EP2022046A1 - Conversion between subband field representations for time-dependent filter banks - Google Patents

Abstract

Conversion between sub-band field representations for time-dependent filter banks. The invention relates to a transcoding processing operation between different sub-band fields, aiming to compact the application of a first vector representing the signal in a first sub-band field to a synthesis filter bank, and then to an analysis filter bank, in order to obtain a second vector representing the signal in a second sub-band field. In particular, the synthesis bank and /or the analysis bank are time-dependent. Within the scope of the invention, matrix filtering of the first vector is anticipated in order to directly obtain the second vector, this matrix filtering being represented by a global conversion matrix comprising pre-calculated sub-blocks of matrices (Ai0,…, Aip2-1) taking into consideration possible time-dependent variations in the filter banks, then stored into memory. The global conversion matrix is then constructed by calls to the memory in order to obtain the sub-blocks at pre-calculated successive instants.

Description

 Converting Representations to Subband Domains for Time-Variable Filter Banks

The present invention relates to data processing for transcoding.

Signal processing, in particular for compression coding, aims to bring a signal back into a subband domain. With reference to FIG. 1, this processing consists in applying a bank of analysis filters BA to a first expression x of the signal (for example temporal) possibly including a subsampling (decimation) DEC, to obtain a second expression of the signal. [y _o , y _ι , ..., y _{M ^ ι} ) in the aforementioned _subband domain. On the other hand, to find the first expression of the signal x, from its second expression (_y ₀ , ^ ₁ , ..., y _u _ _x ), we apply to the second expression (y _Q , y _λ , ..., y _M _ _x ) a synthesis filter bank BS, including oversampling (expansion) EXP.

The so-called "transcoding" processing then aims at a conversion between different subband domains. With reference to FIG. 2, in order to carry out this type of processing, it is sought to compact in the same step TRC the application of a first vector X representing the signal in a first domain of sub-bands to a bank of synthesis filters. BS1, then to an analysis filter bank BA2, to obtain a second vector F representing the signal in a second subband domain. The respective ratings BS1 and BA2 of the synthesis and analysis benches are justified by the fact that the bank BS1 is relative to the conversion in the first domain of sub-bands, while the bank BA2 is relative to the conversion in the second domain. subband domain.

Transcoding is a crucial point in the communication of a digital signal (audio, video, multimedia, more generally a signal representing any data). Indeed, the diversity of coding formats, supported by different terminals and used for signal communication, often poses incompatibility problems, particularly in certain content delivery applications. Transcoding for the adaptation of the format of a signal to the type of decoding supported by a rendering terminal provides a solution to this problem.

The conventional transcoding technique often introduces additional algorithmic delay and requires some processing complexity.

The so-called "intelligent" transcoding aims to reduce these parameters. In digital audio signal processing in particular, the encoders used are based on transform coding. Often, different compression formats use different types of transforms or "filterbanks". A first difficulty to be overcome therefore consists in producing efficient structures for switching between different subband domain representations, especially when the number of filters of a bank of a first subband domain is different from the number of subband filters. a bench of a second domain.

A general solution to this problem has been proposed in document FR-2,875,351 and aims at a single matrix filtering, replacing the successive application of the synthesis bench of the first domain and the analysis bench of the second domain, this unique filter being represented by a square matrix of dimension equal to the smallest common multiple of the number of filters per bank respectively in the first and in the second domain.

Nevertheless, there may be an additional difficulty related to the fact that the aforementioned filter banks may vary over time.

Indeed, most current encoders (MPEG-4 AAC, Dolby AC-3) use time-varying filter banks, while conversions between different subband domains that have been proposed in the state of the art. art are not applicable only for time / frequency representations that are invariant in time.

In particular, the most recent coders (in particular in standard MPEG-2/4 AAC coding, or in Dolby AC-3 coding for digital audio signals) use time / frequency representations where the resolution may be variable over time. . The resolution depends in particular on the short-term properties of the processed signal. In this case, the coefficients defining the banks of analysis and synthesis filters applied for the passage of a first to a second domain of subbands and vice versa, vary in time and the main equations of the conversion system. , proposed in the aforementioned document FR-2,875,351, can no longer be applied directly. Thus, to extend the application of transcoding to the case of variability as a function of time, the conversion equations between signal representations in different subband domains should make it possible to deal with the case of the most recent perceptual coders in which intervene filter banks varying over time.

The present invention improves the situation.

To this end, it proposes a method implemented by computer resources for processing a signal by passing between different subband domains. The method aims at compacting in the same process the application of a first vector representing the signal in a first domain of sub-bands to a bank of synthesis filters, then to a bank of analysis filters, to obtain a second vector representing the signal in a second domain of subbands.

In this type of method, the application of matrix filtering to the first vector is provided to directly obtain the second vector.

According to the invention, the synthesis bench and / or the analysis bench are variant in time. The matrix filtering is represented by a global conversion matrix comprising matrix sub-blocks:

• pre-calculated taking into account the possible variations in time of the banks of filters, • and stored in memory, and the global matrix of conversion is built by calling to said memory to obtain said pre-calculated sub-blocks at successive times .

Advantageously, a finite number of possible states are provided with respective sets of coefficients of the synthesis and / or analysis banks, and the aforementioned sub-blocks are pre-calculated from said respective sets for all possible states. , while the overall conversion matrix is determined for at least one possible state defined from the properties of the signal to be processed, in particular stationary properties of the signal.

The present invention is also directed to a device for processing a signal by passing between different subband domains. An example of such a device is illustrated in Figure 11 which will be described in detail later. For the implementation of the method within the meaning of the invention, it comprises, in addition to general computer resources including in particular a processor (not shown):

a memory DD storing the pre-calculated sub-blocks,

a clock HOR for determining successive instants, and

an MFM matrix filtering module arranged to recover from the DD memory the pre-calculated sub-blocks for these successive instants, for the construction of the global conversion matrix.

Advantageously, the device further comprises a SW toggle control for:

- Define, from the signal to be processed, one of said possible states and sets of associated coefficients, and - manage access to said memory according to the defined state. Such a device can be integrated into an equipment such as a server, a gateway, or a terminal, intended for a communication network.

The present invention also relates to a computer program, intended to be stored in a memory of such a device and including instructions for the implementation of the method within the meaning of the invention. A possible algorithm of such a program can be represented very schematically by the flowchart of FIG. 14 which will be described in detail later.

Other advantages and characteristics of the invention will appear on examining the detailed description given below, given by way of example of embodiments, and the appended drawings in which, in addition to FIGS. 1 and 2 previously described:

FIG. 3 illustrates recoveries of long and short successive blocks occurring during two transitions of a TV-MLT transform, in comparison with a temporal axis TEMP;

FIG. 4A represents a transition function A _itart (») of a TV-transform

MLT;

FIG. 4B represents the windowing occurring during two changes of resolution of the TV-MLT transform; FIG. 5A illustrates a bank of time-varying analysis filters with maximum decimation;

FIG. 5B illustrates a bank of time-varying synthetic filters with maximum decimation;

FIG. 6 is a detailed conventional diagram of the conversion between different subband domains;

FIG. 7 is a diagram illustrating the conversion between the representations of a signal by two TV-MLT transforms of different sizes, as an example for a transcoding between the Dolby AC-3 format and the MPEG-2/4 format AAFC;

FIG. 8A illustrates an intermediate step of the construction of the states of a conversion sub-matrix based on a first form, referred to as "form A"below; FIG. 8B illustrates an intermediate step of the construction of the states of a conversion sub-matrix based on a second form, called "form B"below;

FIG. 9A illustrates the construction of the states of the global conversion matrix T (w, Z) in a general case K = ppcm (L, M) in the form A; FIG. 9B illustrates the construction of the states of the global conversion matrix T (Z, n) in a general case K = ppcm (L, M) in the form B;

FIG. 10A illustrates an example of global conversion as a recovery transform in a first particular case where M = pL;

FIG. 10B illustrates an example of global conversion as a recovery transform in a second particular case where L = pM;

FIG. 11 illustrates an exemplary embodiment of a global conversion system within the meaning of the invention;

FIG. 12A illustrates the operation of an order subsystem i of the system of FIG. 11, to deliver a converted polyphase component V ₁ . (n) an output signal vector, in the manner of a linear time-varying system, for an implementation of the form A;

FIG. 12B illustrates a representation of the global conversion system, defined in the form A, as a set of linear subsystems varying in time;

FIG. 12C illustrates the operation of an order subsystem / of the system of FIG. 11, for delivering a converted polyphase component V. (n) of an output signal vector, in the manner of a system linear time-varying, for implementation in form B;

FIG. 12D illustrates a representation of the global conversion system, defined in the form B, as a set of linear subsystems varying in time; FIG. 12E illustrates the development of the overall conversion system, as a time-varying linear system using overlapping transformations (OLA);

FIGS. 13A and 13B illustrate a global, three-dimensional conversion matrix represented by sub-blocks; FIG. 14 illustrates an exemplary embodiment of the steps for constructing the global conversion matrix.

Before describing in detail one or more embodiments, the choice of the approach proposed by the present invention is justified below. In particular, the fact that time-varying transforms are represented by filter banks is justified in the following, and an equivalence in their representation by filter banks is demonstrated.

The coders in particular of the MPEG-2/4 AAC and Dolby AC-3 types use variable resolution time / frequency representations. They operate by performing time-varying overlap transform analyzes, an example of which is the so-called "TV-MLT" transform ("time-varying modulated lapped tmnsform") which translates to "modulated transform overlay". , varying in time ") where the size of the processed blocks depends on the instantaneous properties of the signal. The time / frequency representation of these encoders is qualified as adaptive because the basic functions of the overlay transform vary over time, depending on the short-term characteristics of the signal.

The representation of a classical MLT transform (invariant in time) by a uniform filter bank with perfect reconstruction is known. It is recalled that an MLT transform is a special case of analysis / synthesis by cosine-modulated filter bank, where the length N of the filters (equivalent to the degree of the "plus 1" filters) is equal to twice the number of sub-filters. -bands M (equivalent to the number of filters per bank), ie Λ ^r = 2Af.

The principle of time-invariant MLT transforms is not described in detail, it being understood that it is widely disclosed in the prior art, especially in HS Malvar's Signal Processing with Lapped Transform, Artech House, Boston, 1992. . The case of a temporal variation of the conversion is described here, following, for example, a change of resolution of one of the coders involved in the transcoding.

The MPEG-2/4 AAC and Dolby AC-3 encoders operate with MLT transforms whose parameter M can take two values which define two different window function sizes h (n) (M ₁ or M ₂ according to the table below). -after).

Window sizes of MPEG-2/4 AAC and Dolby AC-3 encoders.

The transition from one window size to another creates a variation in the time of the frequency resolution of the transform. Moreover, this passage must be operated while retaining the property of perfect reconstruction of the signal. The TV-MLT transforms used by the above-mentioned coders verify this condition. More particularly, the Windows switching technique, defined in the MPEG-2/4 AAC standard, uses asymmetrical transition window functions noted below, h _start and h _stop , during the changeover periods. resolution.

The operations implemented by the TV-MLT transforms are defined below by following the shape of the windows of transitions h _start and h _stop which guarantee the property of perfect reconstruction.

The overlap transform matrix, P, is decomposed in the following manner

P = D _M ®h _{Λ /} where the operator ® is defined as the product component to components and lines to lines of the matrix elements. D _w is the modulation matrix, size, M x 2M, defined by:

with basic functions such as:

and * = O, ..., M -1, w = 0.1, ..., (2M-I).

We denote h _w the vector associated with the window function of length 2M, with: h _M = (h _M (O) h _M (\) ... h _M (2M - \)) Its components h _M (n) can be defined for example by the sinusoidal function

(most commonly used in audio signal processing applications), of type:

Finally, we denote by h _M and h _M the vectors respectively associated with the window functions of respective lengths M ₁ and M ₂ , and r the ratio such that r = M _x IM ₁ (> 1).

A representation in polyphase components of the input signal x {n) is adopted such that: u, (m) = x (mM-1), / = O, ..., M -1 The block of samples representing a polyphase component of index m is then defined by: u (m) = {u _M ^ m) ... U ₁ (In) u _o (m)) ^' , where the notation x ^τ designates the transpose of the vector x. To obtain a block of 2M samples, two successive blocks are concatenated such as:

U (m) = (u (m - V) u (m)) ^' (4)

The signal block transform UJm), denoted Y_ {m), is determined by:

Y (m) = ¥ U (m) (5) where Yjjri) = (y _o (m) y \ (m) ... y _M _ _χ (m)) ^' is the vector of the transformed coefficients.

During a transition from a long window to a short window, we take the case of a signal vector U_ {m) of length 2M _{1 to} which we apply a long transition window, denoted h _start , with the matrix of modulation D _M. The previous vector H ( ^m ~ 1) ^es * of length 2M _{1 to} which a standard long window h _M has normally been applied with the modulation matrix D _w . On the other hand, the vectors r at the following instants (m + 1, m + 2, ..., m + r), denoted by W (m + V), W ijn + 2), ..., W (m + r) , are all of short length 2M ₂ . Standard short windows h _{w are} applied with the modulation matrix D _M.

Then, during a passage from a short window to a long window, the signal U_ (m + 2) is of length 2M ₁ and a long transition window, denoted h _stop , is applied with the modulation matrix O _M .

The components of the vectors that intervene during the two successive changes of window size are written:

U (m) = [ _x φ _n - 2) M _ι + 1) ... x (mM _x )) W_ (m + 1) = (x ((m - I) M ₁ + An + 1) .. .x ({m - V) M _x + An + 2M ₁ ))

W (m + r) = (Jt (Cm -I) M ₁ + An + (r -I) M ₂ + V) ... x ((m -I) M ₁ + An + (r + V) M ₂ )) U_ (m + 2) = (x (mM _ι + ï) ... x ((m + 2) M _ι ))

The parameter An is set to the value An = (M _ι -M ₂ ) I2. The provisions of these vectors are illustrated in Figure 3 for the case where MJM ₁ = 2. In particular, FIG. 3 illustrates a long window to short window transition at time mM _λ and a short window to long window transition at time (m + I) M ₁ . The time axis is referenced TEMP. There is an overlap between the long vector UJm) and the following short vectors WJm + 1), WJm + 2). This overlap is the same as that between the short vectors and the first long vector following UJm + 2).

Under these conditions, it has been shown that the perfect reconstruction property of the TV-MLT transform depends, as in the case of a conventional MLT transform, only on the windows functions used and, in particular, on the two transition windows. _start and h _stop of length 2M ₁ . The perfect reconstruction condition is verified during the transition periods if these transition windows are those defined according to the following four conditions, assuming that the dimension of the transform changes at the instant mM _x from M ₁ to M ₂ , then at the instant (m + I) M ₁ of M ₂ to M ₁ .

* First condition: the window function, for a transform of size M ₁ , is such that:

* Second condition: the window function that intervenes at the transition from M ₁ to M ₂ is such that:

* Third condition: the window function, for a transform of size M ₂ , is such that:

* Fourth condition: the window function that intervenes at the transition from M ₂ to M, is such that:

For the third condition, there are successive MLT transforms of dimension M ₂ between two transition periods. The first transform starts at the instant (m - I) M \ + An. The last transform ends at the instant mM _λ + M ₁ + An.

FIG. 4A illustrates the shape of the transition function h _stm (n) which occurs during a change in size from M ₁ to M ₂ defined by the four conditions above ensuring a perfect reconstruction. Note that the transition window h _stop (n) reciprocal intervening during a transition from M ₂ to M _x is simply such than :

FIG. 4B represents the succession of transition windows that occur during the two periods of change of temporal resolution of the transform

TV-MLT. More particularly, FIG. 4B illustrates the windowing occurring during the two resolution changes from M ₁ to M ₁ , then from M ₂ to M ₁ , with M ₁ = 1024 and M ₂ = 128 in the example represented.

In practice, we can then consider several changes in the resolution of the transform. These changes in resolution occur at multiple times of M ₁ and are triggered depending on the properties of the incident signal, including stationarity. This property is known to dynamic resolution change coders.

In particular, with reference to FIG. 4B, there are equivalents of MLT transforms:

on a long window for the instants n between 0 and 2047, hereinafter referred to as the "first region", on a first transition window to ensure a perfect reconstruction, for times n between 1024 and 2623, referred to hereinafter as after "second region",

on a succession of a plurality of short windows (r windows h _M> of size M ₂ ), for instants n between 2496 and 3647, hereinafter called "third region", and

on a second transition window to ensure a perfect reconstruction towards a return to a long window, for instants n between 3520 and 5119, hereinafter called "fourth region".

The observation of the windowing on the transition, including in particular the third region with the succession of short windows, is important for the continuation of the description.

The overall TV-MLT transformation can be defined in a complete way by a global matrix of conversion, of dimension "infinite", noted T (m) and such that:

where P ₀ (m) and P ₁ (W) are sub-matrices of size M xM defined at the block indices m which corresponds to the instant mM _x .

In particular, the concatenation P (m) = [P ₀ (/ w) P ₁ (^)] of size M ₁ X 2M ₁ represents the recovery transformation matrix whose expressions will be given below for any moment mM _x .

The condition of perfect reconstruction provided by the transform TV-MLT is governed by equality:

T ^" (m) Υ (m) = I

Using the formulation (6) of the transformation matrix, the perfect reconstruction condition is equivalently defined simply by the following three equalities:

The perfect reconstruction condition (7) implies that the transform matrix overlap P (Vw) remains orthogonal to the two neighboring matrices P (m-1) and V (m + 1). By taking up the four conditions given above, with the succession of changes in size of the transformation, the overlapping transform matrices are then defined by:

The finite recovery transform matrix, associated with the m + 1 block corresponding to r successive MLT transformations of size M ₂ ("third region" of FIG. 4B) is, for its part, defined by:

where and are the transform transform matrices of the transform MLT size M ₂ x 2M, and which also break down into a form of the type

It is thus shown that there are four possible situations (four regions of FIG. 4B) defined by four possible values of the matrix F (m). It will be already understood that the overlap transform matrix P (w) has four possible "states".

In the following, the expression of the matrix P (m + 1) given above, corresponding to one of the four admissible states, will be denoted Q _M to generally qualify this state among the four admissible states.

Starting from the definitions of possible overlapping matrices P (m), we show that the perfect reconstruction conditions (7) are verified when the window functions of the h _start and h _stop prototype filters are those defined by the four conditions above.

The direct transformation operation of the TV-MLT transform is then defined by:

Y (m) ≈ Ϋ (m) U (m) (10) where Y_ {m) is the vector of the transformed coefficients at time mM _x and U_ {m) is a vector defined from the input vector by relation (3) above.

The inverse transformation operation is defined, as for the invariant case of the MLT transform, by two steps:

inverse transformation of the vectors of the transformed coefficients:

Z (m) = P (m) ^Y (m) (11)

addition with overlay (or OLA for "overlap and add") of the vectors obtained û {m) = z _o (m) + z _ι {m-1) (12) where we note:

"z_ _o ( ^m ) ^e * h ( ^m ) ^ ^es blocks of size M ₁ constituting the vector ZJjn), such that Z (m) = (z _o (m) z, (w)), and - û (m ) the reconstructed vector, supposed to be worth the initial vector u (m) because the reconstruction is perfect.

The bases of a representation of a TV-MLT transform by filter banks are now described.

The TV-MLT transform presented above makes it possible to go from an MLT transform of size M ₁ to an MLT transform of size M ₂ (or vice versa from M ₂ to M ₁ ), while preserving the property of perfect reconstruction of the signal. . We have shown how to treat the direct and inverse transformations of the TV-MLT transformation on vector blocks of the same constant size 2M ₁ .

Considering the case of the transformation of the vector U_ (m + Ï) by the overlap transformation matrix given by the relation (9) above (third region of FIG. 4B), the vector 7 (m + 1) of size M _x , such as:

Y (m + 1) = Ϋ (m + 1) U (m + 1) is defined, by construction, as the concatenation of the following transformed vectors, all of size M ₂ :

.

It is recalled that this construction follows from the observation of FIG. 4B whose importance was underlined above.

The overlap transform matrix of the block (m + 1) is constructed to respect the time offset An (FIG. 3).

In the context of modeling the conversion system between different subband domains, it is advantageous to have an implementation architecture of the TV-MLT transform which leads to constant-size analysis / synthesis operations. It is proposed hereinafter a time-varying maximum decimation filter bank architecture defined as follows.

The TV-MLT transformation used in particular by standard MPEG-2/4 coders

AAC or Dolby AC-3 and previously described has a time-varying maximum decimation filter bank representation. The length of the filters is twice the number M ₁ of sub-bands. The equivalent analysis (respectively synthetic) filter bank is described by the diagram of FIG. 5A (respectively of FIG. 5B) and the representations in the range of the Z variable of the filters H '' (n, Z), ..., H ^{Mι "l} (n, Z) (respectively F ⁰ (Z, n), ..., F ^{M> ~ 1} (Z, n)) at instants mM _x are defined as follows.

Over a period with a time resolution M ₁ , the coefficients of the impulse responses h _ϋ ^k {mM _λ ), ..., h ₂ ^k _M ^ {mM _x ) and f _o ^k (mM _x ), ..., f ₂ ^k _λf ^ _x (mM _x ), with k = 0, ..., M ₁ -1, are given by the relations (13) and (14):

This is a first possible state corresponding to the situation of the first region of FIG. 4B.

During a period with a time resolution M ₂ , the coefficients of the impulse responses , with k = 0, ..., M ₁ -1, are given by relations (15) and (16):

This is a second possible state corresponding to the situation of the third region of FIG. 4B.

During a transition period passing from a resolution M ₁ to M ₁ , the coefficients of the impulse responses and

with k = 0, ..., M _x -l, are given by the relations (17) and (18):

This is a third possible state corresponding to the situation of the second region in FIG. 4B.

During a transition period passing from a resolution M ₂ to M ₁ , the coefficients of the impulse responses and f _c j (mM _r ), ..., f * _{M ^ λ} {mM _x ), with k = 0, ..., M _x ~ \, are given by the relations (19) and (20):

Finally, it is a fourth possible state corresponding to the situation of the fourth region of FIG. 4B.

The above results will be useful for the following, in the sense that the terms defining the filters are finally determined directly from the modulation matrix D, known and expressed by the relation (1), on the one hand, and from the windows h defined by the four conditions above to satisfy the perfect reconstruction, of somewhere else.

The analysis / synthesis filter bank thus defined is then perfectly reconstructed. This is the basis of the representation of the TV-MLT transform by filter banks. Here, only the coefficients of the filters vary in time, the number of subbands remaining fixed.

It will then be retained, in general terms, that each set of coefficients of the analysis or synthesis bench, associated with a possible state, can be calculated as a function of a modulation matrix D and of a vector h characterizing this possible state. and ensuring a perfect reconstruction property (as in the example described above) or still "almost perfect". "Near-perfect" reconstruction is understood to mean the property of reconstruction of the filterbanks used in coders of the MPEG-1/2 type I & I1 type in particular. It will then be understood that, in the case for example of a combination of an encoder of this type with a time-varying coder, the properties described above can still be observed.

It has thus been overcome by a prejudgment of the state of the art according to which it was not possible to represent a variant transform in time by filter banks. Here, it has been shown that a TV-MLT transform is indeed equivalent to a representation in filter banks with a fixed number of sub-bands, maximum, corresponding to the state where the weighting window is long, and this, whatever the state of the TV-MLT transform. This embodiment then makes it possible to anticipate all the possible changes of state of the TV-MLT transform.

In particular, the equivalence of the representation of TV-MLT time varying overlap transforms has been shown by a finite impulse (FIR) filter bank and a time-varying maximum decimation filter. Time-varying systems commonly used, in particular MPEG-2/4 AAC and Dolby AC-3 coders, can then implement adaptive subband representations, which can be defined, as described above, by the formalism of linear systems varying in time.

Details of the formalism of linear time-varying systems are described in particular in: "Time-Varying Filters and Filter Banks: Some Basic Principles", S Phoong and P.P.

Vaidyanathan, IEEE Transactions on Signal Processing, Volume 44, No. 12, pages 2971-

2987 (December 1996), and

"Factorizability of lossless time-varying filters and filter banks", S Phoong and P.P.

Vaidyanathan, IEEE Transactions on Signal Processing, Volume 45, No. 8, pp. 1971-1986 (August 1997). We will now describe the conversion technique within the meaning of the invention, itself, taking into account particular cases of transcoding, as well as the control of the algorithmic delay induced by the conversion in the sense of the invention.

As previously indicated, conversions are described where the time / frequency representations vary over time.

Figure 6 shows the multi-rate block representation to illustrate the conversion.

Signal vectors in sub-bands X (κ) = [x ₀ ("),..., Λ _{i- 1} (n)] ^' are transmitted at the input of a bank of synthesis filters F ° (Z, n), ..., F ^{L ~ ι} (Z, n) having L channels, after having undergone an expansion (oversampling of an L factor). The synthesized signal x (n) is analyzed by the filter bank H ^υ (", Z),..., H ^ ^{" 1} (", Z) having M channels and the output is obtained following the application of decimation (sub-sampling by a factor M), new signals in sub-bands

Y («) = [> Ό («), ---, y _M _ _] («)] ^' • It will be understood that the number of L and M channels remains constant, but the values of the filter coefficients change in particular according to the windowing (long windows, short windows, transition windows, according to the observation of Figure 4B). In FIG. 6, the notation TL corresponds to an oversampling (or expansion) of a factor L whereas the notation XM corresponds to a subsampling (or decimation) of a factor M.

It is then sought to merge in a single step the application of the two banks of synthesis / analysis filters to reduce the algorithmic complexity (number of calculation operations and required memory).

Conversion techniques between signal representations in different domains sub-bands are used to perform the transcodings, in particular between the coders:

- according to the MPEG-1/2 (layer I and II) standard,

and / or MPEG-2/4 AAC, and / or of the Dolby AC-3 type, and

and / or according to standard G 722.1 (for example the so-called "TDAC" coder for "Time Domain Aliasing Cancellation").

The time / frequency representations of the signal used by these coders are specified in the standards and are such that:

• for MPEG-1/2 layer I and layer II, we use a representation of the signal in sub-bands, based on the analysis / synthesis by pseudo-QMF filter banks (for "Quadrature Mirror Filter" which translates by "quadrature mirror filter"), with 32 channels, • for MPEG-2/4 AAC, variable resolution subband representations and TV-MLT time-lapse transform analyzes are used where the length of transformed 2M blocks depends on the properties of the processed signal,

• for Dolby AC-3, we use a representation of the signal TV-MLT transform, recovery variant in time with M = 256 or M = 128,

• for G 722.1 (TDAC), a TDAC filter bank representation with 320 subbands is used.

Under these conditions, the G 722.1 encoder and the MPEG-1/2 (layer I & II) coders use time-invariant filter bank representations. Furthermore, it has been pointed out above that the TV-MLT transforms of the MPEG-2/4 AAC and AC-3 coders admit a representation in the form of a bank of maximum decimation filters and M number of sub-bands. fixed, with filters varying over time.

It is then proposed to define hereinafter the analysis filters H ^k (n, Z) and of synthesis F ^k (Z, n), for all types of coders mentioned. Thus, FIG. 6 formally represents all possible conversions between the various examples of coders mentioned.

We note: the column vector grouping the M filters time-varying analysis, and

- F (Z, n) = [F ° (Z, n), ..., F ^{L "ι} (Z, n)] the row vector regrouping the L time varying synthesis filters.

* Definition of the expression according to form A

The corresponding representations in the Z domain can be noted:

where the respective lengths of the filters N _h (of analysis) and N _f (of synthesis) are constant.

The vector of the sub-band signals, Y ("), at the output of the analysis filter bank, is written:

where we define the matrix operator g (n, Z) = H (n, Z) F (Z, n) by its representation in the domain Z of a form called hereinafter "form A" such that its elements are defined by:

have k _x = 0, ..., (MI) and k ₂ = 0, ..., (LI). Its coefficients g * "* ² (") are defined by:

* Definition of the expression according to form B

We can also define the operator g (/ 7, Z) = H (", Z) F (Z,") in another form, hereinafter called "form B", as follows:

with £,, ..., (MI) and A ₂ = 0, ..., (LI) and the coefficients g ^ ^ι ' ^kl (n) being defined by:

In this case, the general equation of the conversion between the signals in sub-bands, defined according to this form B is written:

It will therefore be understood that these two variants of expression in the form A or in the form B are equivalent but simply differ in the manner of mathematically calculating the matrices g. By repeating the formalism of the time-varying systems described above, we are now seeking to merge operations induced by the conventional conversion scheme.

In the following, the representations of matrix operators g (", Z) or g (Z,") are denoted as follows:

• According to the form

• According to the form

Thus, at a given instant n given, gf (n) (respectively gf (")) defines the matrix of dimension M x L and having all the z-th filter coefficients gf" * ² (") given by the relation (24) above (respectively given by relation (26)).

We now use the principles of document FR-2,875,351 and we note for this purpose K = ppcm (L, M), the smallest multiple common multiple of the numbers M and L.

We also note p _x , p ₂ the natural numbers such that K = P ₁ M = p ₂ L.

We denote U - (Λ) the vector of the j-th component of the polyphase decomposition of order p _n of the vector X (w) defined ar:

The input vector X (") of the subband signals is decomposed as follows

and the conversion equation (22) is written:

Moreover, by decomposing the vector of the signals Y («) into sub-bands into p _λ polyphase components such that, where i = 0, ..., p _{ , we obtain a new conversion equation for the z ^' -th polyphase component of the sub-band signal vector Y (n) such that:

This equation (31) is important because it represents the conversion of the polyphase components of order p ₂ of the input signals to those of order p _λ of the output signals.

Noting T («, Z) the global conversion matrix defined by the representation according to the form A, its filtering sub-elements A ₁ . (n, Z) are such that

It will be noted here that the sub-blocks A _{/ y} . (", Z) have the same dimension (L rows and M columns) as the matrix g whose coefficients are given in relation (24) or (26) above. ₍₁ ^ between 0 and MI and kj between 0 and LI) and that the overall matrix T, square, comprises bienp ₂ = Z ^ -K lines etpiM columns.

Note also a remarkable characteristic of sub-blocks A ₁ ^ (H, Z) of the global conversion matrix T (n, Z). The sub-blocks A. - (", Z) of the same index i can be computed for the same instant i involved in the expression" + iM for the calculation of the matrix g. With reference to FIG. 13A, these blocks A ₁ . (n, Z) calculated for the same instant i are distributed on a "horizontal plane" of the global conversion matrix T (", Z), three-dimensional. The conversion matrix T (n, Z) has a depth (z-axis as shown in Figure 13A) corresponding to the size (or degree) of the filters. If you choose to represent the conversion matrix in two dimensions (projection perpendicular to the z axis), the sub-blocks calculated for the same instant i are distributed on the same line of sub-blocks.

The conversion equation finally comes in a simpler form:

V ()) ≈ T (ι, Z) U (n) (33) where U ()) = [U ₀ ()), ..., U _, ()) T and V ()) = [V ₀ {ri), ..., V _, («)] ^' are the vectors of the polyphase components of the signals, respectively of order p ₂ at the input, and of order P ₁ at the output.

By now choosing an expression according to the form B, we use the expression g (Z, n) here according to the relation (25) to represent the successive operations of filterings and we obtain a conversion equation of the form: V (w) = T (Z, n) U (n) (34)

The conversion matrix T (Z, ri) is then defined by sub-blocks A. _j (Z, n) such that

Again, the sub-blocks A. ₇ (Z ") with the same index j can be calculated for the same instant are involved in the expression n + jL for the calculation of the matrix g. With reference to FIG. 13B, these blocks A ₁ . _; (Z, n) calculated for the same instant are distributed on a "vertical plane" of the global conversion matrix T (w, Z). If one chooses to represent the conversion matrix in two dimensions (projection perpendicular to the z axis), the sub-blocks computed for the same instant / are distributed on the same column of sub-blocks. It is then pressed that the sub-blocks of the global conversion matrix can be pre-calculated and stored in memory for different times and especially for different admissible states. The sub-blocks associated with the same instants can then be recovered from the memory according to the changes in time that occur in the encoding formats. This property of a system within the meaning of the invention will be described in detail below, in particular with reference to FIG. 11.

In more general terms, the following steps are applied when the input vector has a number L of respective subband components and the output vector has a number M of respective subband components, after determining a number K, least common multiple between L and M:

- serial / parallel conversion of the input vector to obtain p ₂ polyphase component vectors, with p ₂ = KfL, and

- parallel / serial conversion to obtain the output vector. The conversion matrix is then applied to the polyphase P ₁ components of the input vector to obtain p _λ polyphase components of the output vector, with P ₁ = KjM. Under these conditions, the conversion matrix is square, of dimension Kx K, and has / ?, rows and p ₂ columns of sub-blocks A _y each having L rows and M columns. In particular, as observed above with reference to FIGS. 13A and 13B, sub-blocks A _y of the same index i (form A) or sub-blocks A _y of the same index y (form B) are pre-calculated for the same moment.

Again, with reference to FIGS. 13A and 13B, the conversion matrix is three-dimensional, with: a first dimension defined by the current index i of the sub-blocks,

a second dimension defined by the current index 7 of the sub-blocks,

- and a third dimension (Z axis) defined by the degree of matrix filtering.

Sub-blocks pre-calculated for the same instant then form matrix planes extending to the third dimension and are: - horizontal and pre-calculated for p _\ successive moments in an expression according to the form 1,

- or vertical and pre-calculated for successive instants in an expression according to form B.

In the conversion between subband domains in the sense of the invention, it is now sought to minimize the algorithmic delay introduced by the processing of the signals in sub-bands.

For this purpose, advances are first introduced in the conventional conversion scheme of Figure 6 to reduce the delay created by the filter banks. It is then a question of controlling the algorithmic delay by adding:

A Z ^α advance at the input of the synthesis filter bank; a Z * advance at the input of the analysis filter bank, where a and b are numerical parameters to be determined.

The control of the algorithmic delay is in all respects to that described in document FR-2,875,351, with the difference that the sub-blocks Ay depend on the time.

Under these conditions, the conversion matrix T («, Z) defined by the domain representation of all its elements, is such that:

The matrix sub-blocks g («, Z) are such that:

with A ₁ = O, ..., (M-1) and A ₂ = 0, ..., (1-1) and the coefficients gf "* ² ( ^w ) of gf (n) are defined by

The conversion matrix T (Z, ή) according to the form B now, defined by the domain representation of all its elements, is such that:

with i = 0, ..., P ₁ -I and j = 0, ..., p ₂ -l. The matrices g (Z, #) are such that:

with A ₁ = 0, ..., (MI) and A ₂ = 0, ..., (ZI) and the coefficients gf ^uk1 (n) of gf (") are defined by:

In both cases according to the form A or the form B, the exponent e _ij = aL + b + iM - jL with i = 0, ..., P ₁ -1 and j = 0, ..., p ₂ -l which appears in the construction of the conversion matrix, varies between the two extreme values: ^e _mm = ^{aL + b} - ^{κ + L} for, z = 0, J = P ₂ -I. e _ιmx = aL + b + KM for, i = p _x - 1, j = 0.

The filters of the conversion matrix are causal if e _^ ≤ K - 1 and so we obtain the following additional condition: aL + b≤Ml

For a minimum algorithmic conversion system, the maximum advance must be entered. The choice of a and b is advantageously so that e _lliax = KI, which implies: aL + bMl

According to the construction equations of the filter matrices g (", Z) and g (Z,"), an advantageous choice of the integers (a, b) consists in taking: a = p ₂ -l and, b = M + LKl (42)

Nevertheless, a possible alternative to the determination of the pair of integers (a, b) is to choose a = 0 and b = M - 1.

In this case, the advance is controlled at the intermediate signal x (n) at the output of the synthesis filter bank and at the input of the analysis filter bank.

To construct the conversion matrix, we seek to identify the components of the K-type polyphase type 1 decomposition of the matrix g ("+ / M, Z). We then distinguish two cases according to the values of e _t . = aL + b + iM - jL when i = 0, ..., _Pι-1 and J = 0, ..., p ₂ -1:

- if 0 <e ,. _; . <KI, the index element i, j of the conversion matrix T («, Z) is the e _t . -the K-type type 1 polyphase component of g ("+ iM, Z), so that:

if {aL + b + L-K) ≤e _tj <- \, the index element i, j of the conversion matrix T («, Z) is the (K + e _tj ) -th polyphase component of type 1 of order K of g ("+ iM + K, Z), composed with a delay Z ^{~ ι} , and we obtain:

In the case of an expression in the form B, to construct the conversion matrix, we first identify the components of the multiphase decomposition of type 2 of order K of the matrix g (Z, n + (J - ά) L). There are two more cases:

- if O≤β _dd ≤K -I, the index element i, j of the T conversion matrix (Z, n) is e _t; . -polyphase component of type 2 of order K of g (Z, n + (j-a) L) and we have:

if aL + b + L-K ββi _j ≤-1, the index element i, j of the conversion matrix T (Z, «) is the {K + e _t ^) -th polyphase component of type 2 of order AT of g (Z, n + (j - a) L) composed with a delay Z ^~! and

In the following, we consider a minimal delay system where a and b are defined by the relation (42).

For conversion systems defined according to the form A, when i = 0, ..., p _x - \ and j = O, ..., p ₂ -l:

• if 0 <e _ij <K - 1, the sub-block A ₁ . _} {n, Z) of T (/ z, Z) is such that:

where the matrices are defined by

• if aL + b + LK≤e _u <-l, the sub-block A _(/ («, Z) of T («, Z) is such that:

where the matrices We define the length N _A intervening in the maximum index of the terms of the sums above by:

1, if 0≤e _{: j} <r ₀ , or if 0≤K + e _t; <r ₀

if r ₀ + 1 <e, _j ≤ K - 1, or if r ₀ + 1 <K + e _l} ≤Kl where r ₀ = (N + N _f -2) mod K, the notation "mod K" designating the function "modulo K".

For the conversion systems defined according to the form B when i = 0, ..., p ₁ -1 and j = 0, ..., p ₂ -i:

• s, the sub-block A _1; (Z, ή) of T (Z, ή) is written

the matrices A ™ _; (n) being defined by • if, the sub-block A ₁ (Z, w) of T (Z, n) is written

the matrices A "'(n) being defined by

• if ai + b + L - K ≤ e _{t> y} <-1, the sub-block A _,; (Z, n) of T (Z, ή) is written

matrices ("AT + (y - a) L). The length N ₄ is determined by

where r _o = _h + N _f -3 + K) mod K.

To simplify the notations, we will use more simply the following representations, hereafter:

to represent the sub-blocks of the conversion matrices respectively defined in a form A or B.

Some elements A ™ _y . (N) are identically zero and thus we obtain a unique length N _τ for all the components of the global conversion matrix, defined by:

The following is the particular case where the numbers of respective subbands are multiples of one another, with, firstly M = pL.

This is the practical case where the number of sub-bands of the analysis filter bank is an integer multiple of that of the synthesis filter bank. The conversion between subband domains is then defined by the conversion equation:

where the conversion matrix T («, Z) is defined by:

The sub-blocks of the conversion matrix are the components (M -1-JL) -th of the M-type polyphase decomposition of order M of g (", Z) such that

Moreover, we choose the relation (42) for the algorithmic delay parameters, namely: a = p - \ and ό = Z -l and, under these conditions, the elements e the matrix of filtering g / (n) are determined by

We will also note two possible alternatives concerning the choice of algorithmic delay control parameters: (a, b) = (p, -1) or (a, h) = (0, M - 1)

A second special case is one in which the number of sub-bands of the synthesis filter bank is an integer multiple of that of the analysis filter bank, ie: L = pM. Here, the choice of the advance parameters (42) is such that: α = 0 and ό = M-1 As a result, the elements of the filter matrix gf (") are determined by:

'(51)

The conversion equation of the component V ("), defined in the form B, becomes

with / = 0, ..., p -l. The conversion between subband domains is defined by the conversion equation V (») = T (Z,«) X (n) ₍₅₂₎ where the conversion matrix T (Z, n) is defined by

Each sub-block of the conversion matrix corresponds to the M-1 + iM -th polyphase component of type 2 of order Z of the filtering matrix g (Z, ") at time nL and we obtain

In the foregoing, the equations underlying the conversion within the meaning of the invention have been given. In what follows, the manner of constructing the main operators intervening in a system within the meaning of the invention, as well as the practical implementation of the treatments, for the execution of the invention is described.

For the practical construction of the operators of the conversion system, it is distinguished first of all the cases where the dimensions M and L are integer multiples of each other, then the general case where the least common multiple K is different from the respective numbers of L and M subbands. In fact, the cases where the dimensions are integers that are multiples of one another, are first described, for the sake of clarity, with a view to the construction of the main conversion matrices T («, Z ) (according to the form A) or T (Z, n) (according to the form B).

The conversion for the case where M = pL is preferentially defined by an application of the form A of the filtering operations. The reciprocal case where L = pM is preferentially defined by an application of the form B. In both cases, the construction of the main conversion matrices follows two steps.

In particular, in the case M = pL: the sub-matrix g (#, Z) whose coefficients are defined by the relation (50) is constructed:

where ^ ₁ = O, ..., MI, ^ ₂ = O, ..., 1-1 and i = 0, ..., (N _h + N _f -2), - then, we build the p polyphase components of type 1 of order M of g (", Z) such that:

with j = 0, ..., p- \, and we apply a concatenation of these p blocks of polyphase components to finally obtain the global matrix T («, Z), defined by the relation (48):

In the case where L = pM:

the matrix g (Z, ri) whose coefficients are defined by the relation (51) is constructed:

where *, = 0, ..., M1, / t ₂ = 0, ..., LI and i = 0, ..., (N _h + N _f ~ 2),

- Then, we build the main conversion matrix T (Z, n), defined by:

where each sub-block of the conversion matrix is the (M - 1 + iM) -th polyphase component of type 2 of order L of the sub-matrix g (Z, n) at time nL.

* first special case M - pL

For the case M = pL, the filter coefficients of the synthesis banks (respectively analysis) are constant in pieces and vary as a function of the instant n, in particular at the multiple instants of L (respectively of M). Therefore, to perform the convolution products impulse responses of the two filter banks account should be taken of variations in the

impulse responses of F (Z, n + L - l - i) when i = 0, ..., (N _k + N _f - 2). Indeed, the coefficient index i of the coefficients of a matrix slice gf (") appears in the convolution product, both as a convolution index and as a temporal variable. This notion of "matrix slice" will be described later with reference to FIG. 8A.

Thereby :

If (N _h + N, - 2) ≤ L, at a time ri = nL, the coefficients of the filters of

F (Z, nL + L -l -i) are constant whatever the value of z = 0, ..., N _h + N _f -2, • if (N ₁₁ + N _f - 2)> L, the impulse responses of

F ° (Z, n + L-1i), ..., F ^{L ~ 1} (Z, n + L-1 -i) of the synthesis bank F (Z, n + L - 1 - 1) make a change at least once with the index i.

In the latter case, to build the matrix sub-block at a given instant, it is necessary to have several successive states of the synthesis filter bank and the current state of the analysis filter bank.

Referring now to Figure 7 illustrating the conversion between two TV-MLT transforms. It is indicated that N _h = 2M ₁ , N _f = 2L ₁ and in this case, ι = 0, ..., 2 (p + I) I ₁ - 2.

Thus, to determine the state of the sub-matrix g (n ', Z) at a time ri = ItM ₁ , the following partial convolution operations are performed:

To construct the matrix g (nM _x , Z) according to the computation relations of its coefficients given above, one gives, on the one hand, the coefficients of the analysis bench H (nM ,, Z) and, on the other hand, the coefficients of the filters of the 2p + 2 synthetic banks: F (Z ₉ MM ₁ XF (Z ₅ WM ₁ -L ₁ ), ..., F (Z, nM _x - (2 p + I ) L ₁ ), which follow one another in time.

This treatment amounts to performing 2p + 2 convolution products and concatenating 2p + 2 obtained segments, of length L ₁ , to obtain the coefficients gf («M _j ) for all i = Q, ..., 2 (p + Y) L ₁ -I. If for example p = 2, group the 2p + 2 = 6 successive states of the synthesis filter bank around the instant ri = nM _x to calculate the convolution products and obtain "slices" (FIG. 8A) g _g (nM _x ), ..., gi _{(p + x)} , _, («M,) which define the state of the submatrix g (n ', Z) at time ri = nM _x .

This result is valid for the general case of conversion between two TV-MLT transforms. Moreover, in the general case of two banks of filters whose lengths are determined by N _h and JV, the term is determined:

A _f = [(N _h + N _f -I) IL] ₊ I (56) corresponding to the number of successive states of the synthesis filter bank and the convolution products according to the relation (50) are calculated with a single state the analysis filter bank to determine all matrix "slices" gf (nM). This construction is illustrated in FIG. 8A, which schematically shows the groupings made to perform the convolution products of the successive states of the synthesis filter bank with those of the analysis filter bank. In the example shown in FIG. 8A, ap = 3 and Δ ^ = 4, in the case M = pL.

With these groupings, it is then possible to calculate the states of the sub-matrix g ("', Z) at times ri ≈ nM, (" + X) M, (n + 2) M, etc.

Then, for the construction of the global conversion matrix, the sub-blocks of this global conversion matrix T («, Z) = [A ₀ («, Z), ..., A _p _ _j («, Z )] are the

(M - 1 - jL) -th components of the type 1 multiphase decomposition of order M, of the submatrix g (n, Z), with:

When the sub-matrix g («, Z) is determined, it remains to extract and order the matrix" slices "gf (" M ") to construct each sub-block of the global matrix T (", Z). It will then be noted that these matrix slices gf (nM) are all determined for the same instant nM. With reference to FIGS. 13A and 13B, these are planes perpendicular to the Z axis and each defined for a power of Z, since it is recalled that the Z axis represents the size of the filters.

Thus, a state of the global conversion matrix T («, Z) is defined following the determination of N ₇ matrix slices of size M xM. Hereinafter, we denote P _m (n) the matrix slice of index m of the conversion matrix T («, Z), defined at the instant of index n by with m = 0, ..., (W ₇ , -1). As a result, the conversion matrix T (n, Z) defined by the relation (48) can also be written:

The number N ₇ . matrix slices P ₀ («), ..., P ^ _-1 OO is defined by the value of the maximum length of the polyphase components of order M of g («, Z) such that

Thus, the matrix T («, Z), expressed in the form A, preferred in the case M = pL, is written as a function of the sub-blocks A _y . according to the relations given above, and each sub-block A ₇ . is expressed as a function of the matrices g whose coefficients g ^ ' ^kτ {n) depend on the coefficients of the filters h _k and f _k determined, themselves, as a function of the four possible cases illustrated in FIG. 4B. Finally, the conversion matrix T («, Z) was completely constructed.

* second special case L = pM

We now describe the construction of the sub-matrix g (Z, ") for the case where L = pM. The main difference with the previous case M = pL is that the conversion matrices are preferentially defined in the form of type B. The calculation of the filtering coefficients gf ¹ '* ² («) is determined by

We find the same property on the index i which is both a convolution index and a temporal variable. It is therefore necessary to take into account the variations of the analysis filter bank H ("-M + 1 + z ^" , Z), that is to say the changes in states of the filter bank, during the calculation of the slices. matrixes gζ (n) ,, .., g ^B _{m + N ^ 2} (n). FIG. 8B illustrates the grouping of the states of the analysis filter bank which is used to determine the states of the sub-matrix g (Z, "') at the times ri = nM _ι , (n + 1) M _ι , (n + 2) M _ι , ....

In the example represented, ap = 3 and A _h = 4, this quantity: determining the number of successive states of the analysis filter bank H (n -M + 1 + i, Z) grouped with a state of the synthesis filter bank F (Z, ri) and allowing the calculation of a state of the sub-matrix g (Z, n) following a partial convolution.

In this second particular case where L = pM, the conversion matrix T (Z, n) is defined by:

each sub-block A ₁ - (Z ₉ W) of the main conversion matrix is the (M -1 + iM) -th polyphase component of type 2 of order L of g (Z, ") at time nL and we get

A state of the main conversion matrix T (Z, n) is constructed from the data of the state g (Z, ") at time nL. It remains to extract and order the matrix slices of g (Z, nL), determined for the same instant nL, to identify the polyphase components of type 2 of order L. This last step is also similar to that described in document FR-2,875,351 for the construction of the conversion matrix T (z) from g (z).

The conversion matrix T (Z, ri) is therefore defined by the data, at each instant n, of its N _τ matrix slices of size Lx L. We denote by P _m (n) the matrix slice of index m of the conversion matrix T (Z, n), defined at time n by

with m = 0, ..., (N _r -l). As a result, the conversion matrix T (Z, n) defined by the relation (53) can also be written

The number of matrix slices P ₀ (Λ), ..., P ^ _-1 (W) is defined by the value of the maximum length of the polyphase components of order L of g (Z, n), here, such that

Again, the conversion matrix T (Z, n) was completely constructed at this point.

* General case K = ppcm {L, M)

Form A

In the general case now where the respective numbers of filters in the banks are not multiples of one another (K = ppcm (L, M)), in the form A, the determination of the states of the sub-matrix g (", Z) is defined by the calculation of all its filter coefficients gf" ^k2 (n) such that:

with A ₁ = O, ..., (M -1) and k ₂ = 0, ..., (L-I) and the algorithmic delay control parameters are determined by the solutions given to the relations (42). Here again, groupings of A _f successive states of the synthesis filter bank are performed to produce a partial convolution product with a state of the H (H, Z) analysis filter bank (FIG. 9A).

The main conversion matrix T («, Z) is defined by the construction of its sub-blocks A .. (n, Z) such that:

with i = 0, ..., P ₁ -1 and j = 0, ..., p ₂ - \.

When O≤e ^ ≤Kl, the element A ₁ . _j (n, Z) of the main conversion matrix T (M, Z) is e. _y- th polyphase component of type 1 of order K of the matrix g (n + iM, Z) and we therefore have

The current index / designates both the number of the polyphase component with e _tj and a time advance iM. Under these conditions, the construction of a state of the main conversion matrix is determined by the data of p _λ successive states of g (ra ', Z) taken at the times ri = nK, nK + M, ..., ( n + 1) KM.

This property is also verified for polyphase components e _i} such that (aL + b + LK) ≤e _tj <-l. The element A _.; (w, Z) of the main conversion matrix T (n, Z) is the (K-Ve ₁ ;.) - polyphase component of type 1 of order K of g ("+ iM + K, Z) composed with a delay Z ^" ', that is:

We thus determine the states of g («', Z) taken at the instants ri = nK, nK + M, ..., (n + \) K -M to build a state of the main conversion matrix.

Figure 9A illustrates the groupings of several states of g (", Z) for calculating a state of the conversion matrix. In the example shown, we chose P ₁ = 3 and P ₂ = A. A state of g (n ', Z) at time ri = nK + ïM is used to extract the series of polyphase components A ₁ (n, Z) with j = 0, ..., /?, - 1. This series represents a line of p ₂ components among the p _χ lines of T («, Z). It is important to observe in this figure 9A that the scheduling of polyphase components A ₁ , (n, Z) represents the states of the transposed matrix T ^' («, Z) of T («, Z).

* General case K = ppcm (L, M)

Form B

In the form B of the operators and always in the general case, the states of g (Z, n) are determined by the calculation of the filtering coefficients g * "* ² (n) such that:

with k _x = 0, ..., (M-I) and k ₂ = O, ..., (I -1) and the algorithmic delay control parameters are determined by the solutions of the relations (42). It is necessary to group Δ _h successive states of the analysis filter bank to produce a partial convolution product with a state of the synthesis filter bank F (n, Z) (FIG. 9B).

The main conversion matrix is determined by the domain representation of all sub-blocks A. (Z, n) such as

with / = 0, ..., / ?, -1 and / = 0, ..., />, -1.

When 0 ≤ e _t; . <K -I, the element A ₁ -. (Z, H) of the conversion matrix T (Z, n) is the e ₍ . -Th polyphase component of type 2 of order iT of g (Z, n + (j -a) L) and therefore Note that the index j occurs both in the number e ₍ of polyphase component and in the time advance (j -a) L. Thus, to calculate the state of the main conversion matrix instant n, we determine p ₂ successive states of g (Z, "') associated with instants n' = (n - X) K + L, (n - I) K + 2L, ..., nK (a = p ₀ -1) This grouping also makes it possible to construct the polyphase components e. that aL + b + L - K ≤ and _{t J} ≤ -1. The element A ^ (Z, w) of the main conversion matrix T (Z, n) is the (X + e _{; /} ) -th polyphase component of type 2 of order K of g (Z, n + ( j - Ci) L), composed with a delay Z ^~] . It is written:

For the same reason, we first determine p ₂ states of g (Z, n ') associated with instants n' = (n - I) K + L, (n-1) K + 2L, ..., nK, to build all polyphase components that constitute a state of the main conversion matrix.

FIG. 9B illustrates the construction of the conversion matrix corresponding to the case where P ₁ = 4 and p ₂ = 3. A state of g (Z, n ') taken at time n' = (n - I) K + (j + I) L makes it possible to construct a complete column, consisting of p _{ polyphase components A. (Z, n) with i = 0, ..., p _ι -l. Finally, the global conversion matrix at each instant is obtained following the construction of P ₁ columns.

We now define a conversion system within the meaning of the invention.

For the case where M = pL, the relation of the conversion (47) established in the form Y (") = T (", Z) U (M) defines, in the form A, a time-varying matrix filtering of the vector U (n) by the global matrix T (n, Z). The Y (n), Y (κ + 1), ..., Y ("+ JV ₇ , -1) subband signals are obtained by the following operations:

Y (n) = F ₀ (n) υ (n) + P _] (n) υ ( _n-1 ) + ... + P _Nτ (n) V (n-N _τ + 1) Y (+ 1) = P ₀ (n + I) U (M + 1) + P ₁ (n + 1) U (n) + ... + P _{V /} _, (n + 1) U (n - N _τ + 2)

Y (n + N _7. -1) = P _o ("+ N _τ-1 ) U (w + N _τ -1) + ... + P _{v + 1} (+ N _τ-1 ) U (w )

The diagram of FIG. 10A illustrates an implementation of the conversion (with Λ ^f _r = 3 in the example represented) of the signals in successive subbands U («),..., U (« + 3). he Thus, it appears that the conversion system can be constructed by simple transform matrices, followed by an overlap addition of the transformed vector blocks.

For the other particular case of the conversions where L = pM, the conversion relation is established in the form V (n) = T (Z, n) X (n) and represents a time-varying type B matrix filtering. vector of the signals in sub-bands X (n) by the conversion operator T (Z, ri). The conversion takes place directly on the sub-band signals at the input of a transcoder, while a polyphase decomposition of order p of the signals after conversion is carried out. The successive polyphase components V (w), V ("+ 1), ..., V (n + iV _r -1), of order p, are obtained by the operations:

V (ή) = ^' P ₀ (n) X (n) + V _i (n - \) X (n-1) + ... + V ^ _ _ι (n -N _τ + 1) X (n - N _τ + 1)

Y (n + 1) = ¥ ₀ (n + 1) X (n + 1) + ¥ ₁ (n) X (n) + ... + P _{N 1 1} (H - N _τ + 2) X (n - N _τ + 2)

V {n + N _τ-1 ) = F ₀ (n + N _τ -1) X (n + N ₁ , -1) + ... + P + ₁ (w) X (n)

The diagram of FIG. 1OB illustrates the conversion (here with N _τ = 3) of the signals in successive subbands X (n),..., X (n + 3). It still appears that the conversion system can be implemented by transform matrices, followed by a recovery addition.

An example of operation of the overall conversion system in the sense of the invention will now be described.

With reference to FIG. 11, a conversion system between signal representations in different subband domains comprises a serial / parallel conversion module CSP of the incident signal vector X (ri) comprising the components x _n (n ') ,. .., x _L , ('') in respective sub-bands. The CSP module performs the equivalent of a polyphase decomposition of order /? ₂ of the signal vector X (n '), to deliver pi components U ₀ (H),. .., U _pi _, (/ i) of a vector U («).

These components of the vector U (") are then applied to a time-varying MFM matrix filtering module and characterized by the global conversion matrix T (n, Z) (or T (Z, n) according to the B form). type defined above. The MFM module then uses time-varying conversion matrices.

The p \ components V ₀ («), ..., V _p _ _j («) of the vector V («) coming from the matrix filter MFM module are finally applied to a parallel / serial conversion CPS module, which delivers the components y _Q {n "\ ..., y _M _ _ι {n") of the output signal vector Y (n ") The CPS module then realizes the equivalent of a recombination of the polyphase components of order / J _1. The output signal vector Y (n "), thus converted, can be used in its new format, for example by quantization and coding, or transported, or stored for subsequent applications.

All of these three successive processes performed by the CSP, MFM and CPS modules are indicated by a SYS outline in dashed lines in FIG. 11 to illustrate the modules carrying out the actual conversion. It is furthermore indicated that a flip-flop control module SW can detect the best time / frequency resolution, taking into account for example the stationarity properties of the incident signals. This control can advantageously control the state switching mechanism among a plurality of admissible states, in particular those described with reference to the different windows of FIG. 4B. In general, it is indicated that the flip-flop control module SW can search in the memory DD for all the pre-calculated sub-blocks as a function of all the possible states of the conversion matrix T, for example matrix slices by matrix slices.

An example of operation of a flip-flop control SW is illustrated in FIG. 14. A clock HOR (step H 145) determines a current instant r. The conversion matrix T was determined at a time t = nKT _e , (with K = ppcm (L, M) in the general case) where T _e is the sampling period of the signal to be processed in the domain. temporal). If this instant reaches a next instant (n + \) KT _e (test T141), we must redetermine the matrix T. However, it is verified that the properties of the signal have not changed (test T142), in which case the matrix slices recovered from the memory DD (step S 146) are given for different states (step AM 144) of those recovered for the previous instant nKT _e (step AM 143). Depending on the state defined in the test T142, the matrix T (step S 147) is determined until a next instant (n + 2) KT _e (loop S 148). In the example shown, it is therefore possible to analyze the properties of the signal on the test T 142, all the KT _e instants, to construct the matrix T globally.

In a variant of the embodiment illustrated in FIG. 14, since the lines (form A) or columns (form B) of sub-blocks A ₁₇ of the conversion matrix T are pre-calculated for the same moments, it is possible to increase the frequency of the test Tl 42 on the properties of the signal, either to reduce the execution period of the test T 142 to MT _e (for the form A) or to LT _e (for the form B) and to recover up to date matrix slices as to the variation in time of the aforementioned possible states. Such a variation, which may occur within a period KT _e , will then be detected and taken into account for the construction of the matrix T.

Thus, in this variant, the global conversion matrix T is progressively built up by calls to the memory DD at successive times for which the sub-blocks A have been pre-calculated _therein .

The flip-flop control SW of FIG. 11 thus manages the DD memory calls of the states of the conversion matrix. The memory DD delivers, in return, the matrix slices denoted P ₀ («), ..., P _V _, («) pre-calculated for the same instant n. It is advantageous to provide for this purpose a fast memory. Thus, the slices P ₀ («), ..., P _Λ _ _j («) can be pre-calculated taking into account the different admissible states, while the calls in DD memory of these filtering slices can be made to the fly, at each successive instant nK (or, in the aforementioned variant of FIG. 14: at each instant nM or nL to call lines (form A) or columns (form B) of sub-blocks and progressively calculate the matrix global conversion T).

A relationship between the index n relative to the states of the conversion system, on the one hand, and the time indices denoted r 1 and r 1 in FIG. 11, relating to the signals in sub-bands, is specified below.

It is noted for this purpose _e f the sampling frequency of the time signal X _t and f _x the sampling frequency of the X sub-band signals (V). By construction, the X (V) signals are the subband signals defined in the transformed domain of the synthesis filter bank and we have a relation of the following type: f _x = fJL The serial / parallel conversion corresponds to a polyphase decomposition of order p ₂ of each of the sub-signals. As a result, the sampling frequency, denoted f _u , of the component vectors U («) is p ₂ times smaller so that: f _u = fjp ₂ In principle, the conversion of the vectors U (ri) in order to getting the vectors \ (n) does not involve a change of frequency. Therefore, the sampling frequency f _v relative to V (n) is such that / _v = f _u .

On the other hand, the parallel / series conversion corresponds to a recombination of the polyphase components of order p _x of the signal in sub-bands Y (n "). We note / the sampling frequency of the signals in subband of output, of so that: Therefore, to guarantee the cadence adaptation of the three samplings involved in the conversion system, the three temporal indices ri, n and ri satisfy the equality relation: n 'L = nK = ri M with K = ppcm (L , M). Therefore, at a sampling frequency f _e given, relative to the time domain, a new L -uplet of coefficients in sub-bands X (V) arrives at the input of the conversion system at multiple instants of L, it is after a time equal to LIf _e has elapsed. State changes in the conversion matrix intervene at multiple moments of K. The filtering slices P ₀ (w),..., P _Vτ (n) therefore come back from the memory when a duration K / f _e has elapsed in the embodiment illustrated by way of example in FIG. 14. It will also be noted that in the aforementioned variant of this FIG. 14, it is still possible to deliver the lines (form A) or the columns (form B) of sub-blocks A _tj for the same instants n, all the M / f _e or all L / f _e , respectively, to progressively build the matrix T. Finally, the output of the conversion system a new M -uplet of coefficient in sub-bands at multiple instants of M, that is, say after a period of M / f _e has elapsed.

Thus, in more general terms, for the form A, the signal to be processed being digital and initially sampled at a period T _e , the global conversion matrix is determined periodically for multiple instants of a quantity KT _e and is expressed in function of matrices of type g («, Z), calculated for successive multiple instants of a quantity MT _e .

In particular, the computation of the coefficients of each matrix of type g (", Z) at a time multiple of the quantity MT _e is then carried out by taking:

Successive successive sets (or "allowable states") of coefficients of the synthesis filter bank determined for Δ / successive instants in a period MT _e , and starting from a multiple instant of MT _e ,

and a set of coefficients of the analysis filter bank determined for this multiple instant of MT _e , and applying a partial convolution between the successive sets of coefficients of the synthesis bench and the coefficients of the analysis bench, with Δ / = [(N _h ⁺ Nf-I) / L] + 1, where Nj ₁ and Nf are the respective lengths of the analysis and synthesis filters.

For form B, the global conversion matrix is determined periodically for multiple instants of a quantity KT _e and is expressed as a function of matrices of type g (Z, n), calculated for successive multiple instants of a quantity

LT _e .

More particularly, the computation of the coefficients of each matrix of type g (Z, «) at a multiple instant of the quantity LT _e is then carried out by taking: - Δ _/ , successive sets (or" admissible states ") of coefficients of the bank of analysis filters determined for Δ ;, successive instants in a period LT _e , and starting from a multiple instant of LT _e ,

and a set of coefficients of the synthesis filter bank determined for this multiple instant of LT _e , and by applying a partial convolution between said successive sets of coefficients of the analysis bank and the synthesis bench coefficients, with Δ _/ , = [(N _h + Nf-1) / M] + 1, where N _h and Nf are the respective lengths of the analysis and synthesis filters.

We now describe how the conversion in the sense of the invention can be represented by a scheme similar to a representation by a linear system, periodically varying in time, or LPTV (for "Linear Periodically Time Varying"), described in the document FR -2875351. Hereinafter, a representation thus similar to a representation by an LPTV system will be noted "s-LPTV".

* Implementation according to form A

In the form A, for i = 0, ..., p _ι - \, the conversion relation is such that the polyphase component numbered i of the output subband signals is determined by

Under these conditions and taking into account the form A, we obtain a subsystem numbered / which delivers the component V ₁ - (Ji) of the output signal as shown in FIG. 12 A. As an illustration, a switch is represented COM input subsystem, to schematize the "path" of p ₂ stages of the subsystem in turn. The filtering operations performed by the subsystem are characterized by the A. components. (n, Z) of the main conversion matrix (with j = O, ..., p ₂ - 1).

The operation of the overall conversion system, in the general case, defined as A, can be seen as the structure of Figure 12B. It then comprises />, linear subsystems varying in time and the "switch" COM1 at the input operates periodically (with a period p ₂ / ^' f _x ).

Each subsystem out of this set (numbered i with i = 0, ..., p _ι-1 in FIG. 12B) is characterized by the p ₂ filters A _.; (", Z) with / = 0, ..., / ?, -1. These subsystems operate in parallel and the output "switch" COM2 also selects one of their outputs periodically as output from the conversion system with a period p _× lf. The filter coefficients of the main conversion matrix

T (n, Z) vary with time and its changes of state occur after each period of duration Ki f _e . The global system is thus equivalent to a linear system, periodically varying in time, and of period KI f _e , with:

K = P ₂ L = P ₁ PI eI f _e = Lf _x = Mf _y

The two switches at the input COM1 and at the output COM2 of the system operate with a frequency f _e l K which corresponds to the frequency of change of state of the components A _; . {n, Z). The output Y («) of the conversion, at the instant» //, is equal to the output of the subsystem s-LPTV numbered i, at the instant n / 'f _v , when i = n modp,. The entry X (n), at the moment kl f _x , contact the numbered connections j of each p _λ subsystems s-LPTV when j - k moâp ₂ .

In the particular case where M = pL, it suffices to simply put p _λ = 1 and / ?, = p and the conversion equation is reduced to:

The representation of the system as an LPTV system, in this particular case, corresponds in every respect to the diagram of the figure completely represented by the structure of FIG. 12A and the output V _; (") Corresponds directly to the Y (n) signal in sub-bands after conversion.

* Implementation according to form B

For / = 0, ..., / ", -1, the conversion equation defined in the form B is such that the polyphase component numbered i of the output subband signals is determined by

In the particular case where L - pM, we have ap ₂ = 1 and P ₁ = p and the conversion equation is simply reduced to

Under these conditions and taking into account the form B, we obtain a subsystem numbered / which determines the component V ₍ (") of the output signal as shown in Figure 12C. The COM switch of the input travels the p ₂ floors of this subsystem and carries out the filtering operations characterized by the components A _{; j} (Z, n) with j = O, ..., p ₂ - 1 of the main conversion matrix.

The conversion system in the general case and defined in the form B can be interpreted as a set of subsystems as shown in FIG. 12D. This structure comprises p _× linear subsystems varying in time and the COM1 switch at the input is period periodic P ₂ Zf _x - The subsystem numbered / with i = O, ..., p _r -l, among this set, is characterized by the p-, filters A ₁ . _j (Z, n) with j = 0, ..., p ₂ -1. These subsystems operate in parallel and one of their outputs is periodically selected as the output of the conversion system with a period pj f _y . The filter coefficients of the main conversion matrix T (Z, n) vary with time and its changes of state occur after each period of duration KI f _e . The global system is therefore linear periodically varying in the period of time Kl f _e , with:

K = P ₂ L = P ₁ M and f _e = Lf _x = Mf _y

The two switches at the input COM1 and at the output COM2 of the structure of FIG. 12D operate with a frequency fJK which is also the frequency of change of state of the components A ₁ . (Z, ri).

The output Y («) of the conversion, at the instant ni f _y , is equal to the output of the subsystem s-LPTV numbered /, at the instant ni f _y , when i = n mod / j,. The input X («), at the instant kl f _x , contacts the connections numbered j of each of the p _{ LPTV subsystems when j = k mod p ₂ . An embodiment based on overlap transformations is now described. We note for this purpose, as in FR-2,875,351, B (") (i = 0, ..., p _ι -1 and j = 0, ..., p ₂ -I) matrices of size N _x M xL, "rearranged" and associated with each of the components A (n, Z) for the form A and associated with each of the components A (Z, ή) for the form B such that:

Form A:

With these definitions, the s-LPTV representations of the global systems according to FIGS. 12B and 12D respectively associated with the forms A and B, are rearranged naturally and lead to the diagram of FIG. 12E. The storage operations are performed after matrix multiplications of the input signals by the matrices B _hJ (n). The OLA-rated blocks (for "overlap and add" in English) perform the storage and addition operations with final recovery of the vectors transformed by the matrices B _^ (n). The calculation procedure for the conversion between subband domains is preferentially as follows:

each new vector X (w ') such that U («) = X (n') _} with n '= np ₂ + j, is placed at the input of the matrix blocks B (n) (i = O, ... , p _} - 1);

- for each "number" i fixed, apply:

A matrix transformation of U ₇ (n) by the matrix B _{1 y} (n), a summation of all the vectors transformed at the output of the matrices

An overlap addition on these vectors, the OLA operation being carried out on vectors of length N _r M with a recovery of

(N ₁ -I) M, the output Y ("") of the conversion system corresponds to the output V ₁ (n) of the subsystem s-LPTV numbered i with n "-np _x + i.

It is recalled that the matrices B _{; y} (/ i) vary in time. Apart from this important point, the treatment carried out globally remains similar to that described in document FR-2,875,351. FIG. 12E shows the principle of global processing.

In general, it will be remembered that the overall conversion involves an addition-recovery transform, taking into account in particular a temporal evolution in the quantities which are added with overlap.

* Examples of realization

The following are applications of the invention in the case of MPEG-1/2, MPEG-2/4, Dolby AC-3, G722.1 audio coders (TDAC type of the Applicant), most of which are standardized.

According to the characteristics of each of the banks of filters used by these coders, we obtain a conversion system generally corresponding to the case K = ppcm (L, M), but with also frequent occurrences of the two particular cases M = pL and L = pM . It may also happen that one of the analysis or synthesis filter banks is invariant in time. Of course, the cases where the two banks of filters are invariant in time are commonly treated by the state of the art, in particular in the document FR-2,875,351.

The following table summarizes the different cases observed with existing types of coders.

It will be noted that the conversion cases where M = pL correspond to the particular cases where the number of "determining" channels of the filterbanks are integer multiples. In these cases, we simply note that K = M (P ₁ = I) and p ₂ = p.

Most of the representations used by MPEG-2/4 AAC or Dolby AC-3 encoders are defined by two dimensions denoted M ₁ and M ₂ . Nevertheless, as shown above, the two dimensions are equivalently TV-MLT time-lapse transforms (defined as a function of the ratio M ₁ ZM ₂ ). With regard to the above-mentioned coders, the cases M = pL implicitly indicate that the largest dimension M ₁ of the TV-MLT transform (with MJMj) of the analysis filter bank is a multiple of that (denoted L ₁ ). of the TV-MLT transform (with L _x IL ₁ ) of the synthesis filterbank. More explicitly, we can speak of a "conversion of the cases where M ₁ = pL _λ ".

By way of example, the conventional scheme of the conversion between the Dolby audio encoder AC-3 and the MPEG-2/4 AAC encoder is shown in FIG. a L ₁ = 256 and M ₁ = 1024, so simply p = A satisfying M \ = pL \. Thus, the condition of proportionality applies only to the largest dimension of the filter bank varying over time.

* Example of conversion between a P-QMF (L) type filter bank and a TV-MLT (M ₁ IM ₂ ) filter bank with multiple L and M ₁

Consider the case where the synthesis filter bank is of the P-QMF (L) type, for a transcoding between an MPEG-1/2 layer I and II encoder to an MPEG-2/4 AAC type encoder and / or an MPEG-1/2 layer I and II encoder to a Dolby AC-3 type encoder.

These are typically two conversion examples according to the case M = pL.

The synthesis filter bank of the conventional scheme is invariant in time. It has L = 32 subbands and the length of the filters is N _f ≈ 512. The transformed

TV-MLT (M _x IM ₂ ) is defined by the values M ₁ / M ₂ = 1024/128 for the MPEG-2/4 AAC encoder and MJM ₂ = 256/128 for the Dolby AC-3 encoder. The characteristic constants of the conversion system are then as follows:

The number Δ _/ is not defined in this case since the filter bank P-QMF is invariant in time and, therefore, the matrix slices of g (n, Z) are defined simply as:

The index / is a simple convolution index and the coefficients of the synthesis filters do not vary.

We denote Δ _r the number of admissible states of the main conversion matrix

T («, Z). There exists A ₁ , = 4 possible and different states for the temporal variations (index n) of the global matrix T («, Z). The analysis filter bank H (n, Z) indeed has four distinct states. As a result, at one instant "M, the main conversion matrix T (", Z) is constructed, on the one hand, from the coefficients of the synthesis filter P-QMF (L) and on the other hand :

coefficients of the TV-MLT transform defined by the relation (13), if the transform has a long time resolution 2M ₁ ;

or coefficients of the TV-MLT transform defined by the relation (15), if the transform has a short time resolution 2M ₂ ;

or coefficients of the TV-MLT transform defined by the relation (17), if the transform makes a long 2M ₁ to short 2M ₂ resolution change;

or coefficients of the TV-MLT transform defined by the equation (19), if the transform makes a short resolution change from 2M ₂ to 2M ₁ long.

The Δ _r = 4 acceptable states of the conversion matrix T («, Z) are determined from the N ₇ . slices that are all of size M ₁ x M ₁ .

In the case of a reciprocal conversion with I ₁ = pM where the P-QMF filter bank (M) is the analysis filter bank, while the TV-MLT transform (I ₁ ZZ-,) is the bench of synthesis filters, the conversion system is defined as B.

The conversion matrix T (Z, n) admits Δ ₇ = 4 different states and each state is determined by N _τ slices comprising L _x x L _x filter coefficients. If 1 / Z ₂ = 1024/128 (case of the MDCT transform of the MPEG-2/4 AAC encoder), then N ₁ . = 4 and if L ₁ IL ₂ = 256/128 (case of the MDCT transform of the Dolby AC-3 encoder), then N _τ = 3.

* Cases of transformations TV-MLT (L ₁ ZL ₂ ) and TV-MLT (M _x IM ₂ ) with L _x and M ₁ multiples

This is the case, for example, of transcoding between the Dolby AC-3 audio coder and the MPEG-2/4 AAC coders. The conversion system corresponds to the particular case where M ₁ = PL ₁ with L ₁ IL ₂ = 256/128 and M ₁ ZM, = 1024/128. The constants of the conversion system are thus determined by p = AA ₇ = IO N _τ = 3

A state of the conversion matrix has N ₇ . = 3 slices of filter coefficients P ₀ («),?, («), P ₂ (n). Each coefficient range is 1024x1024.

It is shown that the maximum number of different states of the main conversion matrix T («, Z) is equal to A ₇ . = 1152. This number is obtained from the value of the term u _k of a Fibonacci sequence, defined for the initial values u _\ = A, " ₂ = 6, when k = A _f . It has been observed that, in general, the enumeration of possible states of the matrix T respects the variations of a sequence of Fibonacci. This number of different states A ₇ is determined by assuming that the state changes of the synthesis filter bank F (Z, n) and those of the analysis filter bank H (n, Z) are independent. It is preferentially provided two independent SW flip-flop commands that control the resolution changes of the two TV-MLT transforms. For the TV-MLT transform (L ₁ IL ₂ ), this control is carried out at all the multiple instants of L ₁ and for the TV-MLT transform (M ₁ IM ₂ ), this control is carried out at all the multiple instants. of M ₁ . As indicated above, the SW toggle controls advantageously operate on the basis of an analysis of the statistical properties of the incident signal and determine, in particular by perceptual entropy criteria, which are the most suitable resolutions for each block of length. 2I ₁ or 2M ₁ . These commands are at least partly consistent and certain changes in the resolution of the TV-MLT transform (Z ₁ ZL ₂ ) are advantageously synchronous with those of the TV-MLT transform (M ₁ ZM ₂ ). For example, if the TV-MLT transform (L ₁ ZI ₂ ) proceeds over several periods, by transformations of resolution L ₂ , the transform TV-MLT (M ₁ ZM ₂ ) does not carry out, a priori, a change of resolution M ₂ - »M, or does not pass through states defined by the resolution M ₁ . It should therefore be specified that the number of admissible states A _τ = 1152 is maximum because some states among the Δ _r states are no longer admissible if they are no longer consistent with the operation of the transition control of the transcoder.

For the case of the conversion involved in the transcoding between the MPEG-2Z4 AAC format and the dolby AC-3 format, we have L ₁ = PM ₁ with p = 4 and the conversion system is defined as B. The construction of the matrix g (Z, «) requires grouping of Δ _ft = 10 successive states of the transform TV-MLT (M ₁ ZM ₂ ). Each state of the conversion matrix T (Z, n) is determined by the data of N ₇ . = 4 slices of 1024x 1024 coefficients. There may be a maximum total of 1022 different states eligible for the conversion matrix.

* TDAC coder (L) and TV-MLT transform (M _x IM ₂ ) with K = PfCm (L ₇ M ₁ )

In the case where the synthesis filter bank is a TDAC type filterbank comprising L = 320 subbands, each filter being of length N = 640, there is no multiplicity between the dimension L and the dimension M ₁ = 1024 of the MPEG encoder 2/4 AAC, or between the L dimension and the M ₁ = 256 dimension of the Dolby AC-3 encoder. In these two conversion cases, the conversion system is determined by the value of K = PpCm (L ₇ M ₁ ) such that K = 5120 with the MPEG-2/4 AAC encoder and iit = 1280 with the Dolby AC coder. 3. The system can be implemented in the form A or in the form B.

In the case of an implementation of the form A, there are four admissible states for the filtering sub-matrix g (n, Z) because the coefficients of the synthesis filter bank are invariant in time, while those of the analysis filter bank relating to the TV-MLT transform (M ₁ ZM ₂ ) admit four different definitions.

For the construction of the principal matrix, we group p _λ successive states of g («, Z) in order to build a state of T («, Z). Assuming that the state change rules of g (n, Z) are the same as those of the TV-MLT transform (Af ₁ / M ₂ ), the total number of states A _τ of T («, Z ) is deduced from the values of a Fibonacci sequence. We thus obtain A ₁ = u _k , calculated with k = p _x .

In the case of transcoding involving the MPEG-2/4 AAC encoder, we have ^ ₁ = 16 and Δ _r = 8362. A state of the conversion matrix has N ₁ , = 1 single slice with 5120 coefficients. In the case of transcoding where the Dolby AC-3 format intervenes, we have P ₁ = 4 and

Δ _r = 26. A state of the conversion matrix has N ₁ . = 1 single slice with 1280 filter coefficients.

Of course, the present invention is not limited to the embodiment described above by way of example; it applies to other variants. In general, the invention applies to any transcoding between coding formats, in particular audio formats, using banks of filters that vary over time. These transcoders may be implemented in gateways, in particular in telecommunication network nodes, or in multimedia content servers in the context of "streaming" mode broadcasting applications, or downloading or broadcasting applications. digital television (MPEG-4 AAC format to MPEG-2 Layer II or Dolby AC-3 format), or others.

It can also be applied to any implementation for a transition between two representations of sub-bands, in particular within MPEG-4 encoders HE-AAC and / or MPEG Surround Audio Coding.

Moreover, most of the coding formats indicated above operate on digital audio signals, but the present invention applies to any type of transcoding that varies over time and operates on any type of signal.

Claims

A method implemented by computer resources for processing a signal by passing between different subband domains, aiming at compacting in a single process the application of a first vector representing the signal in a first subband domain to a synthesis filter bank, then to an analysis filter bank, to obtain a second vector representing the signal in a second subband domain, wherein the application of matrix filtering to the first vector is provided for directly obtaining the second vector, characterized in that the synthesis bench and / or the analysis bench are time-variant, in that the matrix filtering is represented by a global conversion matrix comprising matrix sub-blocks: • pre-calculated taking into account the possible variations in time of the filter banks,

And stored in memory, and in that the global conversion matrix is constructed by calling said memory to obtain said pre-calculated sub-blocks at successive instants.

2. Method according to claim 1, characterized in that the global conversion matrix is built progressively by calls to said memory at successive times for which said sub-blocks have been pre-calculated.

3. Method according to one of claims 1 and 2, characterized in that the first vector having a first number L of components in respective subbands while the second vector comprises a second number M of components in respective subbands after determining a third number K, the least common multiple between the first number L and the second number M: a series / parallel conversion of the first vector is applied to obtain polyphase component vectors, with p ₂ = K / L, and

- applying a parallel / serial conversion to obtain said second vector, in that: * the conversion matrix is applied to said p ₂ polyphase components of the first vector to obtain p _x polyphase components of the second vector, with p ₁ = K / M , and

the conversion matrix is square, of dimension K x K, and has p _x lines and P ₁ columns of sub-blocks Ay each having L rows and M columns, and in that sub-blocks Ay of the same index / ^'or sub-blocks of the same Ay indicey are pre-calculated for the same instant.

4. Method according to claim 3, characterized in that the conversion matrix is three-dimensional, with: a first dimension defined by the current index / sub-blocks,

a second dimension defined by the current index y of the sub-blocks,

and a third dimension defined by a degree of matrix filtering, and in that the sub-blocks pre-calculated for the same instant form matrix planes extending towards said third dimension.

5. Method according to one of claims 3 and 4, characterized in that the Ay sub-blocks are each expressed:

• according to a type of matrix g (n, Z), whose elements are given by:

• or, equivalently, according to a type of matrix g (Z, n), whose elements are given by:

or :

- Ni, is the length of the analysis filters,

Nf is the length of the synthesis filters,

n is a time variable, Z is a transformed domain variable,

k \ is between O and MI and & ₂ between O and LI, and

the coefficients gf "* ² ("), in each case, are expressed as a function of the coefficients of the analysis and synthesis filters.

6. Method according to claim 5, taken in combination with claim 4, characterized in that each sub-block of index i, expressed as a function of a matrix of type g (n, Z) is given by:

A., (n, Z) = [g (n + ïM, Z) Z ^iM'jL 1 where the notation i K denotes a decimation of a factor K, and the matrix planes consist of sub-blocks of the same index line i and are horizontal, and in that the overall conversion matrix is constituted by said predefined horizontal matrix planes rotten successive instants.

7. Method according to claim 5, taken in combination with claim 4, characterized in that each sub-block of index j, expressed as a function of a matrix of t3Φ ^e g (Z, n), is given by:

AT . (Z, n) = | Z ^lM'jL g (Z, n + jL) \, where the notation i K denotes a decimation of a factor K, and the matrix planes consist of sub-blocks with the same column index j and are vertical, and that the global conversion matrix is constituted by said vertical matrix planes pre-calculated for / ^ ₂ successive instants.

8. Method according to one of claims 5 and 6, characterized in that the number M is a multiple of the number L (M = pL), and in that each sub-block is expressed as a function of a matrix of type g (", Z).

9. Method according to one of claims 5 and 7, characterized in that the number L is a multiple of the number M (L = pM), and in that each sub-block is expressed as a function of a matrix of type g (Z, r).

10. Method according to one of claims 5, 6 and 8, characterized in that, the signal to be processed being digital and initially sampled at a period T _e , the overall conversion matrix is determined periodically for multiple instants of a quantity KT _e and is expressed as a function of matrices of type g (", Z), calculated for successive multiple instants of a quantity MT _e .

11. Method according to claim 10, characterized in that the calculation of the coefficients of each matrix of type g (M, Z) at a time multiple of the quantity MT _{e is} carried out by taking:

- Δ / successive sets of coefficients of the synthesis filter bank determined for Δ / successive instants in a period MT _e , and from a multiple instant of MT _e , - and a set of coefficients of the analysis filter bank determined for said multiple instant of MT _e , and applying a partial convolution between said successive sets of coefficients of the synthesis bench and the coefficients of the analysis bench, with Af = [(N _h + Nfl) / L] + 1, where Nt, and Nf are the respective lengths of the analysis and synthesis filters.

12. Method according to one of claims 5, 7 and 9, characterized in that, the signal to be processed being digital and sampled at a period T _e , the global conversion matrix is determined periodically for multiple instants of a quantity. KT _e and is expressed according to matrices of type g (Z, n), computed as for them for multiple successive instants of a quantity LT _e .

13. Method according to claim 12, characterized in that the computation of the coefficients of each matrix of type g (Z, n) at a multiple instant of the quantity LT _{e is} carried out by taking:

- Δ _/ , successive sets of coefficients of the bank of analysis filters determined for Δ / ₍ successive instants in a period LT _e , and from a multiple instant of LT _e ,

and a set of coefficients of the synthesis filter bank determined for said multiple instant of LT _e , and applying a partial convolution between said successive sets of coefficients of the analysis bank and the synthesis bench coefficients, with A _/ , = [(N _k ⁺ NfY) IM] + !, where N _h and Nf are the respective lengths of the analysis and synthesis filters.

14. Method according to one of the preceding claims, characterized in that a finite number of possible states are provided which are associated respective sets of coefficients of the synthesis and / or analysis banks, and in that said sub-blocks are pre-calculated from said respective sets for all possible states, while the overall conversion matrix is determined for at least one possible state defined from properties of the signal to be processed.

15. Method according to claim 14, characterized in that each set is calculated as a function of a modulation matrix and of a vector h characterizing a possible state and ensuring a perfect or quasi-perfect reconstruction property.

16. The method according to claim 15, wherein the synthesis and / or analysis banks are time-variant by resolution changes, characterized in that there are four possible states and in that said vectors h define: a long window corresponding to a first possible state, a succession of short windows corresponding to a second possible state,

a transition window from the long window to the succession of short windows corresponding to a third possible state, and

a transition window from the succession of short windows to the long window corresponding to a fourth possible state.

17. Method according to one of claims 3 to 16, characterized in that one takes into account and applies accordingly a control of an algorithmic delay produced by a processing of the signals in sub-bands.

18. Method according to one of the preceding claims, characterized in that the global conversion involves an overlap transform with addition, taking into account a temporal evolution in the quantities that are added.

19. Apparatus for processing a signal by passing between different subband domains, characterized in that it comprises, for the implementation of the method according to one of the preceding claims:

a memory (DD) storing the pre-calculated sub-blocks,

a clock (HOR) for determining successive instants, and a matrix filtering module (MFM) arranged to recover from said memory the pre-calculated sub-blocks for said successive instants for the construction of the global conversion matrix.

20. Device according to claim 19, for carrying out the method according to claim 14, characterized in that it further comprises a rocker control (SW) for:

defining, from the signal to be processed, one of said possible states and sets of associated coefficients, and

- Manage access to said memory according to the defined state.

21. Device according to one of claims 19 and 20, for the implementation of the method according to claim 3, characterized in that it further comprises:

a serial / parallel converter (CSP) upstream of the matrix filtering module, and

- a parallel / serial converter (CPS) downstream of the matrix filtering module.

22. Device according to one of claims 19 to 21, characterized in that it is integrated in a device such as a server, a gateway, or a terminal for a communication network.

23. Computer program intended to be stored in a memory of a device according to one of claims 19 to 22, characterized in that it comprises instructions for the implementation of the method according to one of claims 1 to 18.