EP2168121B1 - Quantification after linear conversion combining audio signals of a sound scene, and related encoder - Google Patents

Description

The present invention relates to audio signal coding devices, intended in particular to take place in applications for transmission or storage of digitized and compressed audio signals.

The invention relates more specifically to the quantization modules included in these audio coding devices.

The invention more particularly relates to 3D sound stage coding. A 3D sound scene, also called spatialized sound, comprises a plurality of audio channels each corresponding to monophonic signals.

A signal coding technique for a sound stage used in the "MPEG Audio Surround" encoder (see "Text of ISO / IEC FDIS 23003-1, MPEG Surround", ISO / IEC JTC1 / SC29 / WG11 N8324, July 2006 , Klagenfurt, Austria), includes the extraction and coding of spatial parameters from the set of monophonic audio signals on the different channels. These signals are then mixed to obtain a monophonic or stereophonic signal, which is then compressed by a conventional mono or stereo encoder (for example of the MPEG-4 AAC, HE-AAC type, etc.). At the level of the decoder, the synthesis of the rendered 3D sound scene is made from the spatial parameters and the decoded mono or stereo signal.

The coding of the multichannel signals in certain cases requires the introduction of a transformation (KLT, Ambiophonic, DCT, etc.) making it possible to better take into account the interactions that may exist between the different signals of the sound scene to be encoded.

It is always necessary to increase the audio quality of the sound scenes restored after a coding and decoding operation.

DERRIEN O & DUHAMEL P: "A statistical approach for the optimization of MPEG-2/4 AAC (Advanced Audio Coder) in stereo stereophonic mode (stereo MS)", ACTS OF SYMPOSIUM OF THE GROUP OF STUDIES OF SIGNAL PROCESSING AND IMAGES (GRETSI), 2003, pages 1-4 discloses a method of quantizing components in a stereo MS system.

The object of the invention is to find an improvement for the quantization in a multichannel system. This object is solved by the independent claims. According to a first aspect, the invention proposes a method for quantifying components, at least some of these components being each determined according to a plurality of audio signals of a scene. sound and calculable by applying a linear transformation on said audio signals.

According to the method, a quantization function is determined to be applied to said components in a given frequency band by testing a condition relating to at least one audio signal and depending at least on a comparison made between a psychoacoustic masking threshold relative to the audio signal. in the given frequency band, and a value determined according to the inverse linear transformation and quantization errors of the components by said function on the given frequency band.

Such a method therefore makes it possible to determine a quantization function which makes it possible to mask, in the playback listening field, the noise introduced with respect to the audio signal of the initial sound scene. The sound scene restored after the coding and decoding operations thus presents a better audio quality.

Indeed, the introduction of a multichannel transform (for example of the ambiophonic type) transforms the real signals into a new domain different from the listening domain. The quantification of the components resulting from this transform according to the methods of the state of the art, based on a perceptual criterion (ie respecting the masking threshold on the latter), does not guarantee a minimal distortion on the real signals restored in the listening domain. Indeed, the calculation of the quantization function according to the invention makes it possible to guarantee that the quantization noises induced on the real signals by the quantization of the transformed components are minimal in the sense of a perceptual criterion. The condition of a maximum improvement of the perceptual quality of the signals in the listening domain is then verified.

In one embodiment, the condition is relative to several audio signals and depends on several comparisons, each comparison being made between a psychoacoustic masking threshold relative to a respective audio signal in the given frequency band, and a value determined according to the inverse linear transformation and quantization errors of the components by said function.

This arrangement further enhances the audio quality of the restored sound stage.

In one embodiment, the determination of the quantization function is repeated when updating the values of the components to be quantized. This arrangement also makes it possible to increase the audio quality of the restored sound scene, by adapting the quantization over time according to the characteristics of the signals.

où s est la bande de fréquence donnée, r est le nombre de composantes, h_i,j est le coefficient de la transformée linéaire inverse relatif au signal audio et à la j^ème composante avec j=1 à r, B_j (s) représente un paramètre de la fonction de quantification dans la bande s relative à la j^ème composante et ${\mu }_{\begin{array}{c}1\\ 2\end{array},j}\left(s\right)$

est l'espérance mathématique dans la bande s de la racine carrée de la j^ème composante.In one embodiment, the condition relating to an audio signal is tested at least by comparing the psychoacoustic masking threshold relative to the audio signal and an element representing the value. ${\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\left(h_{i,j}^2{\mathrm{<figure-callout\; id="3"\; label="B\; j\; s"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">B\; </figure-callout>}}_j{\left(s\right)}^{}{\left(\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\begin{array}{c}1\\ 2\end{array},j}\left(s\right)\right),}$

where s is the given frequency band, r is the number of components, h _{i, j} is the coefficient of the inverse linear transform relative to the audio signal and the j ^th component with j = 1 to r, B _j ( s ) represents a parameter of the quantization function s in the band on the j ^th component and ${\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\begin{array}{c}1\\ 2\end{array},j}\left(s\right)$

is the expected value in the strip s of the square root of the ^jth component.

In one embodiment, a quantization function is determined to apply components in the given frequency band using an iterative process generating at each iteration a parameter of the candidate quantization function satisfying the condition and associated with a corresponding flow rate, the iteration being stopped when the flow rate is below a given threshold.

Such an arrangement thus makes it possible to simply determine a quantization function based on the determined parameters, allowing the noise to be masked in the playback listening domain while reducing the coding bit rate below a given threshold.

In one embodiment, the linear transformation is an ambiophonic transformation.

In a particular embodiment, the linear transformation is an ambiophonic transformation (called "ambisonic"). This This arrangement makes it possible on the one hand to reduce the number of data to be transmitted since, in general, the N signals can be very satisfactorily described by a reduced number of ambiophonic components (for example, a number equal to 3 or 5). , which is smaller than N. This arrangement also allows coding adaptability to any type of sound rendering system, since it is sufficient at the decoder level to apply an inverse surround transform of size Q'x (2p '+ 1). , (where Q 'is equal to the number of loudspeakers of the sound rendering system used at the output of the decoder and 2p' + 1 the number of received surround components), to determine the signals to be supplied to the sound rendering system.

The invention can be implemented with any linear transformation, for example the DCT or the KLT (in English "Karhunen Loeve Transform") transform which corresponds to a decomposition on principal components in a space representing the statistics of the signals and allows to distinguish the most energetic components from the least energy components.

According to a second aspect, the invention proposes a quantization module adapted to quantify components, at least some of these components being each determined according to a plurality of audio signals of a sound scene and calculable by application of a transformation. linearly on said audio signals, said quantization module being adapted to implement the steps of a method according to the first aspect of the invention.

• un module de transformation adapté pour calculer par application d'une transformation linéaire sur lesdits signaux audio, des composantes dont certaines au moins sont déterminées chacune en fonction d'une pluralité des signaux audio d'une scène sonore ; et
• un module de quantification suivant le deuxième aspect de l'invention adapté pour déterminer au moins une fonction de quantification sur au moins une bande de fréquence donnée et pour quantifier les composantes sur la bande de fréquence donnée en fonction d'au moins la fonction de quantification déterminée ;
• le codeur audio étant adapté pour constituer un flux binaire en fonction au moins de données de quantification délivrées par le module de quantification.

According to a third aspect, the invention provides an audio coder adapted to encode an audio scene comprising a plurality of respective signals into an output bit stream, comprising:

• a transformation module adapted to calculate by applying a linear transformation on said audio signals, components at least some of which are determined each according to a plurality of audio signals of a sound scene; and
• a quantization module according to the second aspect of the invention adapted to determine at least one quantization function over at least a given frequency band and for quantizing the components on the given frequency band as a function of at least the determined quantization function;
• the audio coder being adapted to constitute a bit stream according to at least quantization data delivered by the quantization module.

According to a fourth aspect, the invention proposes a computer program to be installed in a quantization module, said program comprising instructions for implementing the steps of a method according to the first aspect of the invention during an execution. of the program by means of processing said module.

According to a fifth aspect, the invention proposes coding data, determined following the implementation of a quantization method according to the first aspect of the invention.

• la figure 1 représente un codeur dans un mode de réalisation de l'invention ;
• la figure 2 représente un décodeur dans un mode de réalisation de l'invention ;
• la figure 3 est un organigramme représentant des étapes d'un procédé dans un mode de réalisation de l'invention.

Other features and advantages of the invention will become apparent on reading the description which follows. This is purely illustrative and should be read in conjunction with the attached drawings in which:

• the figure 1 represents an encoder in one embodiment of the invention;
• the figure 2 represents a decoder in one embodiment of the invention;
• the figure 3 is a flowchart showing steps of a method in one embodiment of the invention.

The figure 1 represents an audio coder 1 in one embodiment of the invention. It relies on the technology of perceptual audio coders, for example MPEG-4 AAC type.

The encoder 1 comprises a time / frequency transformation module 2, a linear transformation module 3, a quantization module 4, a Huffman entropy coding module 5 and a masking curve calculation module 6, for transmission. a bit stream Φ representing the signals supplied at the input of the encoder 1.

A 3D sound scene comprises N channels on each a respective audio signal S ₁ , ..., S _N is delivered.

The figure 2 represents an audio decoder 100 in one embodiment of the invention.

The decoder 100 comprises a bit sequence reading module 101, an inverse quantization module 102, an inverse linear transformation module 103, a frequency / time transformation module 104.

The decoder 100 is adapted to receive as input the bitstream Φ transmitted by the encoder 1 and to output Q 'signals S' ₁ , ..., S ' _Q , for supplying the Q' speakers H1, H2 ..., HQ 'of a sound rendering system 105.

Operations performed at the encoder level:

The time / frequency conversion module 2 of the encoder 1 receives as input the N signals S ₁ ,... S _N of the 3D sound scene to be encoded, in the form of successive blocks.

Each block m received has N time frames each indicating different values taken over time by a respective signal.

On each time frame of each of the signals, the time / frequency transformation module 2 performs a time / frequency transformation, in this case a modified discrete cosine transform (MDCT).

Thus, following the reception of a new block comprising a new frame for each of the signals S _i , it determines, for each of the signals S _i , i = 1 to N, its spectral representation X _i , characterized by M coefficients MDCT X _{i, t} , with t = 0 to M-1. An MDCT coefficient X _{i, t} thus represents the spectrum of the signal Si for a frequency F _i .

The spectral representations X _i of the signals S _i , i = 1 to N, are provided at the input of the linear transformation module 3.

The spectral representations X _i of the signals S _i , i = 1 to N, are further provided at the input of the module 6 for calculating the masking curves.

The coding of multichannel signals comprises in the case considered a linear transformation, making it possible to take into account the interactions between the different audio signals to be coded, before the monophonic coding, by the quantization module 4, of the components resulting from the linear transformation.

The linear transformation module 3 is adapted to perform a linear transformation of the coefficients of the spectral representations ( X _i ) _{1 i i N N} provided. In one embodiment, it is adapted to perform spatial transformation. It then determines the spatial components of the signals ( X _i ) _{1 i i ≤ N} , in the frequency domain, resulting from the projection on a spatial reference system depending on the order of the transformation. The order of a spatial transformation is related to the angular frequency according to which it "scans" the sound field.

In the embodiment considered, the linear transformation module 3 performs an ambiophonic transformation of order p (for example p = 1), which gives a compact spatial representation of a 3D sound scene, by making projections of the sound field onto the spherical or cylindrical harmonic functions associated.

For more information on surround transformations, refer to the following documents: «Representation of acoustic fields, application to the transmission and reproduction of complex sound scenes in a multimedia context», Doctoral thesis of Paris 6 University, Jérôme DANIEL, July 31, 2001 , "A highly scalable spherical array based microphone on an orthonormal decomposition of the sound field," Jens Meyer - Gary Elko, Vol. He - pp. 1781-1784 in Proc. ICASSP 2002 .

The spatial transformation module 3 thus delivers r (r = 2p + 1) _ambiophonic components ( Y _j ) 1 _{≤ j ≤r} . Each ambiophonic component Y _j considered in the frequency domain, has M spectral parameters Y _{j, t} for t = 0 to M-1. The spectral parameter Y _{j, t} relates to the frequency F _t for t = 0 to M-1.

où $\mathrm{R}={\left(R_{i,j}\right)}_{\begin{array}{c}1\le i\le r\\ 1\le j\le N\end{array}}$

est la matrice de transformation ambiophonique d'ordre p pour la scène sonore spatiale, avec $R_{i,j}=1\mathrm{}{R}_{i,j}=\sqrt{2}\cos \left[\left(\frac{1}{2}\right){\theta }_j\right]$

si i pair et $R_{i,j}=\sqrt{2}\sin \left[\left(\frac{i-1}{2}\right){\theta }_j\right]$

si i impair supérieur ou égale à 3, et θj est l'angle de propagation du signal S_j dans l'espace de la scène 3D.The surround components are determined as follows: $$\left[\begin{array}{ccccc}{Y}_{1.0}& \cdot & \cdot & Y_{1M-1}& \\ \cdot & \cdot & \cdot & \cdot & \\ & & & & \cdot \\ \cdot & \cdot & \cdot & \cdot & \\ Y_{r\mathrm{,\; 0}}& \cdot & \cdot & Y_{r,M-1}& \end{array}\right]=\mathrm{R}\left[\begin{array}{ccccc}{X}_{1.0}& \cdot & \cdot & X_{1M-1}& \\ \cdot & \cdot & \cdot & \cdot & \\ & & & & \cdot \\ \cdot & \cdot & \cdot & \cdot & \\ X_{\mathrm{NOT}\mathrm{,\; 0}}& \cdot & \cdot & & X_{\mathrm{NOT},M-1}\end{array}\right]$$

or $\mathrm{R}={\left(R_{i,\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}\right)}_{\begin{array}{c}1\le i\le \mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}\\ 1\le j\le \mathrm{NOT}\end{array}}$

is the p-order ambiophonic transformation matrix for the spatial sound scene, with $R_{i,j}=1\mathrm{}{R}_{i,j}=\sqrt{2}\mathrm{<figure-callout\; id="1"\; label="cos"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">cos</figure-callout>}\left[\left(\frac{1}{2}\right){\theta }_j\right]$

if i pair and $R_{i,j}=\sqrt{2}\sin \left[\left(\frac{i-1}{2}\right){\theta }_j\right]$

if i odd greater than or equal to 3, and θj is the propagation angle of the signal S _j in the space of the 3D scene.

Each of the ambiophonic components is therefore determined according to several signals ( S _i ) _{1 i i ≤ N.}

The masking curve calculation module 6 is adapted to determine the spectral masking curve of each frame of a signal Si considered individually in the block m, using its spectral representation Xi and a psychoacoustic model.

relatif à la trame de chaque signal (S_i )_1≤i≤N dans le bloc m, pour chaque bande de fréquence s considérée lors de la quantification. Chaque bande de fréquence s est élément d'un ensemble de bandes de fréquence comprenant par exemple les bandes telles que normalisées pour le codeur MPEG-4 AAC.The masking curve calculation module 6 thus calculates a masking threshold $M_T^m\left(s,i\right),$

relating to the frame of each signal ( S _i ) _{1 i i ≤ N} in the block m, for each frequency band s considered during the quantization. Each frequency band s is part of a set of frequency bands including for example the bands as normalized for the MPEG-4 AAC encoder.

pour chaque signal S_i et chaque bande de fréquences s sont délivrés au module 4 de quantification.Masking thresholds $M_T^m\left(s,i\right)$

for each signal S _i and each frequency band s are delivered to the quantization module 4.

The quantization module 4 is adapted to quantize the components ( Y _j ) _{1 j j ≤ r} that are input to it, so as to reduce the bit rate required for transmission. Respective quantization functions are determined by the quantization module 4 on each frequency band s.

tel que la fréquence F_t est élément de la bande de fréquence s. Il détermine ainsi un indice de quantification i(k) pour chaque coefficient spectral ${\left(Y_{j,t}\right)}_{\begin{array}{c}1\le i\le r\\ 0\le t\le M-1\end{array}}$

tel que la fréquence F_t est élément de la bande de fréquence s.In any band, the quantization module 4 quantizes each spectral coefficient ${\left(Y_{j,\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}\right)}_{\begin{array}{c}1\le i\le \mathrm{<figure-callout\; id="0"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}\\ 0\le t\le M-1\end{array}}$

such that the frequency F _t is an element of the frequency band s. It thus determines a quantization index i (k) for each spectral coefficient ${\left(Y_{j,\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}\right)}_{\begin{array}{c}1\le i\le \mathrm{<figure-callout\; id="0"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}\\ 0\le t\le M-1\end{array}}$

such that the frequency F _t is an element of the frequency band s.

For a considered band s, k takes the values of the set { k _{min, s} , k _{min + 1 , s} , ... k _{max , s} }, and ( k _{max , s} - k _{min + 1 , s} + 1) is equal to the number of spectral coefficients to be quantified in the band s for all the surround components.

calculés pour un bloc m de signaux prend la forme suivante, conformément à la norme MPEG-4 AAC :
${\mathrm{Q}}^{\mathrm{m}}\left(Y_{j,t}\right)=\mathrm{Arr}\left({\left(\frac{Y_{j,t}}{B_j^m\left(s\right)}\right)}^{\frac{3}{4}}\right)$

avec la fréquence F_t élément de la bande de fréquence s, et il existe k élément de {k _min,s ,k _min+1,s ,... _kmax,s } tel que Q^m(Y_j,t ) = i(k). $B_j^m\left(s\right),$

coefficient d'échelle relatif à la composante ambiophonique Y_j, prend des valeurs discrètes. Il dépend du paramètre d'échelle entier relatif ${\varphi }_j^m\left(s\right):B_j^m\left(s\right)=2^{\frac{1}{4}{\varphi }_j^{m\left(s\right)}}.$

The quantization function Q ^m applied by the quantization module 4 for the coefficients ${\left(Y_{j,\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}\right)}_{\begin{array}{c}1\le j\le \mathrm{<figure-callout\; id="0"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}\\ 0\le t\le M-1\end{array}}$

calculated for a m-block of signals takes the following form, in accordance with MPEG-4 AAC:
${\mathrm{Q}}^{\mathrm{m}}\left(Y_{j,t}\right)=\mathrm{Arr}\left({\left(\frac{Y_{j,t}}{B_j^m\left(s\right)}\right)}^{\frac{3}{4}}\right)$

with the frequency F _t element of the frequency band s, and there exists k element of { k _{min , s} , k _{min + 1 , s} , ... _{k max, s} } such that Q ^m ( Y _{j, t} ) = i (k). $B_j^m\left(s\right),$

scale coefficient relative to the surround component Y _j , takes discrete values. It depends on the relative whole scale parameter ${\phi }_j^m\left(s\right):B_j^m\left(s\right)=2^{\frac{1}{4}{\phi }_j^{m\left(s\right)}}.$

Arr is a rounding function that delivers an integer value. Arr (x) is for example the function providing the integer closest to the variable x, or the function "integer part" of the variable x, etc.

de chaque signal S_i dans le domaine d'écoute, avec 1 ≤ i ≤ N, est supérieur à la puissance de l'erreur apportée, sur un signal audio restitué dans le domaine d'écoute correspondant au canal i (et non pas dans le domaine de transformation linéaire), par les erreurs de quantification apportée aux composantes ambiophoniques.The quantization module 4 is adapted to determine a quantization function to be applied on a frequency band that verifies that the masking threshold $M_T^m\left(s,i\right)$

of each signal S _i in the listening domain, with 1 ≤ i ≤ N, is greater than the power of the error made, on an audio signal restored in the listening domain corresponding to the channel i (and not in the linear transformation domain), by the quantization errors made to the ambiophonic components.

relatifs à chaque bande s, telle que, pour tout i, 1 ≤ i ≤ N, l'erreur introduite sur le signal S_i dans la bande s par la quantification des composantes ambiophoniques est inférieure au seuil de masquage $M_T^m\left(s,i\right)$

du signal S_i sur la bande s.The quantization module 4 is therefore adapted to determine, during the processing of a block m of signals, the quantization function defined using the scale parameters. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

relating to each band s, such that, for all i, 1 ≤ i ≤ N, the error introduced on the signal S _i in the band s by the quantification of the surround components is less than the masking threshold $M_T^m\left(s,i\right)$

of the signal S _i on the band s.

vérifiant la formule (1) suivante : $${\left\{B_j^m/P_e^m\left(s,i\right)\le M_T^m\left(s,i\right)\mathrm{,1}\le i\le N\right\}}_{1\le j\le r}$$

où $P_e^m\left(s,i\right)$

est la puissance d'erreur introduite sur le signal S_i suite aux erreurs de quantification introduites par la quantification, définie par les coefficients d'échelle ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r},$

des composantes ambiophoniques.A problem to be solved by the quantization module 4 is therefore to determine, on each band s, the set of scaling coefficients. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

verifying the following formula (1): $${\left\{B_j^m/P_e^m\left(s,i\right)\le M_T^m\left(s,i\right)\mathrm{,\; 1}\le i\le \mathrm{NOT}\right\}}_{1\le j\le r}$$

or $P_e^m\left(s,i\right)$

is the error power introduced on the signal S _i following the quantization errors introduced by the quantization, defined by the scaling coefficients ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r},$

ambiophonic components.

Thus, B _j (s) is a parameter characterizing the quantization function s in the band on the ^j-th component. The choice of B _j ( s ) determines in a bijective manner the quantization function used.

This arrangement has the effect that the noise brought into the listening domain by the quantization on the components resulting from the linear transformation remains masked by the signal in the listening domain, which contributes to a better quality of the signals restored in the listening domain.

où α est un taux fixé de respect du seuil de masquage.In one embodiment, the problem indicated above by the formula (1) is translated as the following formula (2): $${\left\{B_j^m/\mathrm{Probability}\left(P_e^m\left(s,i\right)\le M_T^m\left(s,i\right)\right)\ge \alpha \mathrm{,\; 1}\le i\le \mathrm{NOT}\right\}}_{1\le j\le r},$$

where α is a fixed rate of compliance with the masking threshold.

The probability is calculated for the frame relating to the signal S _i of the block m considered and on all the frequency bands s.

The justification for this translation is realized in the document "Optimization of the quantization by statistical models in the MPEG encoder Advanced Audio coder (AAC) - Application to the spatialization of a compressed signal in MPEG-4 environment", PhD thesis of Olivier Derrien - ENST Paris, 22 November 2002 , hereinafter referred to as "Derrien Document". According to this document, it is sought to modify the quantization so as to reduce the distortion perceived by the ear of a signal resulting from a spatialization filtering HRTF (in English "Head Related Transfer Function" also called head filter modeling the propagation path effect between the position of the sound source and the human ear and taking into account the effect due to the head and the torso of a listener, applied after the decoding.

où ${\left\{e_i^m\left(k\right)\right\}}_{k_{\min }\le k\le k_{\max }}$

sont les erreurs introduites sur les K_s = (k _max,s - k _min+1,s +1) coefficients spectraux du signal S_i correspondant à des fréquences dans la bande s.Otherwise, $P_e^m\left(s,i\right)={\displaystyle \underset{k=k_{\min }}{\overset{k=k_{\max }}{\Sigma }}{e}_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2,}$

or ${\left\{e_i^m\left(k\right)\right\}}_{k_{\min }\le k\le k_{\max }}$

are the errors introduced on the K _s = ( k _{max, s} - k _{min + 1, s} +1) spectral coefficients of the signal S _i corresponding to frequencies in the band s.

la matrice inverse de la matrice de transformation ambiophonique R, alors $e_i^m\left(k\right)={\displaystyle \sum _{j=1}^{j=r}{h}_{i,j}{v}_j^m\left(k\right),}$

où ${\left\{v_j^m\left(k\right)\right\}}_{k_{\min ,s}\le k\le k_{\max ,s}}$

sont les erreurs de quantification introduites sur les (k _{max ,s} - k _min+1,s + 1) coefficients spectraux de composantes ambiophoniques correspondant à des fréquences dans la bande s.Is $\mathrm{H}={\left(h_{i,\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}\right)}_{\begin{array}{c}1\le i\le \mathrm{NOT}\\ 1\le j\le r\end{array}}$

the inverse matrix of the ambiophonic transformation matrix R, then $e_i^m\left(k\right)={\displaystyle \underset{j=1}{\overset{j=r}{\Sigma }}{h}_{i,j}{v}_j^m\left(k\right),}$

or ${\left\{v_j^m\left(k\right)\right\}}_{k_{\min ,s}\le k\le k_{\max ,s}}$

are the quantization errors introduced on the ( k _{max , s} - k _{min + 1 , s} + 1) spectral coefficients of ambiophonic components corresponding to frequencies in the band s.

So $P_e^m\left(s,i\right)={\displaystyle \underset{k=k_{\mathrm{min,}s}}{\overset{k=k_{\max },s}{\Sigma }}{\left({\displaystyle \underset{j=1}{\overset{j=r}{\Sigma }}{h}_{i,j}{v}_{\mathrm{<figure-callout\; id="2"\; label="j\; m\; k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j\; </figure-callout>}}^m\left(k\right)\left(\right)}\right)}^2.}$

• les erreurs de quantification $e_i^m\left(k\right)$
  
  sont des variables aléatoires indépendantes équi-distribuées selon l'indice k ;
• les erreurs de quantification $e_i^m\left(k\right)$
  
  sont des variables aléatoires selon l'indice i ;
• le nombre d'échantillons dans une bande s est suffisamment grand ;
• le codeur 1 travaille à haute résolution.

The following assumptions are made:

• quantification errors $e_i^m\left(k\right)$
  
  are independent random variables equi-distributed according to the index k;
• quantification errors $e_i^m\left(k\right)$
  
  are random variables according to the index i;
• the number of samples in a band s is large enough;
• the coder 1 works at high resolution.

de l'erreur de quantification, dans une sous-bande s et pour un signal S_i , tend, lorsque le nombre de coefficients dans une bande s augmente, vers une gaussienne dont la moyenne $m_{P_e^m\left(s,S_i\right)}$

et la variance ${\sigma }_{P_e^m\left(s,S_i\right)}$

sont données par les formules suivantes : $$\{\begin{array}{ll}{m}_{P_e^m\left(s,i\right)}& ={\displaystyle \sum _{k=k_{\min ,s}}^{k_{\max ,s}}\mathrm{E}\left[e_i^m{\left(k\right)}^2\right]}\\ {\sigma }_{P_e^m\left(s,i\right)}^2& ={\displaystyle \sum _{k=k_{\min ,s}}^{k_{\max ,s}}\mathrm{E}\left[e_i^m{\left(k\right)}^4\right]-\mathrm{E}{\left[e_i^m{\left(k\right)}^2\right]}^2}\end{array}$$

où la fonction E[x] délivre la moyenne de la variable x.Under these assumptions and by applying the central limit theorem, the power $P_e^m\left(s,i\right)$

the quantization error, in a sub-band s and for a signal S _i , tends, when the number of coefficients in a band s increases, to a Gaussian whose average $m_{P_e^m\left(s,S_i\right)}$

and the variance ${\sigma }_{P_e^m\left(s,S_i\right)}$

are given by the following formulas: $$\{\begin{array}{ll}{m}_{P_e^m\left(s,i\right)}& ={\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}\mathrm{E}\left[e_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}\\ {\sigma }_{P_e^m\left(s,\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="imgf0002.png"\; state="\{\{state\}\}">i</figure-callout>}\right)}^2& ={\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}\mathrm{E}\left[e_i^m{\left(k\right)}^4\right]-\mathrm{E}{\left[e_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}^2}\end{array}$$

where the function E [x] delivers the average of the variable x.

» indiquée dans la formule 2 ci-dessus s'écrit alors à l'aide de la formule (3) suivante : $$m_{P_e^m\left(s,i\right)}+\beta \left(\alpha \right){\sigma }_{P_e^m\left(s,i\right)}\le M_T^m\left(s,i\right)$$

Avec : $$\beta \left(\alpha \right)=\sqrt{2}{\mathrm{Erf}}^{-1}\left(2\alpha -1\right)$$

et la fonction Erf ^-1(x) est l'inverse de la fonction d'erreur d'Euler.The "Probability" constraint $\left(P_e^m\left(s,i\right)\le M_T^m\left(s,i\right)\right)\ge \alpha$

Indicated in formula 2 above is then written using the following formula (3): $$m_{P_e^m\left(s,i\right)}+\beta \left(\alpha \right){\sigma }_{P_e^m\left(s,i\right)}\le M_T^m\left(s,i\right)$$

With: $$\beta \left(\alpha \right)=\sqrt{2}{\mathrm{Erf}}^{-1}\left(2\alpha -1\right)$$

and the function Erf ^-1 ( x ) is the inverse of the error function of Euler.

étant indépendantes selon l'indice i, on en déduit : $$\mathrm{E}\left[e_i^m{\left(k\right)}^2\right]={\displaystyle \sum _{j=1}^r{h}_{i,j}^2\mathrm{E}\left[v_i^m{\left(k\right)}^2\right]}$$

The variables $e_i^m\left(k\right)$

being independent according to the index i, we deduce: $$\mathrm{E}\left[e_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]={\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{h}_{i,j}^2\mathrm{E}\left[v_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}$$

Therefore, we get: $$m_{P_e^m\left(s,i\right)}={\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{h}_{i,j}^2\mathrm{E}\left[v_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}}={\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{h}_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2}{\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}\mathrm{E}\left[v_{\mathrm{<figure-callout\; id="2"\; label="j\; m\; k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j\; </figure-callout>}}^m{\left(k\right)}^{}{\left(\right)}^2\right]}$$

étant indépendantes et équi-distribuées selon l'indice k, les variables aléatoires $v_i^m\left(k\right)$

sont également indépendantes et équi-distribuées selon l'indice k. Par conséquent : $$m_{P_e^m\left(s,i\right)}=K_s\cdot {\displaystyle \sum _{j=1}^r{h}_{i,j}^2}\mathrm{E}\left[{\left(v_i^m\left(s\right)\right)}^2\right]$$

avec : $$K_s=k_{\max ,s}-k_{\min ,s}+1$$

Random variables $e_i^m\left(k\right)$

being independent and equi-distributed according to the index k, the random variables $v_i^m\left(k\right)$

are also independent and equi-distributed according to the index k. Therefore : $$m_{P_e^m\left(s,i\right)}=K_s\cdot {\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{h}_{i,j}^2}\mathrm{E}\left[{\left(v_i^m\left(s\right)\right)}^2\right]$$

with: $$K_s=k_{\max ,s}-k_{\min ,s}+1$$

d'erreur de quantification tendent vers des gaussiennes, alors : $$\mathrm{E}\left[e_i^m{\left(k\right)}^4\right]=3\mathrm{E}{\left[e_i^m{\left(k\right)}^2\right]}^2$$

It is assumed that the powers $P_e^m\left(s,i\right)$

of quantification error tend to Gaussians, then: $$\mathrm{E}\left[e_i^m{\left(\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="imgf0001.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^4\right]=3\mathrm{E}{\left[e_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}^2$$

From where : $${\sigma }^2{}_{P_e^m\left(s,i\right)}=2{\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}\mathrm{E}{\left[e_i^m{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2\right]}^2}$$

So we can write: $${\sigma }^2{}_{P_e^m\left(s,i\right)}=2{\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}{\left(h_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\mathrm{E}\left[v_{\mathrm{<figure-callout\; id="2"\; label="j\; m\; k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j\; </figure-callout>}}^m{\left(k\right)}^{}{\left(\right)}^2\right]}\right)}^2}$$

From this last equation, and applying the Cauchy-Schwartz inequality: $${\sigma }_{P_e^m\left(s,i\right)}=\sqrt{2}\sqrt{{\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}{\left(h_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\mathrm{E}\left[v_{\mathrm{<figure-callout\; id="2"\; label="j\; m\; k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j\; </figure-callout>}}^m{\left(k\right)}^{}{\left(\right)}^2\right]}\right)}^2}}\le \sqrt{2}{\displaystyle \underset{k=k_{\min ,s}}{\overset{k_{\max ,s}}{\Sigma }}{h}_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\mathrm{E}\left[v_{\mathrm{<figure-callout\; id="2"\; label="j\; m\; k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j\; </figure-callout>}}^m{\left(k\right)}^{}{\left(\right)}^2\right]}}$$

Which implies : $${\sigma }_{P_e^m\left(s,i\right)}\le \sqrt{2}{m}_{P_e^m\left(s,i\right)}$$

avec ${\mu }_{\frac{1}{2},j}$

représentant l'espérance mathématique de ${\left|Y_j^m\right|}^{\frac{1}{2}}$

dans la sous bande s traitée et e_R l'erreur d'arrondi propre à la fonction d'arrondi Arr.In addition, in high resolution: $$\mathrm{<figure-callout\; id="2"\; label="E\; v\; j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[v_j^{}\right]\left[{}_2^{}\right]\approx \frac{16}{9}\mathrm{E}\left[e_R^2\right]B_j^m{\left(s\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)$$

with ${\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}$

representing the mathematical expectation of ${\left|Y_j^m\right|}^{\frac{1}{2}}$

in the sub-band treated and e _R the rounding error specific to the rounding function Arr.

For example, if Arr (x) is the function providing the integer closest to the variable x, e _R is equal to 0.5. If Arr (x) is the function "integer part" of the variable x, e _R is equal to 1.

Thus the constraint given by the formula (3) relating to the signal S _i , i = 1 to N, on a band s, is written in the following form: $$K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\left(h_{i,j}^2{B}_j^m{\left(s\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)\right)}\le M_T^m\left(s,i\right)$$

calculés par le module 4 de quantification pour coder les composantes de la transformée, permettent ou non de respecter le seuil de masquage tel que considéré dans le domaine du signal.It is thus possible, from this last equation, to determine whether scaling coefficients ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

calculated by the quantization module 4 to code the components of the transform, allow or not to respect the masking threshold as considered in the signal domain.

This last equation represents a sufficient condition for the noise corresponding to the channel i to be masked at the output in the listening domain.

garantissant que le bruit dans le domaine d'écoute est masqué.In one embodiment of the invention, the quantization module 4 is adapted to determine using the latter equation, for a block m of current frames, scaling coefficients. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

ensuring that noise in the listening domain is hidden.

garantissant que le bruit dans le domaine d'écoute est masqué et en outre permettant de respecter une contrainte de débit.In a particular embodiment of the invention, the quantization module 4 is adapted to determine, for a block m of current frames, scaling coefficients. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

guaranteeing that the noise in the listening domain is masked and furthermore making it possible to respect a flow constraint.

• Minimiser le débit global $D^m={\displaystyle \sum _{j=1}^r{D}_j^m}$
  
• Sous la contrainte : $$K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \sum _{j=1}^r\left(h_{i,j}^2{B}_j^m{\left(s\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)\right)}\le M_T^m\left(s,i\right)$$
  
  pour toute bande s, avec $D_j^m$
  
  le débit global attribué à la composante ambiophonique Y_j .

In one embodiment, the conditions to be respected are the following:

• Minimize overall throughput $D^m={\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{D}_j^m}$
  
• Under duress : $$K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\left(h_{i,j}^2{B}_j^m{\left(s\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)\right)}\le M_T^m\left(s,i\right)$$
  
  for any band s, with $D_j^m$
  
  the overall bit rate assigned to the surround component Y _j .

où $D_j^m\left(s\right)$

est le débit attribué à la composante ambiophonique Y_j dans la bande s.We can write that: $$D_j^m={\displaystyle \underset{s}{\Sigma }{D}_j^m\left(s\right)}$$

or $D_j^m\left(s\right)$

is the bit rate assigned to the surround component Y _j in the band s.

dans chaque bande s. Dans une première approximation, on peut écrire que le débit attribué à une composante ambiophonique dans une bande s est une fonction logarithmique du coefficient d'échelle, soit : $$D_j^m\left(s\right)=D_{j\mathrm{,0}}^m-\gamma \ln \left(B_j^m\left(s\right)\right)$$

Minimize the overall flow D ^m is therefore to minimize the flow $D^m\left(s\right)={\displaystyle \underset{j=1}{\overset{r}{\Sigma }}{D}_j^m\left(s\right)}$

in each band s. In a first approximation, it can be written that the bit rate attributed to an ambiophonic component in a band s is a logarithmic function of the scale coefficient, namely: $$D_j^m\left(s\right)=D_{j\mathrm{,\; 0}}^m-\gamma \ln \left(B_j^m\left(s\right)\right)$$

The new function to be minimized is written in the following form: $$\mathrm{F}\left(s\right)=-{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\ln \left(B_j^m\left(s\right)\right)}$$

To solve the band quantization problem by minimizing the overall rate under the constraint (3), we must therefore minimize the function F under the constraint (3).

$$\mathrm{L}\left(\mathbf{B},\mathrm{\lambda }\right)=-{\displaystyle \sum _{j=1}^r\ln \left(B_j^m\left(s\right)\right)+{\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)B_j^m{\left(s\right)}^{\frac{3}{2}}-{\displaystyle \sum _{i=1}^N{\lambda }_i{M}_T^m\left(s,i\right)}}$$

The resolution of this constrained optimization problem is for example carried out using the Lagrangian method.
The Lagrangian function is written in the following form: $$\mathrm{The}\left(\mathbf{B},\mathrm{\lambda }\right)=-{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\ln \left(B_j^m\left(s\right)\right)}+{\displaystyle \underset{i=1}{\overset{\mathrm{NOT}}{\Sigma }}{\lambda }_i\left[K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\left(h_{i,j}^2{B}_j^m{\left(s\right)}^{\frac{3}{2}}{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)\right)-M_T^m\left(s,i\right)}\right]}$$

$$\mathrm{The}\left(\mathbf{B},\mathrm{\lambda }\right)=-{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\ln \left(B_j^m\left(s\right)\right)+{\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)B_j^m{\left(s\right)}^{\frac{3}{2}}-{\displaystyle \underset{i=1}{\overset{\mathrm{NOT}}{\Sigma }}{\lambda }_i{M}_T^m\left(s,i\right)}}$$

et les valeurs λ_j , 1 ≤ j ≤ N, sont les coordonnées du vecteur de Lagrange λ.With: $${\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)={\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \underset{i=1}{\overset{\mathrm{NOT}}{\Sigma }}{h}_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2{\lambda }_i}$$

and the values λ _j , 1 ≤ j ≤ N , are the coordinates of the Lagrange vector λ.

The implementation of the Lagrangian method allows us to write first that for 1 ≤ j ≤ r: $$B_j^m\left(s\right)=\frac{3}{2}\frac{1}{{\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)}$$

par exemple à l'aide de la méthode du gradient de la fonction ω.These terms are used to replace the scale coefficients in the Lagrange equation. And we then try to determine the value of the Lagrange vector λ which maximizes the function $\omega \left(\lambda \right)=\mathrm{The}\left(\left(B_1^m\left(s\right),...,B_r^m\left(s\right)\right),\lambda \right),$

for example using the gradient method of the function ω .

les dérivées partielles ne sont autres que les contraintes calculées pour les $B_j^m\left(s\right)=\frac{3}{2}\frac{1}{{\mathrm{\Delta }}_j^m\left(\lambda \right)}.$

According to the Uzawa gradient method ∇ w ( λ ), where $$\nabla \omega \left(\lambda \right)=\left(\begin{array}{l}\frac{\partial \omega }{\partial {\lambda }_1}\left(\lambda \right)\\ ⋮\\ \frac{\partial \omega }{\partial {\lambda }_{\mathrm{NOT}}}\left(\lambda \right)\end{array}\right)$$

partial derivatives are just the constraints calculated for the $B_j^m\left(s\right)=\frac{3}{2}\frac{1}{{\mathrm{\Delta }}_j^m\left(\lambda \right)}.$

The iterative relative gradient method (see in particular the Derrien document) is used to solve this system.

avec le vecteur de Lagrange λ avec un exposant (k+1) indiquant le vecteur actualisé et le vecteur de Lagrange λ avec un exposant k indiquant le vecteur calculé précédemment lors de la k^ième itération, ⊗ désignant le produit terme à terme entre deux vecteurs de même taille, ρ désignant le pas de l'algorithme itératif et m étant un vecteur de pondération.The general equation (formula (4)) for updating the Lagrange vector during a (k + 1) ^th iteration of the method is then written in the following form: $${\mathrm{\lambda }}^{k+1}={\mathrm{\lambda }}^k\otimes \left(1+\rho \mathbf{m}\otimes \nabla \omega \left({\mathrm{\lambda }}^k\right)\right)$$

with the vector of Lagrange λ with an exponent (k + 1) indicating the update vector and the vector of Lagrange λ with an exponent k indicating the previously calculated vector at the k ^th iteration, ⊗ denotes the product term term between two vectors of the same size, ρ designating the pitch of the iterative algorithm and m being a weighting vector.

In one embodiment, in order to ensure the convergence of the iterative method, the vector m is chosen equal to: $$\left(\begin{array}{l}\frac{1}{M_T^m\left(s\mathrm{,\; 1}\right)}\\ ⋮\\ \frac{1}{M_T^m\left(s,\mathrm{NOT}\right)}\end{array}\right)$$

In the embodiment considered, the quantization module 4 is adapted to implement the steps of the method described below with reference to FIG. figure 3 on each quantization band s when quantizing a block m of signals ( S _i ) _{1 i i ≤ N.}

The method is based on an iterative algorithm comprising instructions for implementing the steps described below during the execution of the algorithm on the calculation means of the quantization module 4.

In a step a / of initialization (k = 0): one defines the value of the iteration step ρ , a value D representing a threshold of flow and the value of the coordinates ( λ ₁ , ... λ _N ) of the vector initial Lagrange with λ _j = λ ⁰ , 1 ≤ j ≤ N.

The steps of the iterative loop for a (k + 1) ^th iteration, with k integer greater than or equal to 0, are as follows.

In a step b /, the coordinate values λ _j, 1 ≤ j ≤ N Lagrange vector considered being those calculated previously at the ^kth iteration, is calculated for 1 ≤ j ≤ N: $${\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)={\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_{\frac{1}{2},j}\left(s\right)K_s\frac{16}{9}\mathrm{<figure-callout\; id="2"\; label="E\; e\; R"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E\; </figure-callout>}\left[e_R^{}\right]\left[{}_2^{}\right]\left(1+\sqrt{2}\beta \left(\alpha \right)\right){\displaystyle \underset{i=1}{\overset{\mathrm{NOT}}{\Sigma }}{h}_{i,\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="imgf0002.png"\; state="\{\{state\}\}">j</figure-callout>}}^2{\lambda }_i}$$

Then in a step c /, the scaling coefficients are calculated for 1 ≤ j ≤ r: $$B_j^m\left(s\right)=\frac{3}{2}\frac{1}{{\mathrm{\Delta }}_j^m\left(\mathrm{\lambda }\right)}$$

In a step d /, the value of the function F is calculated on the band s, representing the corresponding bit rate for the band s: $$\mathrm{F}\left(s\right)=-{\displaystyle \underset{j=1}{\overset{r}{\Sigma }}\ln \left(B_j^m\left(s\right)\right)}$$

In a step e /, the calculated value F ( s ) is compared with the given threshold D.

If the calculated value F ( s ) is greater than the given threshold D, the value of the Lagrange vector λ for the (k + 1) ^th iteration is calculated in a step f / using the equation (4 ) indicated above and the Lagrange vector calculated during the k ^th iteration.

Then, in a step g /, the index k is incremented by one unit and the steps b /, c /, d / and e / are repeated.

pour la bande de quantification s permettant de masquer, dans le domaine d'écoute, le bruit dû à la quantification dans la bande s, des composantes ambiophoniques (Y_j )_1≤j≤r , tout en garantissant que le débit nécessaire pour cette quantification dans la bande s est inférieur à une valeur déterminée, fonction de D.If the value F ( s ) calculated in step e / is less than the given threshold D, the iterations are stopped. Scale coefficients were then determined ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

for the quantization band s making it possible to mask, in the listening domain, the noise due to the quantization in the band s, of the _ambiophonic components ( Y _j ) _{1 j j ≤ r} , while ensuring that the bit rate required for this quantization in the band s is less than a determined value, function of D.

The quantization function thus determined for the respective s-bands and respective surround components is then applied to the spectral coefficients of the surround components. The quantization indices as well as definition elements of the quantization function are provided to the Huffman coding module.

The coding data delivered by the Huffman coding module 5 is then transmitted as a bit stream Φ to the decoder 100.

Operations performed at the decoder:

The bit sequence reading module 101 is adapted to extract coding data present in the stream Φ received by the decoder and to deduce, in each band s, quantization indices i (k) and scale coefficients. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}.$

dans chaque bande s.The inverse quantization module 102 is adapted to determine the spectral coefficients, relative to the band s, of the corresponding ambiophonic components as a function of the quantization indices i (k) and the scale coefficients. ${\left(B_j^m\left(s\right)\right)}_{1\le j\le r}$

in each band s.

Thus, a spectral coefficient Y _{j, t} relative to the frequency F _t of the band s of the ambiophonic component Y _j and represented by the quantization index i (k) is returned by the inverse quantization module 102 using of the following formula: $Y_{j,t}={\mathrm{AT}}_j^m\left(s\right)i{\left(\mathrm{<figure-callout\; id="4"\; label="k"\; filenames="imgf0001.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^{\frac{4}{3}}$

Ambiophonic decoding is then applied to the decoded surround components, so as to determine the signals S ' ₁ , S' ₂ ,..., S ' _Q , for the speakers H1, H2 ..., HQ. .

The quantization noise at the output of the decoder 100 is a constant which depends only on the transform R used and the quantization module 4 because the psychoacoustic data used during the coding do not take into account the processing performed during the rendering by the decoder. Indeed, the psychoacoustic model does not take into account the acoustic interactions between the different signals, but calculates the masking curve of a signal as if it were the only one listened to. The error calculated on this signal therefore remains constant and masked for any surround decoding matrix used. This surround decoding matrix will simply change the distribution of the error on the different speakers output.

Claims (9)

1. Method for quantizing components, some at least of said components ((Y_j )_1≤j≤r) each being determined as a function of a plurality of audio signals ((S_j )_1≤j≤N) of a sound scene and computed by applying an ambiophonic multichannel linear transformation with more than two channels to said audio signals,
   according to which a quantization function (Q^m) to be applied to said components in a given frequency band (s) is determined by testing a condition relating to at least one audio signal (S_i ) and depending at least on a comparison performed between:

   - a psychoacoustic masking threshold $\left(M^m{}_T\left(s,i\right)\right)$

   

   relating to the audio signal in the given frequency band, and

   - a value determined as a function of the inverse multichannel linear transformation and of errors of quantization of the components by said function on the given frequency band.
2. Method according to Claim 1, according to which the condition relates to several audio signals and depends on several comparisons, each comparison being performed between a psychoacoustic masking threshold relating to a respective audio signal in the given frequency band, and a value determined as a function of the inverse multichannel linear transformation and of errors of quantization of the components by said function.
3. Method according to Claim 1 or Claim 2, according to which the determination of the quantization function (Q^m) is repeated during the updating of the values of the components to be quantized.
4. Method according to any one of the preceding claims, according to which the condition relating to an audio signal at least is tested by comparing the psychoacoustic masking threshold relating to the audio signal and an element representing the mathematical value ${\displaystyle \sum _{j=1}^r\left(h_{i,j}^2{B}_j{\left(s\right)}^{\frac{3}{2}}{\mu }_{{}_2^1,j}\left(s\right)\right)},$

   

   where s is the given band of frequencies, r is the number of components, h_i,j is that coefficient of the inverse multichannel linear transform relating to the audio signal (Si) and to the j^th component with j=1 to r, B_j(s) is a scale coefficient relating to the ambiophonic component Yj taking discrete values and characterizing the quantization function (Q^m) in the band s relating to the j^th component and µ_12,j (s) is the mathematical expectation in the band s of the square root of the j^th component.
5. Method according to any one of the preceding claims, according to which a quantization function to be applied to said components in the given frequency band is determined with the aid of an iterative process generating at each iteration a parameter of the candidate quantization function satisfying the condition and associated with a corresponding bit rate, the iteration being halted when the bit rate is below a given threshold.
6. Quantization module (4) adapted for quantizing at least components ((Y_j )_1≤j≤r) each determined as a function of a plurality of audio signals ((S_j )_1≤j≤N) of a sound scene and computed by applying a multichannel linear transformation to said audio signals, said quantization module being adapted for implementing the steps of a method according to any one of Claims 1 to 5.
7. Audio coder (1) adapted for coding an audio scene comprising several respective audio signals ((S_j )_1≤j≤N) as a binary output stream (Φ), comprising:

   - a transformation module (3) adapted for computing by applying a multichannel linear transformation to said audio signals, components ((Y_j )_1≤j≤r) at least some of which are each determined as a function of a plurality of the audio signals; and

   - a quantization module (4) according to Claim 6 adapted for determining at least one quantization function (Q^m) on at least one given frequency band (s) and for quantizing the components on the given frequency band as a function of at least the determined quantization function;

   said coder being adapted for constructing a binary stream as a function at least of quantization data delivered by the quantization module.
8. Computer program to be installed in a quantization module (4), said program comprising instructions for implementing the steps of a method according to any one of Claims 1 to 5 during execution of the program by processing means of said module.
9. Coding data (Φ), determined following the implementation of a quantization method according to any one of Claims 1 to 5.

Images