$
  

In a substep 46, the parameter RM ( f ) defining the radiation pattern of the elements constituting the reproduction assembly, is determined automatically by defaulting to the spherical radiation pattern.

• si le paramètre W(r,f) représentatif de la fenêtre spatiale dans le repère sphérique est fourni ou saisi, W_l (f) est déduit de sa valeur en appliquant l'expression : $$W_l\left(f\right)=16{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2{\int }_0^{\infty }W\left(r,\mathrm{<figure-callout\; id="2"\; label="f\; j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f</figure-callout>},\right)j_l^{}{}_2^{}\left(\mathit{kr}\right)r^2\mathrm{d}r$$
  
• si le paramètre R(f), qui représente un rayon lorsque la fenêtre spatiale est une boule de rayon R(f), est fourni par des moyens extérieurs ou saisi, W_l (f) est déduit de sa valeur en appliquant l'expression : $$W_l\left(f\right)=8{\pi }^2{R}^3\left(\mathrm{<figure-callout\; id="2"\; label="f\; j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f</figure-callout>},\right)\left(j_l^{}\right)\left({}_2^{}\left(\mathit{kR}\left(f\right)\right)+j_{l+1}^2\left(\mathit{kR}\left(f\right)\right)-\frac{2l+1}{\mathit{kR}\left(f\right)}{j}_l\left(\mathit{kR}\left(f\right)\right)j_{l+1}\left(\mathit{kR}\left(f\right)\right)\right)$$
  
  sinon, W_l (f) est déduit de L(f), en appliquant l'expression : $$W_l\left(f\right)=8{\pi }^2{R}^3\left({\mathrm{<figure-callout\; id="2"\; label="j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">j</figure-callout>}}_l^{}\left(\mathit{kR}\right)+j_{l+1}^2\left(\mathit{kR}\right)-\frac{2l+1}{\mathit{kR}}{j}_l\left(\mathit{kR}\right)j_{l+1}\left(\mathit{kR}\right)\right)\mathrm{avec}R=\frac{\mathrm{<figure-callout\; id="2"\; label="L\; f\; c"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">L</figure-callout>}\left(f\right)c}{2\mathit{\pi f}};$$
  
• En variante, si la fenêtre spatiale n'est pas spécifiée, les moyens de simulation 8 attribuent au paramètre W_l (f), une valeur par défaut, par exemple une fenêtre de Hamming de taille 2L(f) + 1, évaluée en l.

In a sub-step 47, the parameter W _l ( f ) which describes the spatial window representative of the distribution in the space of reconstruction constraints of the acoustic field in the form of weighting of Fourier-Bessel coefficients is determined by the following way:

• if the parameter W ( r, f ) representative of the spatial window in the spherical coordinate system is supplied or entered, W _l ( f ) is deduced from its value by applying the expression: $$W_l\left(f\right)=16{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2{\int }_0^{\infty }W\left(r,\mathrm{<figure-callout\; id="2"\; label="f\; j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)j_l^{}{}_2^{}\left(\mathit{kr}\right)r^2\mathrm{d}r$$
  
• if the parameter R ( f ), which represents a radius when the spatial window is a ball of radius R ( f ), is provided by external means or grasped, W _l ( f ) is deduced from its value by applying the expression : $$W_l\left(f\right)=8{\pi }^2{R}^3\left(\mathrm{<figure-callout\; id="2"\; label="f\; j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)\left(j_l^{}\right)\left({}_2^{}\left(\mathit{kR}\left(f\right)\right)+j_{l+1}^2\left(\mathit{kR}\left(f\right)\right)-\frac{2l+1}{\mathit{kR}\left(f\right)}{j}_l\left(\mathit{kR}\left(f\right)\right)j_{l+1}\left(\mathit{kR}\left(f\right)\right)\right)$$
  
  otherwise, W _l ( f ) is deduced from L ( f ), applying the expression: $$W_l\left(f\right)=8{\pi }^2{R}^3\left({\mathrm{<figure-callout\; id="2"\; label="j\; l"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">j\; </figure-callout>}}_l^{}\left(\mathit{kR}\right)+j_{l+1}^2\left(\mathit{kR}\right)-\frac{2l+1}{\mathit{kR}}{j}_l\left(\mathit{kR}\right)j_{l+1}\left(\mathit{kR}\right)\right)\mathrm{with}R=\frac{\mathrm{The}\left(f\right)\mathrm{vs}}{2\mathit{\pi f}};$$
  
• Alternatively, if the spatial window is not specified, the simulation means 8 attribute parameter W _l (f), a default value, e.g., a Hamming window size 2 L (f) + 1, evaluated l .

The parameter W _l ( f ) is determined for the values of l ranging from 0 to L ( f ).

• Dans un premier temps, les moyens 9 calculent les coefficients $$G_{l,m,n*}=y_l^m\left({\theta }_{n*},{\phi }_{n*}\right)$$
  
  où (θ_n* , φ _n*) est la direction de l'élément de restitution 3 _n*. Dans un second temps, les moyens 9 calculent les coefficients $$G_{l,m}=\sqrt{{\displaystyle \sum _{n=1}^{N_f}}{G}_{l,m,n*}^2}$$
  

In a substep 48, the parameter {( l _k , m _k )} ( f ) is derived from the parameters L ( f ) and x _{n *} as follows:

• As a first step, the means 9 calculate the coefficients $${\mathrm{BOY\; WUT}}_{l,m,\mathrm{not}*}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}*},{\phi }_{\mathrm{not}*}\right)$$
  
  where ( θ _{n *} , φ _{n *} ) is the direction of the element of restitution 3 _{n *} . In a second step, the means 9 calculate the coefficients $${\mathrm{BOY\; WUT}}_{l,m}=\sqrt{{\displaystyle \underset{\mathrm{not}=1}{\overset{{\mathrm{NOT}}_f}{\Sigma }}}{\mathrm{BOY\; WUT}}_{l,m,\mathrm{not}*}^2}$$
  

• recherche de G_l = max(G_l,m ) ;
• détermination de la liste C_l des coefficients (l, m) tels que G_l,m (en dB) soit compris entre G_l - ε(en dB) et G_l (en dB).

In a third step, the means 8 calculate, using an additional parameter ε , the list of parameters {( l _k , m _k )} ( f ) , which is called C and which is initially empty. For each value of the order l , starting at 0, the means 8 perform the following substeps:

• search for G _l = max ( G _{l, m} );
• determination of the list C _l of coefficients ( l, m) such that G _{l, m} (in dB) is between G _l - ε (in dB) and G _l (in dB).

If the sum of the number of terms in C and the number of terms in C _l is greater than or equal to the number N _f of restitution elements active at the frequency f , the list C is complete, otherwise C ₁ to C is added and we start looking for G _l for l +1.

• La liste des coefficients {(l_k, m_k )}(f) prend la forme : $$\left\{\left(0,0\right),\left(1,-1\right),\left(1,1\right),\left(2,-2\right),\left(2,2\right)\dots \left({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">L</figure-callout>}}_1,-{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\right),\left(L_1,{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\right)\right\}$$
  
  où L₁ est choisi de sorte que le nombre d'éléments dans cette liste soit inférieur au nombre N _f d'éléments 3 _n* actifs à la fréquence f. L ₁ peut prendre pour valeur la partie entière de (N_f -1)/2, mais il est préférable de prendre pour L ₁ une valeur plus faible.

In the case where all the elements 3 _{1 *} to 3 _{Nf *} are in a horizontal plane and the list of {( l _k , m _k )} ( f ) is neither input nor provided, the simulation means 8 perform a simplified treatment:

• The list of coefficients {( l _k , m _k )} ( f ) takes the form: $$\left\{\left(0,0\right),\left(1,-1\right),\left(1,1\right),\left(2,-2\right),\left(2,2\right)...\left({\mathrm{The}}_1,-{\mathrm{The}}_1\right),\left({\mathrm{The}}_1,{\mathrm{The}}_1\right)\right\}$$
  
  where L ₁ is chosen such that the number of elements in this list is less than the number N _f of elements 3 _{n *} active at the frequency f. L ₁ can take as value the integer part of ( N _f -1) / 2, but it is better to take for L ₁ a lower value.

During a substep 49, the parameter μ ( f ), which represents at the current frequency f the desired local adaptation capacity, varying between 0 and 1, is determined automatically by taking for example the default value 0, 7.

Thus, the simulation means 9 make it possible, during step 40, to complete the signals SL, RP and OS so as to deliver to the means 12 for determining reconstruction filters all the parameters necessary for their implementation.

Depending on the parameters entered or measured, some of the simulation sub-steps described are not performed.

The simulation step 40 consisting of all the substeps 41 to 49, is repeated for all the frequencies considered. Alternatively, each substep is performed for all frequencies before proceeding to the next substep.

In another embodiment, all the intervening parameters are provided to the decoder 1 and the step 40 then comprises only the substep 41 for receiving and checking the signals SL, RP and OS and the substep 44 for determining the active elements at the frequency f considered.

The simulation means 8 implementing step 40 are, for example, computer programs or dedicated electronic cards for such an application or any other appropriate means.

We will now describe in more detail the step 50 of determining reconstruction filters and the means 12 which implement it.

On the figure 7 the means 12 for determining reconstruction filters comprising a module 82 for determining transfer matrices from the parameters of the signals SL, RP and OS and means 84 for determining a decoding matrix D are represented . .

The means 12 also comprise a module 86 for storing the response of the reconstruction filters and a module 88 for setting up reconstruction filters.

On the figure 8 , the detail of the step 50 of determining reconstruction filters is shown.

Step 50 is repeated for each operating frequency and comprises a plurality of sub-steps for determining matrices representative of previously defined parameters.

The step 50 of determining reconstruction filters comprises a sub-step 51 of determining an acoustic field weighting matrix W from the signals L ( f ) and W _l ( f ) .

W is a diagonal matrix of size ( L ( f ) +1) ² containing the weighting coefficients W _l ( f ) and in which each coefficient W _l ( f ) is 2 l + 1 times later on the diagonal. The matrix W thus has the following form: $$W=\left[\begin{array}{cccccccc}{W}_0\left(\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0007.png"\; state="\{\{state\}\}">f</figure-callout>}\right)& 0& \cdots & \cdots & \cdots & \cdots & \cdots & 0\\ 0& W_1\left(f\right)& \ddots & & & & & ⋮\\ ⋮& \ddots & W_1\left(f\right)& \ddots & & & & ⋮\\ ⋮& & \ddots & W_1\left(f\right)& \ddots & & & ⋮\\ ⋮& & & \ddots & \ddots & \ddots & & ⋮\\ ⋮& & & & \ddots & W_{\mathrm{The}}\left(f\right)& \ddots & ⋮\\ ⋮& & & & & \ddots & \ddots & 0\\ 0& \cdots & \cdots & \cdots & \cdots & \cdots & 0& W_{\mathrm{The}}\left(f\right)\end{array}\right]$$

Similarly, step 50 comprises a sub-step 52 of determining a matrix M representative of the radiation of the restitution set from the parameters N _{l, m, n *} ( f ) , RM (f ), H _{n *} ( f ), x _{n *} and L ( f ) .

M is a matrix of size ( L ( f ) +1) ² on N _f , consisting of elements M _{l, m, n *} , the indices l, m denoting the line l ² + l + m and n * denoting the column n. The matrix M thus has the following form: $$\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{0,0,1*}& {\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="2"\; label="M"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{0,0,2*}& \cdots \cdots & {\mathrm{<figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout>}}_{0,0,{\mathrm{NOT}}_f*}\\ {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1,1*}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1,2*}& \cdots \cdots & {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout>}}_{1,-1,{\mathrm{NOT}}_f*}\\ {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{1,0,1*}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="2"\; label="M"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{1,0,2*}& \cdots \cdots & {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="M"\; filenames="imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout>}}_{1,0,{\mathrm{NOT}}_f*}\\ {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{1,1,1*}& {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="2"\; label="M"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout></figure-callout>}}_{1,1,2*}& \cdots \cdots & {\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="M"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">M</figure-callout></figure-callout>}}_{1,1,{\mathrm{NOT}}_f*}\\ ⋮& ⋮& \cdots \cdots & ⋮\\ M_{\mathrm{The},-\mathrm{The},1*}& M_{\mathrm{The},-\mathrm{The},2*}& \cdots \cdots & M_{\mathrm{The},-\mathrm{The},{\mathrm{NOT}}_f*}\\ ⋮& ⋮& \cdots \cdots & ⋮\\ M_{\mathrm{The},0,1*}& M_{\mathrm{The},0,2*}& \cdots \cdots & M_{\mathrm{The},0,{\mathrm{NOT}}_f*}\\ ⋮& ⋮& \cdots \cdots & ⋮\\ M_{\mathrm{The},\mathrm{The},1*}& M_{\mathrm{The},\mathrm{The},2*}& \cdots \cdots & M_{\mathrm{The},\mathrm{The},{\mathrm{NOT}}_f*}\end{array}\right]$$

• si RM(f) définit un modèle de rayonnement en ondes planes, $$M_{l,m,n*}=y_l^m\left({\theta }_{n*},{\phi }_{n*}\right)H_{n*}\left(f\right)$$
  
• si RM(f) définit un modèle de rayonnement en ondes sphériques, $$M_{l,m,n*}=y_l^m\left({\theta }_{n*},{\phi }_{n*}\right)H_{n*}\left(f\right){\xi }_l\left(r_{n*},f\right)$$
  
• si RM(f) définit un modèle utilisant les mesures effectuées des réponses spatio-temporelles, avec recours au modèle d'ondes planes pour les mesures manquantes, alors M_l,m,n* = N_l,m,n* (f) pour les indices l,m,n* fournis et la fréquence courante f. Le reste des M_l,m,n* est déterminé selon la relation : $$M_{l,m,n*}=y_l^m\left({\theta }_{n*},{\phi }_{n*}\right)H_{n*}\left(f\right)$$
  
• si RM(f) définit un modèle utilisant les mesures effectuées des réponses spatio-temporelles, avec recours au modèle d'ondes sphériques pour les mesures manquantes, alors M_l,m,n* = N_l,m,n* (f) pour les indices l,m,n* fournis et la fréquence courante f. Le reste des M_l,m,n* est déterminé selon la relation : $$M_{l,m,n*}=y_l^m\left({\theta }_{n*},{\phi }_{n*}\right)H_{n*}\left(f\right){\xi }_l\left(r_{n*},f\right)$$
  

The elements M _{l , m, n * are} obtained according to the radiation pattern RM ( f ):

• if RM ( f ) defines a plane wave radiation pattern, $$M_{l,m,\mathrm{not}*}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}*},{\phi }_{\mathrm{not}*}\right)H_{\mathrm{not}*}\left(f\right)$$
  
• if RM ( f ) defines a radiation pattern in spherical waves, $$M_{l,m,\mathrm{not}*}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}*},{\phi }_{\mathrm{not}*}\right)H_{\mathrm{not}*}\left(f\right){\xi }_l\left(r_{\mathrm{not}*},f\right)$$
  
• if RM ( f ) defines a model using measurements made of spatio-temporal responses, using the plane wave model for the missing measurements, then M _{l, m, n *} = N _{l, m, n *} ( f ) for the indices l, m, n * provided and the current frequency f. The remainder of M _{l, m, n *} is determined according to the relation: $$M_{l,m,\mathrm{not}*}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}*},{\phi }_{\mathrm{not}*}\right)H_{\mathrm{not}*}\left(f\right)$$
  
• if RM ( f ) defines a model using the measurements made of spatio-temporal responses, using the spherical wave model for the missing measurements, then M _{l, m, n *} = N _{l, m, n *} ( f ) for the indices l, m, n * provided and the current frequency f . The remainder of M _{l, m, n *} is determined according to the relation: $$M_{l,m,\mathrm{not}*}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}*},{\phi }_{\mathrm{not}*}\right)H_{\mathrm{not}*}\left(f\right){\xi }_l\left(r_{\mathrm{not}*},f\right)$$
  

In these expressions ξ _l ( r _{n *} , f ) is defined by the expression: $${\xi }_l\left(r_{\mathrm{not}*},f\right)={\displaystyle \underset{k=0}{\overset{l}{\Sigma }}}\frac{\left(l+k\right)!}{2^{k}k!\left(l+k\right)!}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">j</figure-callout>}2\pi r_{\mathrm{not}*}f}{\mathrm{vs}}\right)}^{-k}$$

The matrix M thus defined is representative of the radiation of the reproduction unit. In particular, M is representative of the spatial configuration of the restitution set.

When the method uses the coefficients N _{/ , m, n} ( f ) , the matrix M is representative of the spatio-temporal responses of the elements 3 ₁ to 3 _N and therefore in particular of the room effect induced by the listening location 4 .

Step 50 also includes a substep 53 for determining a matrix F representative of the Fourier-Bessel functions for which a perfect reconstruction is required. This matrix is determined from the parameter L ( f ), as well as the parameters {( l _k , m _k )} ( f ) as follows.

From the list {( l _k , m _k )} ( f ) , by calling K the number of elements ( l _k , m _k ) of the list {( l _k , m _k )} ( f ) , the matrix F constituted is of size K on ( L ( f ) +1) ² . Each line k of the matrix F contains a 1 on the column l _k ² + l _{k +} m _k , and 0 elsewhere. For example, for a configuration of the restitution set of type called "5.1", whose list {(l _k , m _k )} ( f ) can take the form {(0,0), (1, -1 ), (1,1)}, the matrix F is written: $$\mathit{F}=\left[\begin{array}{ccccccccc}1& 0& 0& 0& 0& 0& 0& \cdots & 0\\ 0& 1& 0& 0& 0& 0& 0& \cdots & 0\\ 0& 0& 0& 1& 0& 0& 0& \cdots & 0\end{array}\right]$$

When the parameter μ ( f ) is zero, the decoder 1 reproduces only the Fourier-Bessel functions enumerated by the parameters {( l _k , m _k )} ( f ) , the others being ignored. When μ ( f ) is set to 1, the decoder perfectly reproduces the Fourier-Bessel functions designated by {( l _k , m _k )} ( f ) but also partially reproduces many other Fourier-Bessel functions among those available. up to the order L ( f ) so that the reconstructed field is generally closer to that described in input. This partial reconstruction allows the decoder 1 to adapt to very irregular restitution configurations in their angular distribution.

The substeps 51 to 53 implemented by the module 82 may be executed sequentially or simultaneously.

The step 50 of determining reconstruction filters then comprises a substep 54 for taking into account all the parameters determined previously, implemented by the module 84 in order to deliver a decoding matrix D * representative of the filters of FIG. reconstruction.

avec $$\mathit{A}={\left(\left(1-\mu \right){\mathit{I}}_N+\mu {\mathit{M}}^{\mathrm{T}}\mathit{WM}\right)}^{-1}$$

où M ^T désigne la matrice transposée conjuguée de M. This matrix D * is delivered from matrices M, F, W and the parameter μ ( f ) according to the following expression: $$\mathit{D}*=\mu \mathit{AT}{\mathit{M}}^{\mathrm{T}}\mathit{W}+\mathit{AT}{\mathit{M}}^{\mathrm{T}}{\mathit{F}}^{\mathrm{T}}{\left(\mathit{FM}\mathit{AT}{\mathit{M}}^{\mathrm{T}}{\mathit{F}}^{\mathrm{T}}\right)}^{-1}\mathit{F}\left({\mathit{I}}_{{\left(\mathrm{The}+1\right)}^2}-\mu \mathit{MY}{\mathit{M}}^{\mathrm{T}}\mathit{W}\right)$$

with $$\mathit{AT}={\left(\left(1-\mu \right){\mathit{I}}_{\mathrm{NOT}}+\mu {\mathit{M}}^{\mathrm{T}}\mathit{WM}\right)}^{-1}$$

where M ^T denotes the conjugated transposed matrix of M.

The elements D * _{n, l , m} of the matrix D * are organized as follows: $$\left[\begin{array}{cccccccccc}{D*}_{1,0,0}& {D*}_{1,1,-1}& {D*}_{1,1,0}& {D*}_{1,1,1}& \cdots & {D*}_{1,\mathrm{The},\mathrm{The}}& \cdots & {D*}_{1,\mathrm{The},0}& \cdots & {D*}_{1,\mathrm{The},\mathrm{The}}\\ {D*}_{2,0,0}& {D*}_{2,1,-1}& {D*}_{2,1,0}& {D*}_{2,1,1}& \cdots & {D*}_{2,\mathrm{The},-\mathrm{The}}& \cdots & {D*}_{2,\mathrm{The},0}& \cdots & {D*}_{2,\mathrm{The},\mathrm{The}}\\ ⋮& ⋮& ⋮& ⋮& & ⋮& & ⋮& & ⋮\\ {D*}_{{\mathrm{NOT}}_f,0,0}& {D*}_{{\mathrm{NOT}}_f,1,-1}& {D*}_{{\mathrm{NOT}}_f,1,0}& {D*}_{{\mathrm{NOT}}_f,1,1}& \cdots & {D*}_{{\mathrm{NOT}}_f,\mathrm{The},-\mathrm{The}}& \cdots & {D*}_{{\mathrm{NOT}}_f,\mathrm{The},0}& \cdots & {D*}_{{\mathrm{NOT}}_f,\mathrm{The},\mathrm{The}}\end{array}\right]$$

The matrix D * is therefore representative of the configuration of the reproduction assembly, the acoustic characteristics associated with the elements 3 ₁ to 3 _N and optimization strategies.

In the case where the method uses the coefficients N _{l , m , n} ( f ), the matrix D * is representative in particular of the room effect induced by the listening room 4.

Subsequently, during a substep 55, the module 86 for storing the response of the reconstruction filters at the current frequency f completes for the frequency f the matrix D ( f ) representative of the frequency response of the filters of reconstruction, receiving as input the matrix D *. The elements of the matrix D * are stored in the matrix D ( f ), by inverting the method for determining the list { n *} ( f ) described above with reference to the figure 6 . More precisely, each element D * _{n , l , m} of the matrix D * is stored in the element D _{n *, l, m} ( f ) of the matrix D ( f ). The elements of D ( f ) not determined at the end of this substep are set to 0.

Such a use of the list { n *} ( f ) makes it possible to take into account heterogeneous templates of the rendering elements 3 ₁ to 3 _N.

The elements D _{n, l, m} ( f ) of the matrix D ( f ) are organized as follows: $$\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="D"\; filenames="imgf0007.png"\; state="\{\{state\}\}">D</figure-callout></figure-callout>}}_{1,0,0}\left(\mathrm{<figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{1,1,-1}\left(\mathrm{<figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{1,1,0}\left(\mathrm{<figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{1,1,1}\left(\mathrm{<figure-callout\; id="1"\; label="f\; \cdots \; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)& \cdots & D_{}{}_{1,\mathrm{The},\mathrm{The}}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">D</figure-callout>}}_{1,\mathrm{The},0}\left(\mathrm{<figure-callout\; id="1"\; label="f\; \cdots \; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)& \cdots & D_{}{}_{1,\mathrm{The},\mathrm{The}}\left(\mathrm{<figure-callout\; id="2"\; label="f\; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="0"\; label="f\; D"\; filenames="imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& \\ D_{}{}_{}{}_{2,0,0}\left(\mathrm{<figure-callout\; id="2"\; label="f\; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{2,1,-1}\left(\mathrm{<figure-callout\; id="2"\; label="f\; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{2,1,0}\left(\mathrm{<figure-callout\; id="2"\; label="f\; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}"><figure-callout\; id="1"\; label="f\; D"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout></figure-callout>},\right)& D_{}{}_{}{}_{2,1,1}\left(\mathrm{<figure-callout\; id="2"\; label="f\; \cdots \; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)& \cdots & D_{}{}_{2,\mathrm{The},-\mathrm{The}}\left(f\right)& \cdots & {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">D</figure-callout>}}_{2,\mathrm{The},0}\left(\mathrm{<figure-callout\; id="2"\; label="f\; \cdots \; D"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">f\; </figure-callout>},\right)& \cdots & D_{}{}_{2,\mathrm{The},\mathrm{The}}\left(f\right)\\ ⋮& ⋮& ⋮& ⋮& & ⋮& & ⋮& & ⋮\\ D_{\mathrm{NOT},0,0}\left(f\right)& D_{\mathrm{NOT},1,-1}\left(f\right)& D_{\mathrm{NOT},1,0}\left(f\right)& D_{\mathrm{NOT},1,1}\left(f\right)& \cdots & D_{\mathrm{NOT},\mathrm{The},-\mathrm{The}}\left(f\right)& \cdots & D_{\mathrm{NOT},\mathrm{The},0}\left(f\right)& \cdots & D_{\mathrm{NOT},\mathrm{The},\mathrm{The}}\left(f\right)\end{array}\right]$$

The set of substeps 51 to 55 is repeated for all the frequencies f considered and the results are stored in the storage module 86. At the end of this processing, the matrix D ( f ) representative of the frequency responses of the set of reconstruction filters is addressed to module 88 for setting up reconstruction filters.

In a substep 58, the reconstruction filter parameterization module 88 then supplies the signal FD representative of the reconstruction filters, while receiving the matrix D (f) as input . Each element D _n , _{l, m} ( f ) of the matrix D ( f ) is a reconstruction filter which is described in the signal FD by means of parameters which may take different forms.

• une réponse en fréquence, dont les paramètres sont directement les valeurs de D _n, _l,m (f) pour certaines fréquences f ;
• une réponse impulsionnelle finie, dont les paramètres d_n,l,m (t) sont calculés par transformée de Fourier temporelle inverse de D _n,l,m (f). Chaque réponse impulsionnelle d_n,l,m (t) est échantillonnée puis tronquée à une longueur propre à chaque réponse ; ou
• des coefficients d'un filtre récursif à réponse impulsionnelle infinie calculé à partir des D_n,l,m (f) avec des méthodes d'adaptation classiques.

For example, the parameters of the signal FD associated with each filter D _{n, l, m} ( f ) can take the following forms:

• a frequency response whose parameters are directly the values of D _n , _{l , m} ( f ) for certain frequencies f ;
• a finite impulse response whose parameters d _{n, l, m} ( t ) are calculated by inverse time Fourier transform of D _{n, l, m} ( f ). Every answer impulse d _{n, l, m} ( t ) is sampled then truncated to a length specific to each response; or
• coefficients of an infinite impulse response recursive filter calculated from D _{n, l, m} ( f ) with conventional adaptation methods.

Thus, the means 12 for determining reconstruction filters deliver at the end of step 50 a signal FD to the means 11 for determining control signals.

• configuration spatiale des éléments de l'ensemble de restitution ;
• caractéristiques acoustiques associées aux éléments de l'ensemble de restitution, notamment les réponses en fréquence et les réponses spatio-temporelles représentatives, entre autre, de l'effet de salle induit par le lieu d'écoute 4 ;
• stratégies d'optimisation, notamment les fonctions spatio-temporelles dont on impose la reconstruction, la répartition dans l'espace de contraintes de reconstruction du champ acoustique et la capacité d'adaptation locale souhaitée à l'irrégularité spatiale de la configuration de l'ensemble de restitution 2.

In this embodiment, this signal FD is representative of the following parameters:

• spatial configuration of the elements of the rendering set;
• acoustic characteristics associated with the elements of the restitution ensemble, in particular the frequency responses and the spatio-temporal responses representative, inter alia, of the room effect induced by the listening place 4;
• optimization strategies, in particular the spatio-temporal functions whose reconstruction is imposed, the spatial distribution of acoustic field reconstruction constraints and the desired local adaptation capacity to the spatial irregularity of the configuration of the ensemble of restitution 2.

The means 12 for determining reconstruction filters may be implemented in the form of software dedicated to this function or may be integrated in an electronic card or any other appropriate means.

We will now describe in more detail the step 60 of formatting the input signal.

• un environnement sonore codé selon une distribution angulaire tel que par exemple le format communément appelé « format B » ;
• une description d'un environnement sonore au moyen d'informations de position de sources virtuelles qui composent l'environnement sonore et des signaux émis par ces sources ;
• un environnement sonore codé en multicanal, c'est-à-dire au moyen de signaux destinés à alimenter des haut-parleurs dont la répartition angulaire est fixée et connue et qui inclut notamment les techniques dites «7.1 », «5.1», quadriphoniques, stéréophoniques, et monophoniques.
• un environnement sonore donné par son champ acoustique sous la forme de coefficients de Fourier-Bessel.

When the system is implemented, it receives the input signal SI which includes temporal and spatial information of a sound environment to be rendered. This information can be of several types, including:

• a sound environment encoded according to an angular distribution such as for example the format commonly called "format B";
• a description of a sound environment using virtual source position information that composes the sound environment and signals from these sources;
• a multichannel coded sound environment, ie by means of signals intended to supply loudspeakers whose angular distribution is fixed and known and which includes in particular the so-called "7.1", "5.1", quadraphonic, stereophonic, and monophonic techniques.
• a sound environment given by its acoustic field in the form of Fourier-Bessel coefficients.

As has been said with reference to the figure 3 during step 60, the shaping means 6 receive the input signal S1 and decompose it into Fourier-Bessel coefficients representative of an acoustic field corresponding to the sound environment described by the signal S1. These Fourier-Bessel coefficients are delivered to the decoder 1 by the signal IF _FB .

Depending on the nature of the input signal S1, the shaping step 60 varies.

With reference to the figure 9 the decomposition in Fourier-Bessel coefficients will now be described in the case where the sound environment is coded in the signal SI in the form of the description of a sound scene by means of position information of the virtual sources which compose it and signals emitted by these sources.

A matrix E makes it possible to assign to each virtual source s a radiation model, for example a spherical wave. E is a matrix of size ( L +1) ² on S, where S is the number of sources present in the scene and L is the order in which the decomposition is conducted. The position of a source s is designated by its spherical coordinates r _s , θ _s and φ _s . The elements E _{l, m, s} of matrix E are written in the following way: $$E_{l,m,s}\left(f\right)=\frac{1}{r_s}{e}^{-2{\mathit{\pi jr}}_{s}f/\mathrm{vs}}{\mathrm{there}}_l^m\left({\theta }_s,{\phi }_s\right){\xi }_l\left(r_{s,f}\right)$$

We also introduce the vector Y which contains the temporal Fourier transforms Y _s ( f ) of the signals y _s (t) emitted by the sources. Y is written: $$Y={\left[\begin{array}{cccc}{Y}_1\left(f\right)& Y_2\left(f\right)& \cdots & Y_S\left(f\right)\end{array}\right]}^{\mathrm{t}}$$

The Fourier-Bessel coefficients P _{l , m} (f ) are placed in a vector P of size ( L +1) ² , where the 2 l + 1 order terms 1 are placed one after the other by increasing the order. The coefficient P _{l , m} ( f ) is thus the element of index l ² + / + m of the vector P which is written: $$P=\mathit{E}\mathit{Y}$$

As is shown with reference to the figure 9 , obtaining the Fourier-Bessel coefficients P _{l, m} ( f ), constituting the signal IF _FB , corresponds to a filtering each signal Y _s ( f ) by means of the filter E _{l, m, s} ( f ), and then summing the results. The coefficients P _{l, m} ( f ) are thus expressed as follows: $$P_{l,m}\left(f\right)={\displaystyle \underset{s=1}{\overset{S}{\Sigma }}}{Y}_s\left(f\right)E_{l,m,s}\left(f\right)$$

• le filtrage dans le domaine fréquentiel ;
• le filtrage à l'aide d'un filtre à réponse impulsionnelle finie ; ou
• le filtrage à l'aide d'un filtre à réponse impulsionnelle infinie. Il s'agit de la méthode la plus directe qui consiste à déduire de l'expression E_l,m,s (f) un filtre récursif, par exemple à l'aide d'une transformée bilinéaire.

The implantation of filters E _{l, m, s} ( f) can be carried out according to conventional filtering methods, such as for example:

• filtering in the frequency domain;
• filtering using a finite impulse response filter; or
• filtering using an infinite impulse response filter. This is the most straightforward method of deducing from the expression E _{l, m, s} ( f ) a recursive filter, for example using a bilinear transform.

In the case where the signal SI corresponds to the representation of a sound environment in a multichannel format, the shaping means 6 perform the operations described below.

A matrix S can be assigned to each channel c a radiation source, for example plane wave direction of arrival (θ _c, φ _c) corresponding to the direction of the return element associated with the channel c in the multichannel format considered. S is a size matrix ( L +1) ² on C , where C is the number of channels. The elements S _{l , m, c} of the matrix S are written: $$S_{l,m,\mathrm{vs}}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{vs}},{\phi }_{\mathrm{vs}}\right)$$

The vector Y which contains the signals y _c ( t ) corresponding to each channel is also defined. Y is written: $$Y={\left[\begin{array}{cccc}{\mathrm{there}}_1\left(t\right)& {\mathrm{there}}_2\left(t\right)& \cdots & {\mathrm{there}}_{\mathrm{VS}}\left(t\right)\end{array}\right]}^{\mathrm{t}}$$

The Fourier-Bessel coefficients p _{l, m} ( t ) grouped as previously in the vector P are obtained by the relation: $$P=\mathit{S}\mathit{Y}$$

Each Fourier-Bessel coefficient p _{l, m} ( t ) constituting the signal SI _FB is obtained by linear combination of the signals y _c ( t ): $$p_{l,m}\left(t\right)={\displaystyle \underset{\mathrm{vs}=1}{\overset{\mathrm{VS}}{\Sigma }}}{\mathrm{there}}_{\mathrm{vs}}\left(t\right)S_{l,m,\mathrm{vs}}$$

$$p_{1,1}\left(t\right)=\sqrt{\frac{3}{8\pi }}X\left(t\right)$$

$$p_{1,-1}\left(t\right)=-\sqrt{\frac{3}{8\pi }}Y\left(t\right)$$

$$p_{1,0}\left(t\right)=\sqrt{\frac{3}{8\pi }}Z\left(t\right)$$

In the case where the signal SI corresponds to the angular description of a sound environment according to the format-B, the four signals W ( t ), X ( t ), Y ( t ) and Z ( t ) of this format decompose by applying simple gains: $${\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="imgf0007.png"\; state="\{\{state\}\}">p</figure-callout>}}_{0,0}\left(t\right)=\frac{1}{\sqrt{4\pi }}\mathrm{<figure-callout\; id="1"\; label="W\; t\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">W\; </figure-callout>}\left(t\right)$$

$$p_{}$$$${}_{1,1}\left(t\right)=\sqrt{\frac{3}{8\pi }}\mathrm{<figure-callout\; id="1"\; label="X\; t\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">X\; </figure-callout>}\left(t\right)$$

$$p_{}$$$${}_{1,-1}\left(t\right)=-\sqrt{\frac{3}{8\pi }}\mathrm{<figure-callout\; id="1"\; label="Y\; t\; p"\; filenames="imgf0005.png,imgf0007.png"\; state="\{\{state\}\}">Y\; </figure-callout>}\left(t\right)$$

$$p_{}$$$${}_{1,0}\left(t\right)=\sqrt{\frac{3}{8\pi }}Z\left(t\right)$$

Finally, in the case where the signal SI corresponds to a description of the acoustic field in the form of Fourier-Bessel coefficients, step 60 consists of a simple signal transmission.

Thus, at the end of the shaping step 60, the means 6 deliver, to the attention of the means 11 for determining driving signals, an IF signal _FB corresponding to the decomposition of the acoustic field to be restored in one direction. finite number of Fourier-Bessel coefficients.

The means 6 may be made in the form of dedicated computer software or may be made in the form of a dedicated computer card or any other appropriate means.

We will now describe in more detail step 70 of determining driving signals.

The means 11 for determining driving signals receive as input the signal IF _FB corresponding to the Fourier-Bessel coefficients representative of the acoustic field to be restored and the signal FD representative of the reconstruction filters coming from the means 12. As mentioned previously , the signal FD integrates characteristic parameters of the reproduction set 2.

From this information, during the step 70, the means 11 determine the signals sc ₁ ( t ) to sc _N ( t ) delivered to the attention of the elements 3 ₁ to 3 _N. These signals are obtained by applying to IF signal _FB the reconstruction filters, frequency response D _{n, l, m} ( f ), and transmitted in the FD signal.

avec P_l,m (f) les coefficients de Fourier-Bessel constituant le signal SI_FB et V_n (f) défini par : $$V_n\left(f\right)=\frac{{\mathit{SC}}_n\left(f\right)}{r_n}{e}^{-2\mathit{\pi j}{r}_{n}f/c}$$

où SC_n (f) est la transformée de Fourier temporelle de sc_n (t). The reconstruction filters are applied as follows: $$V_{\mathrm{not}}\left(f\right)={\displaystyle \underset{l=0}{\overset{\mathrm{The}}{\Sigma }}}{\displaystyle \underset{m=-l}{\overset{l}{\Sigma }}}{P}_{l,m}\left(f\right)D_{\mathrm{not},l,m}\left(f\right)$$

with P _{l, m} ( f ) the Fourier-Bessel coefficients constituting the signal IF _FB and V _n ( f ) defined by: $$V_{\mathrm{not}}\left(f\right)=\frac{{\mathit{SC}}_{\mathrm{not}}\left(f\right)}{r_{\mathrm{not}}}{e}^{-2\mathit{\pi j}{r}_{\mathrm{not}}f/\mathrm{vs}}$$

where SC _n ( f ) is the time Fourier transform of sc _n ( t ) .

• le signal FD fournit directement les réponses en fréquence D_n,l,m (f), et le filtrage est effectué dans le domaine fréquentiel, par exemple, à l'aide des techniques usuelles de convolution par blocs ;
• le signal FD fournit les réponses impulsionnelles finies d_n,l,m (t), et le filtrage est effectué dans le domaine temporel par convolution ; ou
• le signal FD fournit les coefficients de filtres récursifs à réponses impulsionnelles infinies, et le filtrage est effectué dans le domaine temporel au moyen des relations de récurrence.

According to the form of the parameters of the signal FD, each filtering of the P _{l, m} ( f ) by D _{n, l, m} ( f ) can be carried out according to conventional filtering methods, such as for example:

• the signal FD directly supplies the frequency responses D _{n, l, m} ( f ) , and the filtering is performed in the frequency domain, for example, using standard block convolution techniques;
• the FD signal provides the finite impulse responses d _{n, l, m} ( t ), and the filtering is done in the time domain by convolution; or
• the FD signal provides the recursive filter coefficients with infinite impulse responses, and the filtering is performed in the time domain by means of the recurrence relations.

On the figure 10 the case of the finite impulse response filter has been represented.

We define T _{n, l, m} the number of samples specific to each response d _{n, l, m} ( t ), which leads to the following convolution expression: $$v_{\mathrm{not}}\left[t\right]={\displaystyle \underset{l=0}{\overset{\mathrm{The}}{\Sigma }}}{\displaystyle \underset{m=-l}{\overset{l}{\Sigma }}}{\displaystyle \underset{\tau =0}{\overset{T_{\mathrm{not},l,m}-1}{\Sigma }}}{d}_{\mathrm{not},l,m}\left[\tau \right]p_{l,m}\left[t-\tau \right]$$

Step 70 ends with a gain adjustment and the application of delays to temporally align the wave fronts of the elements 3 ₁ to 3 _N of the restitution assembly 2 with respect to the most distant element . The signals sc ₁ ( t ) to sc _N ( t ) intended to feed elements 3 ₁ to 3 _N are deduced from the signals v ₁ ( t ) to v _N ( t ) according to the expression: $${\mathit{sc}}_{\mathrm{not}}\left(t\right)=r_{\mathrm{not}}{v}_{\mathrm{not}}\left(t-\frac{\max \left(r_{\mathrm{not}}\right)-r_{\mathrm{not}}}{\mathrm{vs}}\right)$$

Each element 3 ₁ to 3 _N therefore receives a specific driving signal sc ₁ to sc _N and emits an acoustic field which contributes to the optimal reconstruction of the acoustic field to be restored. Simultaneous control of all elements 3 ₁ to 3 _N allows optimal reconstruction of the acoustic field to be restored.

Moreover, the described system can also operate in simplified modes.

• x _n , représentatif de la position de l'élément 3 _n de l'ensemble de restitution 2 ;
• W_l , décrivant, directement sous forme de pondération des coefficients de Fourier-Bessel, une fenêtre spatiale représentative de la répartition dans l'espace de contraintes de reconstruction du champ acoustique ; et
• L, imposant l'ordre limite de fonctionnement des moyens 12 de détermination de filtres de reconstruction.

For example, in a first simplified embodiment, during step 50, the module 12 for determining filters receives only the following parameters:

• x _n , representative of the position of the element 3 _n of the restitution assembly 2;
• W _l , describing, directly in the form of weighting of the Fourier-Bessel coefficients, a spatial window representative of the distribution in the space of constraints of reconstruction of the acoustic field; and
• L, imposing the limit order of operation of the means 12 for determining reconstruction filters.

In this simplified mode, these parameters are independent of the frequency and the elements 3 ₁ to 3 _N of the restitution set are active and assumed to be ideal for all the frequencies. The substeps of step 50 are therefore performed only once. In substep 52, the matrix M is constructed from a plane wave radiation pattern. The elements M _{l, m, n} of the matrix M are simplified by: $$M_{l,m,\mathrm{not}}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}},{\phi }_{\mathrm{not}}\right)$$

In this simplified mode, μ = 1 and the list {( l _k , m _k )} ( f ) does not contain any term. In the sub-step 54, the module 84 then directly determines the matrix D according to the simplified expression: $$\mathit{D}={\left({\mathit{M}}^T\mathit{WM}\right)}^{-1}{\mathit{M}}^T\mathit{W}$$

The storage of the response of the reconstruction filters is no longer necessary, and the sub-step 55 is not performed. Likewise, since the filters described in the matrix D are simple gains, the sub-step 58 is not carried out either and the module 84 directly supplies the signal FD.

avec $$v_n\left(t\right)={\displaystyle \sum _{l=0}^L}{\displaystyle \sum _{m=-l}^l}{p}_{l,m}\left(t\right)D_{n,l,m}$$

In step 70, the determination of the control signals takes place in the time domain and corresponds to simple linear combinations of the coefficients p _{l , m} ( t ) followed by a time alignment according to the expression: $${\mathit{sc}}_{\mathrm{not}}\left(t\right)=r_{\mathrm{not}}{v}_{\mathrm{not}}\left(t-\frac{\max \left(r_{\mathrm{not}}\right)-r_{\mathrm{not}}}{\mathrm{vs}}\right)$$

with $$v_{\mathrm{not}}\left(t\right)={\displaystyle \underset{l=0}{\overset{\mathrm{The}}{\Sigma }}}{\displaystyle \underset{m=-l}{\overset{l}{\Sigma }}}{p}_{l,m}\left(t\right)D_{\mathrm{not},l,m}$$

The module 11 then supplies the control signals sc ₁ ( t ) to sc _N ( t ) for the reproduction unit.

• x _n , représentatif de la position de l'élément 3 _n de l'ensemble de restitution 2 ;
• {(l_k,m_k )}, constituant la liste des fonctions spatio-temporelles dont la reconstruction est imposée ; et
• L, imposant l'ordre de fonctionnement des moyens 12 de détermination de filtres de reconstruction.

In another simplified embodiment, during step 50, the module 12 for determining filters receives as input the following parameters:

• x _n , representative of the position of the element 3 _n of the restitution assembly 2;
• {( l _k , m _k )}, constituting the list of spatio-temporal functions whose reconstruction is imposed; and
• L, imposing the order of operation of the means 12 for determining reconstruction filters.

In this simplified mode the parameters are independent of the frequency and the elements 3 ₁ to 3 _N of the restitution set are active and assumed ideal for all the frequencies. The substeps of step 50 are therefore performed only once. In substep 52, the matrix M is constructed from a plane wave radiation pattern. The elements M _{l, m, n} of the matrix M are simplified by: $$M_{l,m,\mathrm{not}}={\mathrm{there}}_l^m\left({\theta }_{\mathrm{not}},{\phi }_{\mathrm{not}}\right)$$

Sub-step 53 for determining the matrix F remains unchanged. In this simplified mode μ = 0 and in the sub-step 54, the module 84 directly determines the matrix D according to the simplified expression: $$\mathit{D}={\mathit{M}}^{\mathrm{T}}{\mathit{F}}^{\mathrm{T}}{\left(\mathit{FM}{\mathit{M}}^{\mathrm{T}}{\mathit{F}}^{\mathrm{T}}\right)}^{-1}\mathit{F}$$

The storage of the response of the reconstruction filters is no longer necessary, and the sub-step 55 is not performed. The filters described in the matrix D being simple gains, the sub-step 58 is not carried out either. It is therefore the module 84 which directly supplies the FD signal.

avec $$v_n\left(t\right)={\displaystyle \sum _{l=0}^L}{\displaystyle \sum _{m=-l}^l}{p}_{l,m}\left(t\right)D_{n,l,m}$$

In step 70, the determination of the control signals takes place in the time domain and corresponds to simple linear combinations of the coefficients p _{l, m} ( t ) followed by a time alignment according to the expression: $${\mathit{sc}}_{\mathrm{not}}\left(t\right)=r_{\mathrm{not}}{v}_{\mathrm{not}}\left(t-\frac{\max \left(r_{\mathrm{not}}\right)-r_{\mathrm{not}}}{\mathrm{vs}}\right)$$

with $$v_{\mathrm{not}}\left(t\right)={\displaystyle \underset{l=0}{\overset{\mathrm{The}}{\Sigma }}}{\displaystyle \underset{m=-l}{\overset{l}{\Sigma }}}{p}_{l,m}\left(t\right)D_{\mathrm{not},l,m}$$

The module 11 then supplies the control signals sc ₁ ( t ) to sc _N ( t ) for the reproduction unit.

It appears that according to the invention, the control signals sc ₁ to sc _N are adapted to make the best use of the spatial characteristics of the reproduction unit 2, the acoustic characteristics associated with the elements 3 ₁ to 3 _N and optimization strategies in order to reconstruct a high quality acoustic field.

It therefore appears that the method used makes it possible in particular to obtain an optimum restitution of a three-dimensional acoustic field regardless of the spatial configuration of the reproduction unit 2.

The invention is not limited to the described embodiments.

In particular, the method of the invention can be implemented by digital computers such as one or more computer processors or digital signal processors (DSP).

It can also be implemented from a general platform such as a personal computer.

It is also possible to design an electronic card intended to be inserted into another element and adapted to memorize and execute the method of the invention. For example, such an electronic card integrates into a computer.

In other embodiments, all or part of the parameters necessary for the execution of the step of determining reconstruction filters is extracted from pre-recorded memories or is delivered by another apparatus dedicated to this function.

Claims (35)

1. A method of controlling a reproduction unit (2) for restoring an acoustic field so as to obtain a reproduced acoustic field of specific characteristics independent of the intrinsic characteristics of reproduction of said unit (2), said reproduction unit (2) comprising a plurality of reproduction elements (3₁ to 3_N), characterized in that it comprises at least:

   - a step of establishing a finite number of coefficients corresponding to a decomposition of said acoustic field to reproduce as a linear combination of spatio-temporal functions such that the coefficients are representative of the distribution in time and in the three dimensions in space of said acoustic field to be reproduced;

   - a step (50) of determining reconstruction filters representative of said reproduction unit (2), comprising a substep (54) of taking into account at least spatial characteristics of said reproduction unit (2), the spatial characteristics comprising a distance between the reproduction elements (3₁ to 3_N) and a predetermined arbitrary center (5), and an angular position of the reproduction elements with respect to the center, the angular position comprising an orientation in the vertical plane and an orientation in the horizontal plane;

   - a step (70) of determining at least one control signal (sc₁ to sc_N) for said elements (3₁ to 3_N) of said reproduction unit (2), said at least one signal being obtained by the application, to said coefficients, of said reconstruction filters; and

   - a step of delivering said at least one control signal (sc₁ to sc_N), with a view to an application to said reproduction elements (3₁ to 3_N) so as to generate said acoustic field reproduced by said reproduction unit (2).
2. The method as claimed in claim 1, characterized in that said step of establishing a finite number of coefficients representative of the distribution of said acoustic field to be reproduced comprises:

   - a step consisting in providing an input signal (SI) comprising temporal and spatial information for a sound environment; and

   - a step of shaping (60) said input signal (SI) by decomposing said information over a basis of spatio-temporal functions, this shaping step (60) making it possible to deliver a representation of said acoustic field to be reproduced corresponding to said sound environment in the form of a linear combination of said functions.
3. The method as claimed in claim 1, characterized in that said step of establishing a finite number of coefficients representative of the distribution of said acoustic field to be reproduced comprises:

   - a step consisting in providing an input signal (SI_FB) comprising a finite number of coefficients representative of said acoustic field to be reproduced in the form of a linear combination of spatio-temporal functions.
4. The method as claimed in any one of claims 2 or 3, characterized in that said spatio-temporal functions are so-called Fourier-Bessel functions and/or linear combinations of these functions.
5. The method as claimed in any one of claims 1 to 4, characterized in that said substep (54) of taking into account at least spatial characteristics of said reproduction unit (2) is carried out at least with the help of parameters representative, for each element (3_n), of the three coordinates of its position (x_n) with respect to the center (5) placed in the listening zone (4), and/or of its spatio-temporal response (N_l,m,n(f)).
6. The method as claimed in claim 5, characterized in that said substep (54) of taking into account at least spatial characteristics of said reproduction unit (2) is carried out moreover with the help:

   - of parameters (W_l(f)) describing, in the form of weighting coefficients, a spatial window which specifies the distribution in space of reconstruction constraints for the acoustic field; and

   - of a parameter (L(f)) describing an order of operation limiting the number of coefficients to be taken into account during said step (50) of determining reconstruction filters.
7. The method as claimed in one of claims 5 or 6, characterized in that said substep (54) of taking into account characteristics of said reproduction unit (2) is carried out moreover with the help:

   - of parameters (((l_k,m_k))(f)) constituting a list of spatio-temporal functions whose reconstruction is imposed; and

   - of a parameter (L(f)) describing an order of operation limiting the number of coefficients to be taken into account during said step (50) of determining reconstruction filters.
8. The method as claimed in one of claims 5 to 7, characterized in that said step (54) of taking into account at least spatial characteristics of said reproduction unit (2) is carried out moreover at least with the help of one of the parameters chosen from the group consisting:

   - of parameters (x_n) representative of at least one of the three coordinates of the position of each or some of the elements (3₁ to 3_N), with respect to the center (5) placed in the listening zone (4);

   - of parameters (N_l,m,n(f)) representative of the spatio-temporal responses of each or some of the elements (3₁ to 3_N);

   - of a parameter (L(f)) describing an order of operation limiting the number of coefficients to be taken into account during said step (50) of determining reconstruction filters;

   - of parameters ({(l_k,m_k)}(f)) constituting a list of spatio-temporal functions whose reconstruction is imposed;

   - of parameters (G_n(f)) representative of the templates of said reproduction elements (3₁ to 3_N);

   - of a parameter (µ(f)) representative of the desired local capacity of adaptation to the spatial irregularity of the configuration of said reproduction unit (2);

   - of a parameter (RM(f)) defining the radiation model for said reproduction elements (3₁ to 3_N);

   - of parameters (H_n(f)) representative of the frequency response of said reproduction elements (3₁ to 3_N);

   - of a parameter (W(r,f)) representative of a spatial window;

   - of parameters (W_l(f)) representative of a spatial window in the form of weighting coefficients; and

   - of a parameter (R(f)) representative of the radius of a spatial window when the latter is a ball.
9. The method as claimed in one of claims 5 to 8, characterized in that it comprises a calibration step (30) making it possible to deliver all or part of the parameters used in said step (50) of determining reconstruction filters.
10. The method as claimed in claim 9, characterized in that said calibration step (30) comprises, for at least one of the reproduction elements (3_n):

    - a substep (34) of acquiring signals representative of the radiation of said at least one element (3_n) in the listening region (4); and

    - a substep (39) of determining spatial and/or acoustic parameters of said at least one element (3_n).
11. The method as claimed in claim 10, characterized in that said calibration step (30) comprises:

    - a substep (32) of emitting a specific signal (u_n(t)) to said at least one element (3_n) of said reproduction unit (2), said acquisition substep (34) corresponding to the acquisition of the sound wave emitted in response by said at least one element (3_n); and

    - a substep (36) of transforming said signals acquired into a finite number of coefficients representative of the sound wave emitted, so as to allow the carrying out of said substep (39) of determining spatial and/or acoustic parameters.
12. The method as claimed in claim 10, characterized in that said acquisition substep (34) corresponds to a substep of receiving a number of coefficients representative of the acoustic field generated by said at least one element (3_n) in the form of a linear combination of spatio-temporal functions, which coefficients are used directly during said substep (39) of determining spatial and/or acoustic parameters of said at least one element (3_n).
13. The method as claimed in any one of claims 9 to 12, characterized in that said calibration substep (30) furthermore comprises a substep of determining the position in at least one of the three dimensions in space of said at least one element (3_n) of said reproduction unit (2).
14. The method as claimed in any one of claims 9 to 13, characterized in that said calibration step (30) furthermore comprises a substep (38) of determining the spatio-temporal response (N_l,m,n(f)) of said at least one element (3_n) of said reproduction unit.
15. The method as claimed in any one of claims 9 to 14, characterized in that said calibration step (30) furthermore comprises a substep of determining the frequency response (H_n(f)) of said at least one element (3_n) of said reproduction unit (2).
16. The method as claimed in any one of the preceding claims, characterized in that it comprises a step (40) of simulating all or part of the parameters necessary for carrying out said step (50) of determining reconstruction filters.
17. The method as claimed in claim 16, characterized in that said simulation step (40) comprises:

    - a substep (41) of determining missing parameters from among the parameters used during said step (50) of determining reconstruction filters;

    - a plurality of calculation substeps (42, 43, 44, 45, 46, 47, 48, 49) making it possible to determine the value or values of the missing parameter or parameters as defined previously as a function of the parameters received, of the frequency, and of predetermined default parameters.
18. The method as claimed in claim 17, characterized in that said simulation step (40) comprises a substep (44) of determining a list ({n*}(f)) of elements of the reproduction unit that are active as a function of the frequency, and in that said calculation substeps are carried out just for the elements of said list.
19. The method as claimed in any one of claims 17 or 18, characterized in that said simulation step (40) comprises a substep (45) of calculating a parameter (L(f)) representative of the order of operation limiting the number of coefficients to be taken into account during said step (50) of determining reconstruction filters with the help of at least the position in space of all or part of the elements (3_n) of the reproduction unit.
20. The method as claimed in any one of claims 17 to 19, characterized in that said simulation step comprises a step (47) of determining parameters (W_l(f)) representative of a spatial window in the form of weighting coefficients with the help of a parameter (W(r,f)) representative of the spatial window in the spherical reference frame and/or of a parameter (R(f)) representative of the radius of said spatial window when the latter is a ball.
21. The method as claimed in one of claims 17 to 20, characterized in that said simulation step (40) comprises a substep (43) of determining a list ({l_k, m_k}(f)) of spatio-temporal functions whose reconstruction is imposed with the help of the position of all or part of the elements (3_n) of the reproduction unit (2).
22. The method as claimed in any one of the preceding claims, characterized in that it comprises a step of input (20) making it possible to determine all or part of the parameters used during said step (50) of determining reconstruction filters.
23. The method as claimed in any one of the preceding claims, characterized in that said step (50) of determining reconstruction filters comprises:

    - a plurality of calculation substeps (51, 52, 53) carried out for a finite number of frequencies of operation and making it possible to deliver a matrix (W) for weighting the acoustic field, a matrix (M) representative of the radiation of the reproduction unit (2), and a matrix (F) representative of the spatio-temporal functions whose reconstruction is imposed; and

    - a substep (54) of calculating a decoding matrix (D*), carried out for a finite number of operating frequencies, with the help of the matrix (W) for weighting the acoustic field, of the matrix (M) representative of the radiation of the reproduction unit (2), of the matrix (F) representative of the spatio-temporal functions whose reconstruction is imposed, and of a parameter (µ(f)) representative of the desired local capacity of adaptation to the spatial irregularity of the reproduction unit, representative of the reconstruction filters.
24. The method as claimed in claim 23, characterized in that said calculation substep (52) making it possible to deliver a matrix (M) representative of the radiation of the reproduction unit (2) is carried out with the help of parameters representative for each element (3_n):

    - of the three coordinates of its position ( x _n ) with respect to the center (5) placed in the listening zone (4); and/or

    - of its spatio-temporal response (N_l,m,n(f)).
25. The method as claimed in claim 24, characterized in that said calculation substep (52) making it possible to deliver a matrix (M) representative of the radiation of the reproduction unit (2) is carried out moreover with the help of parameters representative for each element (3_n) of its frequency response (H_n(f)).
26. A computer program comprising program code instructions for the execution of the steps of the method as claimed in any one of claims 1 to 25, when said program is executed on a computer.
27. A removable medium of the type comprising at least one processor and a nonvolatile memory element, characterized in that said memory comprises a program comprising instructions for the execution of the steps of the method as claimed in any one of claims 1 to 25, when said processor executes said program.
28. A device for controlling a reproduction unit (2) for restoring an acoustic field, comprising a plurality of reproduction elements (3₁ to 3_N), characterized in that it comprises at least:

    - means (12) of determining reconstruction filters representative of said reproduction unit (2), adapted so as to make it possible to take into account at least spatial characteristics of said reproduction unit (2), the spatial characteristics comprising a distance between the reproduction elements (3₁ to 3_N) and a predetermined arbitrary center (5), and an angular position of the reproduction elements with respect to the center, the angular position comprising an orientation in the vertical plane and an orientation in the horizontal plane; and

    - means (11) for determining at least one control signal (sc₁ to sc_N) for said elements (3₁ to 3_N) of said reproduction unit (2), said at least one signal being obtained by application of said reconstruction filters to a finite number of coefficients corresponding to a decomposition of said acoustic field to reproduce as a linear combination of spatio-temporal functions such that the coefficients are representative of the distribution in time and in the three dimensions in space of said acoustic field to be reproduced.
29. The device as claimed in claim 28, characterized in that it is associated with means (6) for shaping an input signal (SI) comprising temporal and spatial information for a sound environment to be reproduced, which means are adapted for decomposing said information over a basis of spatio-temporal functions so as to deliver a signal (SI_FB) comprising said finite number of coefficients representative of the distribution in time and in the three dimensions in space of said acoustic field to be reproduced, corresponding to said sound environment, in the form of a linear combination of said spatio-temporal functions.
30. The device as claimed in claim 29, characterized in that said spatio-temporal functions are so-called Fourier-Bessel functions and/or linear combinations of these functions.
31. The device as claimed in any one of claims 28 to 30, characterized in that said means (12) for determining reconstruction filters receive as input at least one of the parameters from the following parameters:

    - parameters (x_n) representative of at least one of the three coordinates of the position of each or some of the elements (3₁ to 3_N), with respect to the center (5) placed in the listening zone (4);

    - parameters (N_l,m,n(f)) representative of the spatio-temporal responses of each of some of the elements (3₁ to 3_N);

    - a parameter (L(f)) describing an order of operation limiting the number of coefficients to be taken into account in the means (12) of determining reconstruction filters;

    - parameters (G_n(f)) representative of the templates of said reproduction elements (3₁ to 3_N);

    - a parameter (µ(f)) representative of the desired local capacity of adaptation to the spatial irregularity of the configuration of said reproduction unit (2);

    - a parameter (RM(f)) defining the radiation model for said reproduction elements (3₁ to 3_N);

    - parameters (H_n(f)) representative of the frequency response of said reproduction elements (3₁ to 3_N);

    - a parameter (W(r,f)) representative of a spatial window;

    - parameters (W_l(f)) representative of a spatial window in the form of weighting coefficients;

    - a parameter (R(f)) representative of the radius of a spatial window when the latter is a ball; and

    - parameters ({(l_k,m_k)}(f)) constituting a list of spatio-temporal functions whose reconstruction is imposed.
32. The device as claimed in any one of claims 28 to 31, characterized in that each of said parameters received by said means (12) of determining reconstruction filters is conveyed by one of the signals from the group of the following signals:

    - a definition signal (SL) comprising information representative of the spatial characteristics of the reproduction unit (2);

    - a supplementary signal (RP) comprising information representative of the acoustic characteristics associated with the elements (3₁ to 3_N) of the reproduction unit (2); and

    - an optimization signal (OS) comprising information relating to an optimization strategy,

    - so as to deliver, with the aid of the parameters contained in these signals, a signal (FD) representative of said reconstruction filters representative of said reproduction unit (2).
33. The device as claimed in claim 32, characterized in that it is associated with means (7) for determining all or part of the parameters received by said means (12) for determining reconstruction filters, said means (7) comprising at least one of the following elements:

    - simulation means (8);

    - calibration means (9);

    - parameters input means (10).
34. The device as claimed in any one of claims 28 to 33, characterized in that said means (12) for determining reconstruction filters are adapted for determining a set of filters representative of the position in space of the elements (3₁ to 3_N) of the reproduction unit (2).
35. The device as claimed in any one of claims 28 to 34, characterized in that said means (12) of determining reconstruction filters are adapted for determining a set of filters representative of the room effect induced by the listening zone (4).

Images