WO2009004263A1

WO2009004263A1 - Conversion between sub-band domains for banks of module filters

Info

Publication number: WO2009004263A1
Application number: PCT/FR2008/051118
Authority: WO
Inventors: Guillaume Picard; Abdellatif Benjelloun Touimi
Original assignee: France Telecom
Priority date: 2007-06-29
Filing date: 2008-06-20
Publication date: 2009-01-08
Also published as: FR2918228A1; EP2174420A1

Abstract

The invention relates to a transition between different sub-band domains for compacting in a single processing operation the application of a first vector X(z), comprising a first number L of components in sub-bands, to a bank of synthesis filters, then to a bank of analysis filters, to obtain a second vector Y(z) comprising a second number of components M in sub-bands. The banks of synthesis and analysis filters implement modulation transforms and each result from the modulation of a prototype filter by a modulation matrix. After determination of a third number K , the lowest common multiple between the first number L and the second number M, there are provided: the application of the first vector X(z) to the transpose of the modulation matrix DTf of the bank of synthesis filters; if the third number K is different from the first number L, an arrangement in blocks by a serial/parallel conversion of the first vector to obtain p2 polyphase component vectors, with p2 - K/L; the application of a chosen matrix filtering, involving a conversion matrix, square and of dimensions 2K × 2K, to the p2 polyphase component vectors to obtain pγ polyphase component vectors of the second vector, with p1 = K/M; if the third number K is different from the second number M, an arrangement in blocks by a parallel/serial conversion to obtain said second vector, and the second vector Y(z) results from the application of the modulation matrix Ch of the bank of analysis filters.

Description

Conversion between subband domains for modulated filterbanks

Technical area

This is a digital data processing in transcoding context.

It relates more particularly to a conversion between different subband domains for modulated filter banks.

Technical background of the invention

The context of the present invention may be that described in documents FR-0409820 and FR-0604507 which propose to merge the synthesis and analysis operations involved in a conventional conversion scheme. These documents also describe a parametric control of the algorithmic delay created by the two banks of filters (synthesis and analysis) placed in cascade. The new conversion schemes thus obtained then make it possible to reduce the algorithmic delay as well as a better parallelism in the treatments implemented. The document FR-0409820 presents a general conversion in transcoding context and the document FR-0604507 presents in particular a conversion in the case where the banks of filters (analysis or synthesis) are likely to vary in time.

The teaching of document FR-0409820 is reproduced in the later publication: "Efficient Conversion Method of Subband Domain Representations", A. Benjelloun Touimi, A. Mouhssine, IEEE International Conference on Multimedia and Expo (Proceedings), Amsterdam (Netherlands) ), 6-8 July 2005.

The teaching of document FR-0604507 is included in the later publication: "Subband Domain Data Conversion for Time-Varying Filter Banks", G. Picard, A. Benjelloun Touimi, International Symposium on Signal Processing and its Applications (Proceedings), Sharjah (United Arab Emirates), 12-15 February 2007.

We are interested here in particular cases of modulated filter banks, such as in particular the cosine modulated filter banks. These cases are predominant in practice. In fact, for transcoding applications, the filter banks used in compression of an audio and / or video signal are almost all of the cosine modulated type.

The modulated cosine filter banks result from the modulation of a prototype filter by a matrix whose terms are expressed by cosine functions. One of their characteristics, which is conventional and advantageous, is the possibility of deriving fast implementation schemes based on discrete cosine transforms (DCT), or even fast Fourier transforms (FFT). These schemas directly benefit from existing fast algorithms for this type of transform, which reduces the complexity of processing. This possibility is particularly advantageous in the field of signal compression and is widely used to implement, for example, the time-frequency transforms that are commonly implemented in audio coders.

Of course, other types of modulated filter banks (sine or other) may have the same advantages and the invention is not limited to the particular case of a cosine modulation only.

The conversion schemes proposed in the documents FR-0409820 and FR-0604507 above allow a merger of the synthesis and analysis operations. They therefore give a reduction in complexity compared to a conventional conversion scheme where the synthesis and analysis benches follow each other but are applied separately. Moreover, this reduction in processing complexity is no longer guaranteed if one uses fast algorithms specific to DCT transforms for the implementation of the synthesis. and analysis in a conventional scheme.

The present invention improves the situation.

Presentation of the invention

Within the meaning of the invention, it is proposed a treatment derived from those referred to in the aforementioned FR-0409820 and FR-0604507, but taking into account the specific structure of the modulated filters, to generate new conversion schemes in this type. of cascading benches.

In the sense of the invention, it is particularly sought to isolate the modulation matrices and to merge the operations relating to the synthesis and analysis prototype filters.

In more specific terms, the present invention is directed to a method implemented by computer resources for processing data by passing between different subband domains, consisting in compacting in the same process the application of a first vector X (z ) having a first number L of respective subband components, to a synthesis filterbank, then to an analysis filter bank, to obtain a second vector Y (z) having a second number of M components in sub respective bands.

The method comprises the following steps, after determining a third number K, the least common multiple between the first number L and the second number M: a) if the third number K is different from the first number L, put in blocks by a serial / parallel conversion of the first vector to obtain p ₂ polyphase component vectors, with p ₂ = K / L, b) application of a chosen matrix filtering, involving a conversion matrix, square and of dimensions 2K × 2K, to said p ₂ polyphase component vectors to obtain p _x polyphase component vectors of the second vector, with

c) if the third number K is different from the second number M, set in blocks by parallel / serial conversion to obtain said second vector,

Within the meaning of the invention, the synthesis filter bank and the analysis filter bank implement modulated transforms and each result from the modulation of a prototype filter by a modulation matrix, and in particular:

before step a), the first vector X (z) is applied first to the transpose of the modulation matrix D ^τ _f of the synthesis filter bank,

after step c), the second vector Y (z) results from the application of the modulation matrix C _h of the analysis filter bank.

The conversion matrix T '(z) is then expressed as a function of:

* 2M polyphase components of the prototype filter of the analysis filter bank, and

* of IL polyphase components of the prototype filter of the synthesis filter bank.

It should be noted that the document US-2005/0018796 proposes a conversion method between domains of cosine modulated filter banks. However, the treatment within the meaning of the invention differs from the teaching of this document in particular in that:

the general treatment scheme in the sense of the invention (FIG. 3) is already different from that described in this document; the treatment in the sense of the invention implicitly incorporates a maximum reduction of the algorithmic delay in the conversion scheme; , since this property was already derived from documents FR-0409820 and FR-0604507,

the treatment in the sense of the invention also manages the particular cases where M and L are multiples of one another than the general case where M and L are arbitrary. Advantageously, a structure within the meaning of the invention makes it possible to use conventional fast algorithms for the modulation matrices and to search for efficient implementation structures for the core where the synthesis / analysis operations are merged, the final objective being, of course, to obtain a reduction in processing complexity compared to a conventional conversion scheme. The implementation of the invention therefore makes it possible to improve the method presented in documents FR-0409820 and FR-0604507 while retaining the advantages of reducing algorithmic delay and parallelism specific to the teaching of these documents.

List of Figures

Other characteristics and advantages of the invention will appear on examining the detailed description below, and the attached drawings in which:

FIG. 1 illustrates a cosine modulated analysis filter bank;

FIG. 2 illustrates a cosine modulated synthesis filter bank;

FIG. 3 schematically represents a structure for a conversion between subband domains, for modulated filter banks, with an isolation of the modulation matrices in the sense of the invention;

FIG. 4 is a representation of the conversion processing of FIG. 3 in the form of a linear system that varies periodically in time (or "LPTV" for "Linear Periodically Time-Varying");

FIG. 5 represents the implementation of the conversion process of FIG. 4 in the particular case M - pL;

FIG. 6 represents the implementation of the conversion process of FIG. 4 in the particular case L-pM inverse,

FIG. 7 illustrates advantageous filtering by subsystems A ' ₀ (z) and A' ₂ (z) in the context of an MPEG-1/2 Layer I & II conversion to Dolby AC-3 in short window. , FIG. 8 illustrates advantageous filtering by subsystems

as part of the MPEG-1/2 Layer I & II conversion to Dolby AC-3 in short window,

FIG. 9 illustrates chains of concatenation with intervening interleaving: * (A): in a subsystem of FIG. 7 or 8,

* (B): in a subsystem

of Figure 7 or 8,

the architecture (C) being equivalent to the architecture (A),

FIG. 10 illustrates an advantageous implementation of the core of the MPEG-1/2 LI & II conversion system to Dolby AC-3 in short window, FIG. 11 illustrates filter matrix systems involved in the implementation. advantage of the MPEG-1/2 Layer I & II conversion to Dolby AC-3 in a long window,

FIG. 12 illustrates multi-channel delay chains involved in the advantageous implementation of the MPEG-1/2 Layer I & II to Dolby AC-3 conversion in a long window, and

FIG. 13 generally illustrates the advantageous implementation of the MPEG-1/2 Layer I & II to Dolby AC-3 conversion in a long window,

FIG. 14 represents by way of illustration an example of a conversion matrix sub-block comprising null anti-diagonal portions; FIGS. 15A to 15C schematically illustrate steps of construction of the conversion matrix T '(z); respectively in the cases M = pL, L = pM and in a general case where there exists a smaller common multiple of the integers Met L,

FIG. 16A details the test T15 of FIG. 15A, and

FIG. 16B details the test T25 of FIG. 15B.

Description of embodiments

* Reminders on modulated filter banks

The following are the classic formulations of modulated filter banks. In the example describes the filterbanks are modulated in cosine.

An advantageous result relating to the techniques of the cosine modulated filter banks consists in the possibility of separating a modulation matrix from the polyphase components of the prototype filter. This technique is described in particular in:

"Multirate Systems and Filters Banks", P.P. Vaidyanathan, Prentice Halls PTR, Englewood Cliffs, New Jersey, 1992.

It is briefly recalled below.

* Expression of the analysis filter bank

We denote h (z) =

, the vector of the M transfer functions of a bank of cosine modulated analysis filters comprising M channels. By construction, the transfer function of the analysis filter of order k (k = 0, ..., M -I) is written:

where h _p (n) with n - 0, ..., N _h -1 is the impulse response of the prototype filter H _p (z), of length N _h , of the filterbank. It is then established that:

where c _kj with k - 0, ..., M - I and j - 0, ..., 2M - I are the elements of the modulation matrix C _h defined by:

The transfer functions G _} (z) with j - 0, ..., 2M - 1 are the j - th components of the 2M polyphase decomposition of the prototype filter H _p (z) and, by definition, we have :

It follows that the vector h (z) is in the form

Furthermore, the polyphase representation of a filter bank with maximum decimation such as:

where E (z) is the polyphase analysis matrix.

Comparing the two expressions of the vector h (z), we identify

E (z) appears as a matrix with 2M lines for M columns.

The analysis part of a maximum decimation filter bank can therefore be represented by the diagram illustrated in FIG. 1 showing a cosine modulated analysis filter bank, where: - x (z) is an input signal,

z ¹ is a time advance,

- "i M" means a subsampling (or "decimation") of a factor M,

- y _j (z) denotes the order component j of the output vector y of the analysis filter bank.

* Expression of the synthesis filter bank

In the same way, equivalence is established between the polyphase expression of the synthesis filterbanks and a formulation using a modulation matrix.

We then write f (z) = [F ⁰ (z), F ⁱ (z), ...,

, the vector of the L transfer functions of a cosine-modulated synthesis filter bank. By construction, the order synthesis filter / is of the form

where f Λή) with n = 0, ..., N _f -l is the impulse response of the noted prototype filter

F _p (z).

It is then established that:

where d, with I - 0, ..., L - 1 and j - 0, ..., 2L - I are the elements of the modulation matrix D ₇ defined by

The transfer functions _K} (z) j - 0, ..., 2L -I are components y ^'th decomposition polyphase 2L order of F _p prototype filter (z) and, by definition, we have :

We deduce that the vector f (z) is in the form: f {z) = {K ₀ {-z ^2L ), z- ⁱ K _ι {-z ^2L ), ..., z- ^(2L - ^V) K 2 _L _ _ι {-z ^2L )) O- _f (11)

Subsequently, we take the polyphase representation of a synthesis filter bank with maximum decimation such that: f (z) =

where R (z) is the polyphase synthesis matrix.

Comparing the two expressions of the line vector f (z), it appears that:

which corresponds to a matrix of M rows for 2M columns.

The synthesis part of a maximum decimation filter bank is represented by the diagram of FIG. 2, where the notation "T L" designates an oversampling (or "expansion") of an L factor.

* Expression of the conversion between subband domains

In an embodiment within the meaning of the invention, the conversion consists in moving from a domain of sub-bands to another domain of sub-bands. A cascade of synthesis filters is then cascaded, followed by an analysis filter bank.

Thus, in general, the main equations of the conversion between subband domains for a first filter bank comprising L channels and a second bank of Filters with M channels are defined as: V (z) = T (z) U (z), where the conversion matrix T (z) is defined by:

T (z) = [v (z) gg (z) | ((13) with K - cmcm (L, M), according to the teaching of the aforementioned document FR-0409820.

The delay matrix v (z) is of size P ₁ X p ₂ . It is defined by its elements:

_{V ij} (z) = z ^M - ^{ι + ιM} - ^jL i = 0, ..., A - 1 and j = Q, ..., p ₂ - \, with K = _{P i} M = p ₂ L.

The sub-matrix of filters g (z) is defined by g (z) = h (z) f (z) (14) where h (z) and f (z) respectively denote the column vector of the M analysis filters and the line vector of the synthesis filters. The definitions and notations of the signal vectors:

are those introduced in document FR-0409820.

Given the expression obtained from the analysis filter vector (5) and the synthesis filter vector (11), a new definition of the elements of the conversion matrix T (z) can then be given, within the meaning of the invention, by:

where the matrix g '(z), of size 2M x 2L, is defined by its elements g' _k , (z) such that

with £ = 0, ..., 2M-1 and / - 0, ..., 2Z-I.

Thus, a sub-block A _tj (z) of the conversion matrix T (z) is put into an arranged form

We then define matrices of transfer functions such as:

According to one advantage that the treatment provides in the sense of the invention, it is then possible to define an expression A _t ' _J (z) from the sub-blocks A _tJ (z) of the conversion matrix such that the two matrices C _h and D ₇ modulation of the respective filter banks are now isolated.

This property advantageously makes it possible to retain the use of fast algorithms for calculating DCT transform or FFT fast Fourier transform to perform part of the operations of the conversion between subband domains, in particular the modulation by the matrices C _h and D ₇ .

FIG. 3 gives the new conversion scheme for the cosine modulated filterbanks where u _y (z) and v '(z) are the modulated signal vectors such that,

The new conversion matrix T '(z) is then defined by:

and is also written:

FIG. 4 illustrates, for its part, the implementation of a conversion equivalent to that illustrated in FIG. 3, in the form of a linear system that varies periodically in time or "LPTV", as described in the document FR. -0409820.

In the embodiment illustrated in FIG. 3, as in the embodiment illustrated in FIG. 4, the implementation in the sense of the invention differs from that proposed in documents FR-0409820 and FR-0604507 in that part of the calculations (in particular the modulations by the matrices D 1 and C _h ) are carried out at the input and at the output of the system and directly on the signals in sub-bands before the switches (flip-flops of FIG. 4).

* Expressions of the matrix subblocks

The transfer function G _km (z) is the m-th component of the polyphase decomposition of order p _γ of the component G _k (z) such that:

G _km (z) also represents the component number 2mM + k of the 2K polyphase decomposition of the prototype filter H _p (z).

The transfer function K _lr (z) is the r-th component of the polyphase decomposition of order p ₂ of K ₁ (Z) such that:

K _{1 r} (z) also represents the component number IrL + 1 of the polyphase decomposition of order 2K of the prototype filter F _p (z).

An index element (k, l) of the sub-block A ' _y (z) is then written:

In this expression (24), an important parameter is then defined in the following description. This is the delay variable

which is written as follows:

where z ^' = 0, ..., / J ₁ -I, j = 0, ..., p ₂ -l, m = 0, ..., P ₁ -I and r = O, ..., p ₂ - \.

Indeed, this last expression (24) of the elements of A _h ' _j (z) is interesting insofar as it appears the operator:

which behaves either as a simple delay operator or as a circuit breaker, according to the following property:

Thus, the variations of the expression are studied below to identify its

values when they are multiples of K and thus determine the only non-zero elements in the sum of equation (24), when they exist. This study will then make it possible to define the properties of simplicity (in terms of number of null elements) of the matrix

and to give explicit and simplified expressions of its non-null elements.

For greater clarity of the exposition and for a didactic purpose, it is first described the particular cases where the Met L variables are multiple of one another, which makes it possible to simplify the expression, as one will see it below.

* Special case where M - pL

Figure 5 shows the implementation of conversion processing (time variant as LPTV system in the example shown) in the particular case where M = pL. In this particular case, the equations of the conversion at the heart of the system, with here

P ₁ = I and p ₂ = p, are in the form:

where we denote v '(z) the modulated signal vector such that Y (z) = C _A v' (z), where the sub-block of filters

is defined by its subscript elements (k, l) such that:

The delay variable noted previously

only depends on four indices and is written:

with j = Q, ..., pl, r = Q, ..., pl, k = 0, ..., 2M-1 and / 0, ..., 2,2 -I

Hereinafter, we seek to identify the indices (j, r, k, l) for which the values of the delay

are multiples of M, in the search for non-null matrix elements of each sub-block

In particular, an antidiagonal portion index of the matrix is

u = k + 1, with 0≤u≤2 (M + L-1). The delay variable is then written:

It is also recalled that the index j denotes the index of a sub-block from among

sub-blocks and thus characterizes a general sub-block A ^ (z). Thus, for any index j fixed, the variations of the delay are limited as follows:

-3M-jL + l≤ε _r ^J (u) ≤M-jL-1 The index r varies too. It is an index of the summation which appears from the polyphase decomposition according to relation (28). However, by fixing it, it is possible to determine the terms of this sum which are non-zero, as follows (also noting that, when j and r are fixed, the variable u representing the diagonal index in the relation (30 ) becomes the only degree of freedom of delay

.

We show that for all j - 0, ..., p - 1 and r - 0, ..., p - 1 fixed: ε ³ (u) is multiple of M such that ε ³ (u) - nM, if and only if u = aL - 1 (31) with a = (ln) p - (j + 2r), where l ≤ a ≤ 2p + 1 and not V (r), V (r) being an interval of Z defined by :

I ³ (32)

It is therefore possible to give an expression of the operator of the form:

where w ^a (j, r; n) - (\ - ή) M - (j + 2r) L - 1 and δ _u (x) (Kronecker symbol) such that:

Thus, for j and r fixed, according to the relation (32), the relative integer n can take only the values lying in the interval V (r). For example, if V (r) = {-1, 0}, we have:

and the diagonal indices u no

none to identify are then: u ^k (j, r; -l) = 2M - (j + 2r) L-1 and u ^k (j, r; 0) = M - (j + 2r) L -l

It will be noted in particular that if u = 2M - (j + Ir) L - 1, then

If we use the index u = k + 1 of numbering the 2 (M + L-Y) anti-diagonal portions in the expression (28) of the sub-blocks A ^ (z) of the conversion matrix, we then obtain:

Thus, in more generic terms, we consider each anti-diagonal portion of index u = k + 1 of a sub-block of matrix elements. If a given value

of this index u does not satisfy the condition (31) stated above (u = aL-1), all the elements of the anti-diagonal portion having this index value u are zero. This is a first condition noted as Cl.

FIG. 14 illustrates the shape of a sub-block A ^ (z) of elements a _M where, by way of purely illustrative example, only the portions of anti-diagonals whose indices u = k + l worth 3, 7 and 11 are non-zero. Note that these are complete anti-diagonal portions where the elements of the sub-block A ^ (z) are zero. As will also be seen in the other cases L = pM and K - pcm (L, M) below, there are still similar properties of zero antidiagonal portions. In the remainder of the talk, it will be pointed out, by misuse of language, that the subscript u is a "diagonal index" and we will speak of "null diagonals" to designate in fact anti-diagonal portions that are null as illustrated in Figure 14.

Other conditions still bear on these "diagonals" so that they are non-zero. Indeed, among the diagonals likely to have non-zero elements (hence for the values of the index u already verifying u = aL - \), two different situations are distinguished in particular according to the parity of the integer p.

It is shown that for all j - 0, ..., p - 1 fixed and two pairs of integers (r, n) and (r ', n) such that ε _r ^J (u) - nM and ε _r ^J , (u) - nM with r ≤ r ':

• if p is an odd integer, then necessarily r = r 'and n = n'. ;

• if p is an even integer such that p - 2p 'then necessarily r' - r + p 'and ri = n - l.

By the way, when the integer /? is even with p - 2p ', only the diagonals of indices u = aL - 1 where (a + j) is an even integer are likely to have nonzero elements. This is a second condition denoted C2 associated with the case p - 2p '.

When the integer p is odd with p - 2p '+ 1, only the diagonals of indices u = aL - 1 where (n -) + a + j is an even integer are likely to have nonzero elements. It is recalled that the relative integer n belongs to the interval V (r) defined above. This is a second condition denoted C'2, actually equivalent to condition C2 above but associated with the case p - 2p + 1. Indeed, this condition C'2 relates directly to the parity of the term (a + j) when the latter belongs to a well-identified interval among different successive intervals as explained in Table I below.

This table I expresses the elements of the diagonals which are non-zero, given for the case M - pL, keeping in mind that O ≤ r ≤ p '-1 to respect the two possible solutions (r, n) and (r + p ', n -l) (case p - 2p). In this table I, the notation "xe 2D" means that the element x is an even relative integer (positive or negative), and "xe 2D +1", that the element x is odd (positive or negative). The other elements of the sub-block A ^ (z) are null. It is recalled that the term "matrix elements" in the sub-blocks refers to transfer functions.

* Special case where L = pM

FIG. 6 represents the implementation of the conversion processing in the particular case where L = pM in a context of time varying filter banks (LPTV system).

Here, the delay variable is written:

where u is the diagonal index as previously defined u = k + 1 and such that 0 <u≤2 (L + MY).

It then appears properties similar to those presented for the previous case where M = pL.

Indeed, according to a first condition Cl, for all i = 0, ..., pl and for all m = 0, ..., pl, fixed:

with a = i-2m-np + 1, where l≤a≤2p + 1, and not V (m), where V (m) is an interval of Z defined by:

Moreover, for i = 0, ..., pl fixed, the two pairs of integers (m, n) and (m ¹ , ri) such that

are defined as follows:

• if p is an odd integer, then necessarily m = rri and n = ri,

• if p is an even integer such that p = 2p, then m = m + p 'and ri = n - 1. Finally, according to a second condition C2 or C'2, for i = 0, ..., p -l and a = 1, ..., 2p + 1 fixed, the equality, admits a solution if and only if,

• if p is even, (i- a) is odd.

• if p is odd, (n + a -i) is odd.

So: if p = 1p then (oc -i) must be odd for there to exist nonzero diagonals, according to the condition C2, and if p = 2p '+ l, then (n + a -i) must be odd so that the elements of the remaining diagonals are non-zero, and the condition C'2 thus bears on the parity of the term (a -i), according to its interval of belonging.

The non-zero expressions of the elements of a sub-block A '(z) satisfying the three possible conditions C1, C2 (and equivalent C'2) are then given in Table II below.

* Study of the general case where K = ppcm (L, M)

We are interested in studying the function of delay according to its general expression:

and detecting conditions on six integers i, j, r, m, k, l, conditions for which

We recall that K = ppcm (L, M) = p _γ M = p ₂ L, the notation "ppcm" denoting the smallest common multiple of L and M, and we then define an integer D such that D = pgcd (L , M), the notation "gcd" denoting the largest common divisor of L and

M We then have the following property M - p ₂ D and L - p ₁ D, p ₁ and p ₂ being prime between them.

We still note u the diagonal index such that u-k + l. The indices of lines k and columns / are such that 0 ≤ k ≤ 2M -1 and 0≤l≤2L-1. Thus, the index u is such that 0 <u≤2 (M + L-1).

We show that: - for all i and all m such that 0 ≤ i, m ≤ P ₁ - 1,

for every j and r such that 0 <j, r≤p ₂ -l, there is, according to a first condition Cl:

with αεZ such that: a = (l-np _ι - (2m-i)) p ₂ - (2r + j) p _ι where l≤ a ≤ 2 {p _γ + p ₂ ) -l

Moreover, for i and j fixed, the admissible integer values of n are such that " _mn ≤" _mn (U j) ≤n≤n _max (U j) ≤ 0, where we note:

" _Mn (U j) = -4 + [(/ + IVp ₁ - JIp ₂ + Vp ₁ P ₂ ]," _πim = -5 + [l / A + Vp ₂ + Vp ₁ P ₂ ] H _^ (Uj) = [Q- + ^I ) Ip ₁ - JIp ₂ ] the notation [je] denoting the integer part of x. We also show that:

- for i and m fixed such that 0 ≤ i, m ≤ p _γ - 1,

- forj and r fixed such that 0 <j, r≤p ₂ -l

with: a- {l-np ₁ - (2m-i)) p ₂ - (2r + j) p ₁ where l≤α ≤2 (/? ₁ + p ₂ ) -l

The bounds of the interval n _imn (i, j, r, m) and n _miiX (i, j, r, m) are determined by

Another condition is the function of delay. When i, j are fixed and for a diagonal index determined by the term a, we try to determine the condition on indices r and m which lead to integer values nK.

Indeed, for i, j and a fixed, one supposes the existence of two triplets of integers (n, m, r) and (n ', m', r ') which verify the equalities

, and one then establishes properties on the two triplets (n, m, r) and (n ', m', r ^f ) which are useful for the development of a simplified expression of the elements of

. Indeed, by fixing:

a value of the diagonal index u such that (with

U = CiD - I), we show that for two triplets of integers (n, m, r) and (n ', m', r ') such that

and

(with r ≤ r 'and m ≤ m'):

• if P ₁ P ₂ is odd then necessarily n = ri, m = m 'and r = r', but

• if P ₁ P ₂ is even and: o if P ₁ = 2p \ is even while p ₂ is odd, then n = n - 1, m = m + p \ and r = /, and o if p ₂ = 2p ' ₂ is even while p _γ is odd, then n' = n - 1, m '= m and r' = r ₊ p ' ₂ .

Remember that p _γ and /? ₂ are first between them and therefore can not be both peers at the same time. Another condition C2 relates to the diagonal indices where the delay function takes an integer value, when AA _> is even, according to the parity of the integers p _γ and p ₂ . Indeed, by fixing i <≡ Dθ, P ₁ - lD and y <≡ Dθ, P ₂ -IU, for every m <≡ Dθ, p _γ - lD and for all r <≡ Dθ, p ₂ - lD, we shows the following conditions on the parameter a:

If P ₁ = 2p \ and p ₂ is odd, then (ia) is odd,

• if p ₂ - Ip ' ₂ and P ₁ is odd, then (j + a) is even.

Another condition relates to the bounds of the relative integer n. Indeed, by fixing / e Dθ, P ₁ - lD, y <≡ Dθ, / ^ ₂ - lD and «<≡ Ql, 2 (A + p ₂ ) - lQ, we show that the values of n such that ε _m ^{ι J} _r (uj) = nK satisfy the inequality: N _101n (i, j; a) ≤ n ≤ N _max (i, j; a), where the integer bounds N ^ iJ; a) and N _miiX (i, j; a) are determined by:

N _mn (i, y; α) = -4 + [2 ( _Pl + p ₂ ) 1 P _i p ₂ + B (i, f, a) 1 P _i p ₂ ], N _max (i, j; a) - [B (i, f, a) 1 P _^ p ₂ ] and we denote B (i, j; a) such that: B (i, j; a) - (i + \) p ₂ - Jp ₁ - a.

Thus, for the general case K - ppcm (M, L), an expression of the delay operator is given by:

with M ^a (i, j, m, r; n) = ((I - np _x - (2m - i)) p ₂ - (2r + y) A) D -1 For a quadruplet (i, j, m , r) set, the interval V _m ^J _r is then completely defined. For example if n ₀ and n _γ are the only two integers included in V ^ ₁ , then

Therefore, only the diagonal index can vary in this equality. The use of the Kronecker symbol δ _u makes it possible to detect the positions of the diagonals which are the solutions associated with the two admissible values n ₀ and n _γ . As a result, it is possible to construct sub-blocks A ' _} (z) from the following general expression:

Thus, the sub-block elements, in the general case K = ppcm (M, L), can be determined as follows.

We fix i and j (subsystem numbers) and matrix indices u of diagonal and / of column number. For any index, m - 0, ..., P ₁ -1 and for all r - 0, ..., p ₂ - \: we determine the two bounds of the set,

the solutions u ^* (i, j, m, r \ ή) are determined for each admissible integer value, in the interval

,

when the diagonal index is such that u = u ^* (i, j, m, r, n) then the term: (-i) ^{m + r} z ⁿ G _{k> m} ((-i) is evaluated ^Λ z ² ) κ _{ι> r} ((-i) ^p * z ² )

The index r is then incremented, then the index m, and the non-null terms identified in the double summations on m and r of the expression (41) are added.

Non-zero expressions of sub-block elements are given in the

Table III below, for 1 - 0, ..., P ₁ -I, j - 0, ..., p ₂ -1. The other diagonal elements are null.

By way of illustrative example, considering practical cases of application of the conversion between subband domains for the case, for example, of transcoding between a standardized coding G.722.1 and a standard coding MPEG-2/4 AAC, one a, according to condition (39):

In short window, p _γ = 2 and p ₂ = 5, so that n _mn = -5,

• in long window, p _γ = 16 and p ₂ = 5, so that n _mn = -5.

For the case of transcoding between a G.722.1 encoding and a Dolby AC-3 encoding, we have:

In short window, p _γ = 2 and p ₂ = 5, so that n _mn = -5, and

• in long window, p _γ = 4 and p ₂ = 5, so that H _101n = -5, again. Thus, in these two cases of transcoding application, the admissible values of n are always included in the entire interval

It should be noted that the precise expressions of the matrix elements

can also be expressed in terms of the direct polyphase components of the prototype filters. For example, in the case M = pL, by noting 5 ' ₀ (z), ..., 5' _2M _ ₁ (z) the 2M components of the type 1M 2M polyphase decomposition of the synthesis prototype filter F _p (z),

with

since K = M = pL, we have here K _{I r} (z) = S _{2rL + ι} (z), for all / = 0, ..., 2L - 1 and for all r = 0, ..., p -l. The elements of a sub-block are then given by:

where n _h is such that N _h - 2n _h M, - the values of the indices r and n being determined by those fixed of the index j and the diagonal index u such that r = ((I - n) p - (a + j)) 12, with u - aL-1;

where S represent the polyphase components of order M (and

no longer 2M) of type 1 of the prototype filter F _p (z), the values of the indices r and n being further determined by those fixed by the sub-block index j and the diagonal index u such that: 0 <r = (ln) p '- (a + j) / 2 ≤ p' -l.

Similarly, for the case L = pM, from the 2L components (denoted R ₀ (Z), ..., R _21-1 (Z)) of the type 1L 2L polyphase decomposition of the prototype filter d 'analysis H _p (z), with:

where the integer n _h is such that N _h - 2n _h L, since K - L - pM here, we have: G _{k, m} ( ^z ) ^~ R _{≥mM + k} ( ^z ) for all £ = 0 _,. .., 2M -l and for all m = 0, ..., /? -l, and the calculation of the sub-block elements A '(z) is determined by the following relations:

- (A [(z)) _ur K ₁ ^ z ² X-IT R ^^ iz ^ z "(46)

where n _f such that N ₇ = 2n _f L,

- the values of m and n are determined by those of the index i of the subsystem and the index u of the diagonal such that m = ((I - n) p + (i + 1 - α)) / 2 , and - (A [(z)) _ur K ₁ CZ ² X-Ir R ₂ ' _{mM + u} _ _ι ((-iy ^' z) z ⁿ (47)

- wherein R ₀ (z), ..., R ¹ ₁ (Z) are the polyphase components of order L type 1 of the prototype filter H _p (z),

the values of m and n are determined by those fixed of the index / subsystem and the index u of the diagonal such that 0 <m = (ln) p '- (i + la) / 2 ≤ p '-l.

Construction of the conversion matrix T '(z)

Advantageously, the conversion matrix T '(z) may be pre-constructed, offline, before it is implemented in a transcoding system, or else encoding or decoding including a cascade of filterbanks.

As illustrated in FIG. 15A, in step S1, it will be determined whether there exists a particular relationship between the integers M and L. For example if M = pL (arrow o at the output of the test

TlO), according to the first case described above, only the diagonals of indices u such that u = aL-1 (test T1) are non-zero. A first set of zero element diagonals is already identified in step S 12 at output n of TI test 1 of FIG. 15A. Among the potentially nonzero diagonals (output o of the TI test l), we study the parity of the integer /? (T13 test). If the integer /? is even (test T13 output o), only the diagonals whose index is such that a + j is even (test T14) are non-zero (output o of test T14) and the other diagonals (output n of test T14) are zero (step S 12). The non-zero elements can then be given in step S16 by the relationships expressed in Table I above. These relationships may be initially stored in a computer memory as instructions of a computer program (step S17). If the integer /? is odd (output n of the test T13), only the diagonals whose index satisfies the condition C'2 on the parity of the term a + j according to the intervals in which it is situated (test T15) are non-zero (output o of the T15 test) and their elements can then be given in step S 16 by the relationships expressed in Table I above. The other diagonals are zero (output n of test T15 to step S 12).

The test T15 illustrated in FIG. 15A has been detailed in FIG. 16A. It is actually a test battery T151 to T155 for locating the term a + j in one of the possible intervals: (test T151 ), in which case a + j must be odd (test T153) so that

diagonals can be non-zero,

-

(test T152), in which case a + j must be odd (test T153) so that diagonals can be nonzero,

-

(test T154), in which case a + j must be even (test T156) so that diagonals can be non-zero, and -

(test T155), in which case a + j must be even (test T156) so that diagonals can be non-zero.

In practice, the T155 test does not need to be executed because it is actually the only remaining possible interval at the sum a + j after the previous series of tests. Referring now to FIG. 15B, if L = pM (arrow o at the output of the T20 test), according to the second case described above, only the diagonals with indices u such that u = aM - \ (test T21) are not zero. We already identify a first set of diagonals of elements all nil at step S22 at output n of test T21. Among the potentially nonzero diagonals (output o of the T21 test), the parity of the integer /? (T23 test). If the integer /? is even (only the output o of the test T23), only the diagonals whose index is such that a -i is odd are non-zero (output o of the test T24) and the other diagonals (output n of the test T24) are zero (step S22). The non-zero elements can then be given in step S26 by the relationships expressed in Table II above. These relationships may again be stored initially in a computer memory as instructions of a computer program (step S27). If the integer /? is odd (output n of the test T23), only the diagonals whose index satisfies the condition C 2 on the parity of the term a -i are non-zero (output o of the test T25) and their elements can then be given to the step S26 by the relations expressed in table IL The other diagonals are zero (output n of test T25 to step S22).

The test T25 shown in FIG. 15B is detailed in FIG. 16B. This is again a battery of tests T251 to T255 to locate the term ia in one of the possible intervals: -

(test T251), in which case ia must be odd (test T253) so that diagonals can be non-zero,

-

(test T252), in which case ia must be odd (test T253) so that diagonals can be non-zero,

-

(test T254), in which case i -a must be even (test T256) so that diagonals can be non-zero, and

-

(test T255), in which case i - a must be even (test T256) so that diagonals can be nonzero.

Again, the T255 test does not need to be performed in practice because it is actually the only possible interval remaining unlike i - a after the previous series of tests. Referring now to FIG. 15C, apart from the cases M = pL and L = pM (arrows n at the output of tests T10 and T20), according to the third case, general, described above, only the diagonals with indices u such as that u - aD -l (test T31) are non-zero (with D = gcd (Z, M)). We already identify a first set of diagonals of elements all nil in step S32 at output n of test T31. Among the potentially non-zero diagonals (output o of the T31 test), we also study the product parity pφx (T33 test). If this product is odd (output n of the test T33), only the diagonals such as the equation E: 2mp ₂ + 2rp _ι = (i + Y) P ₂ -Jp ₁ - a -np _γ p ₂ admits a (and a single) triplet (m, r, n) as solution (T34 test), with:

- m, r ti n integers and included respectively between 0 and P ₁ -I, between 0 and p ₂ -1, and between

N _101n (I, j; a) and _Nmax (i, j; a) are non-zero (T34 test output o) and the other diagonals (T34 test output n) are zero (step S32). The non-zero elements can then be given in step S35 by the relationships expressed in Table III above. These relationships may again be stored initially in a computer memory as instructions of a computer program (step S37).

If the product pφ2 is even (output o of the test T33) and, in particular, if the integer p \ is even (output o of the test T37), only the diagonals such as the equation E:

2mp ₂ + 2rp _ï = (i + Y) P ₂ -Jp ₁ - Cc -Hp ₁ P ₂ admits one (and only one) triplet (m, r, n) as solution (test T38), this time:

- m, r and n integers and included respectively between 0 and p \ -l (with P ₁ - 2p \), between 0 and / 7 ₂ -l, and between N _^ JiJ; a) and N _m Ji, j; a) are non-zero (output o of the test T38) and the other diagonals (output n of the test T38) are zero (step S32). The non-zero elements can then be given in step S35 by the relationships expressed in Table III.

If the product P ₁ P ₂ is even (output o of the test T33) and, in particular, the integer p ₂ is now pair (output n of the test T37), only the diagonals such as the equation E: 2mp ₂ + 2rp _γ = (i + Y) P ₂ -Jp ₁ - U - Up ₁ P ₂ admits one (and only one) triplet {m, r, n) as solution (T40 test), this time:

- m, r and n integers and respectively between 0 and P ₁ -I, between 0 and p \ - \ (by defining p ₂ = 2p \ at step S39), and between N _{^ n} (I, j; a) and N _max (i, j; a), are non-zero (output o of the test T40) and the other diagonals (output n of the test T40) are zero (step S32). The non-zero elements may be further given in step S35 by the relationships expressed in Table III.

Advantageously, it is possible to provide a first computer program comprising instructions for determining the elements of the conversion matrix T '(z) as described above. Typically, the algorithm corresponding to this first program may have an overall flowchart corresponding to all of FIGS. 15A to 15C described above. In this respect, the present invention also aims at this first computer program. It also relates to a device comprising a memory on which this first program is stored, the device then comprising a processor for executing the instructions of the first program.

Detailed description of an example embodiment

An example of application of the invention to a transcoding where M-pL, for example in the context of a conversion of a type MPEG-1/2 (Layer I & II) coding is described below in detail. to Dolby AC-3 encoding.

The input subband domain is defined by the characteristics of a so-called "pseudo-QMF" filter bank, for which L = 32, and the output subband domain is defined by the characteristics of an MLT overlay transform (for "Modulated Lapped Transform"), involving two types of coding window:

a short window, for which M = 128, and

a long window for which M = 256.

a) Case of transcoding to the short window M = 128

Here, the relation M - pL is verified with /? = 4 (remembering that £ = 32), so that /? is even with p - 2p where p '- 2. The values of the lengths n _f and n _h of the polyphase components of order 2M of the prototype filters are such that n _h - 1 and n _f - 2.

The length of the synthetic prototype filter F _p (z) is N _f - 5l2. The length of the components S ₁ (Z) of the polyphase decomposition according to the relation (42), of order 2M = 256, of F _p (z), is such that 2n _f M = 512, hence n _f = 2. The length of the prototype filter H _p (z) of the MDCT transform is N _h - 2M, hence n _h - 1.

It appears here that with n _f - n _h + 1 = 2 and p - 4 (and p '= 2), the computation of the elements of the sub-blocks A! _} (z) is as follows:

(A; (z)) = (-iγh _p (u-1) z "{f _p (2rL + 1) + f _p (M + 2 ₊ 1) Z- ¹ 2 -W

+ / (2Af + 2rL + 1) z ^{~ 2} + f (3M + 2rL + 1) z

The expression of the elements of the sub-blocks A _j '(z) can be detailed by interval slices of the term (a + j) as presented in Table I above.

It appears especially that the indices r = 0, ..., p '-l and j = O, ..., p -l modify the general expression and the position of the transfer functions (nonzero) constituting the elements of matrices A ^ (z). On the one hand, for j = 0, ..., 3:

- if j is even, only the diagonals u = (2L -1), (4L -1), (6L -1), (SL -I) are non-zero and the number of elements on each diagonal is IL, - if j is odd, only the diagonals u = (L - 1), (3L - 1), (5 L - 1), (IL - 1), (9L - 1) are nonzero and the number of elements present on the extreme diagonals is L, while the diagonals u = (3L-1), (5L-1), 7L-1) each have 2L elements. On the other hand, we have r - 0 or r - 1 and because of this, we must distinguish expressions from the form,

Thus, the parity of the index j determines the position of the nonzero diagonals and the value of the index r determines the number 2rL + 1 of the polyphase component of the synthetic prototype filter S ₂ ' _{rL + ι} (z).

It can then be proposed a particularly advantageous implementation scheme by distinguishing the treatment characteristics according to the parity of the index j of the component

, and distinguishing also the operations defined by the components

of the synthesis prototype filter of those defined by the components G ₀ ,..., G _2M _ _X (z) of the prototype analysis filter.

For this purpose, we define four filter matrices, t _y (z), 0 ≤ j <3, each of dimension

2Lx 2L, defined as follows: - for an index j - 0.2 pair, we put:

and for an odd j - 1.3 index, we put:

Here we denote w ^ (z) intermediate vectors at the output of the sub-blocks, such as

than :

Referring to Figure 7 which illustrates the operations performed by the subsystems

of even index (respectively and in Figure 8 which illustrates the operations performed by subsystems A of odd index (respectively

, for a fixed index j, the vector of the signals in sub-bands

is distributed as input to two parallel channels, defined respectively by: - t _o (z), I ₁ (Z) for the case where j is even, and by t ₂ (z), t ₃ (z) for the case where j is odd.

Each channel outputs two vectors each having IL coefficients. A delay z ^"1 is applied to one of the two vectors as shown in Figures 7 and 8 and finally, the four vectors thus delivered are concatenated to reach the dimension 2χ 2χ 2L = 2M.Thus, the transmission channels are subdivided. , create delays on each vector and finally concatenate these vectors Then the vectors of dimension 2M are all multiplied by the window h _p (n) of the prototype analysis filter.

The only difference in treatment between the cases j = 0 and / = 2 (or else between y = 1 and y = 3) is therefore at the level of the concatenation with interleaving upstream of the multiplication by the window h _p (n). Thus, for the case where j is even (odd), it is possible to use only one two-channel filter system, characterized by the simple matrices called "anti-diagonal s" t _o (z) and t _: (z)

(respectively t ₂ (z) and t ₃ (z)). Indeed, these matrices t _o (z) to t ₃ (z) are particularly simple to handle, since they contain only a few non-zero elements (on anti-diagonals), so that, for example, the multiplication of a vector by such a matrix involves only one multiplication to calculate each coefficient of the product vector.

In addition, only two types of concatenation with delay can be provided. In FIG. 9, the diagram (A) illustrates the concatenation with delay occurring at the output of the sub-blocks and the diagram (B) illustrates the concatenation with delay.

at the output of the sub-blocks

. The concatenation resulting from the delay chain (C) is then equivalent to the delay concatenation of the scheme (A): it is a two-channel inversion (with a delay z ^"1 ) followed by the concatenation with delay according to the scheme (B).

With reference to FIG. 10 illustrating the heart of the conversion system, finally, the vector of the coefficients v '(z) in sub-bands, at the output of the conversion, is the simple result of the following overlay addition operation:

Judiciously: - the concatenation chain (B) is pooled for all the subsystems (just before the concatenation), - and so, only one multiplication by the window h _p (n) is expected after the operation of addition with overlap.

Table IV below compares the number of operations (additions and multiplications) necessary for the production of a vector of 2M coefficients Y (n) at the output of the conversion by transcoding:

in the case of a direct implementation as illustrated in FIG. 5, and

in the case of an improved implementation as illustrated in FIG.

Table IV

b) Transcoding case to the long window M = 256

Here, the relation M - pL is still verified with /? = 8 (remembering that £ = 32), so that /? is even with p = 2p where p - 4. The values of the lengths n _f and n _h of the polyphase components of order 2M of the prototype filters are such that n _h - 1 and n _f - 1.

It then appears that with n _f - n _h = 1 and p - S, the computation of the elements of the sub-blocks

is as follows:

We can express again the sub-blocks

according to simple matrices, according to the parity of the index /

For j - 0,2,4,6 pairs, we give:

For j = 1,3,5,7 odd numbers, we give:

Given the high number (p = S) of subsystems involved in the conversion, simplified notations are proposed below to represent the treatments associated with anti-diagonal matrices st _o (z), ..., t ₇ (z). As a result, as illustrated in FIG. 11, the two subsystems t _u (z), t _v (z) that will be useful for the implementation of the heart of the conversion are defined as follows:

the subsystem t _u (z) processes the subband signals of even subscripts and

the subsystem t _v (z) processes the subband signals with odd indices. The subband signals u ^ (z) are vectors of dimension coefficients IL. At the output of the matrix t _u (z) or of the matrix t _v (z), filtered coefficient signals of dimension 4x 2L = M are obtained. The connection lines represented in dotted in FIG. 11 mean that it is the parallel transmission of four vectors comprising 2L coefficients (4χ 2Z = 2M output coefficients).

In addition, advantageously defines four different processing channels, denoted Σ _A, Σ _B Σ _C Σ _D and illustrated by the equivalence shown in Figure 12. The chain

Σ _D admits M-dimensional signal vectors as input and outputs vectors of dimension coefficients 2M. The chains Σ _A , Σ _B , Σ _C admit vectors of coefficients of dimension M and transmit vectors of dimension M as well.

By a complete study of the operations carried out by the sub-systems A ^ (z) characterized by the transfer functions previously expressed, it is proposed in FIG. 13 a preferred implementation of the core of the conversion between subband domains.

The main advantage of the implementation shown in this figure 13 is that:

- each subsystem A ^ (z) of initial dimensions 2M χ 2L is reduced by a factor

2 in number of lines, to finally obtain simple systems t _u (z) and t _v (z) with 4 channels, of dimensions M x 2L; - It is implemented only one multiplication by the weighting window h _p (n) of the prototype analysis filter (shared here too);

the addition is carried out on vectors of dimension M.

By comparing the complexity of the core of the conversion system according to a direct implementation in the sense of FIG. 5 (with even the identification of identically zero filter elements) and that corresponding to the implementation illustrated in FIG. advantageously obtains the results indicated in Table V below, to produce a vector of 2M = 512 coefficients v '(n) at the output of the conversion core.

Table V

Thus, it follows from the foregoing that, at least in the case M = pL with /? peer such that p - 2p, each component resulting from a polyphase decomposition of order /?

an input vector M '(Z), modulated (and therefore resulting from step a) of the process in the sense of the invention), with y between 0 and /? - 1, is multiplied by each matrix d a set of elementary matrices (references t _u (z) and t _v (z) of FIGS. 11 and 13).

Advantageously, only two sets of elementary matrices are provided, one or the other of these two games being chosen simply according to the parity of the indexy. Furthermore, each elementary matrix has only one non-zero element per line and / or column.

Then, in general, permutations, delays z, summations and multiplications, chosen, are applied to the results of the products of the components by these

elementary matrices, to obtain p sub-vectors. These p sub-vectors are then grouped by concatenation in order to preferentially apply them to a modulation by a window of the prototype filter of the analysis filter bank h _p (0),.

A _p (2Af -I).

Finally, a vector v '(z) is obtained, to which the matrix of modulation C _h of the analysis filter bank to deliver the output vector of the system, referenced Y (z) in Figure 5 and corresponding to the "second vector" obtained after step c) according to the generic terminology used ci for the definition of the present invention.

Advantageously, the permutations, delays z ¹ , summations and multiplications are optimized to minimize the number of computations occurring before the concatenation grouping.

Advantageously, it is possible to provide a second computer program comprising instructions for performing the conversion calculations between subband domains themselves. Typically, the algorithm corresponding to this second program may have a corresponding global flowchart, for example in the case of the MPEG-1/2 (LI & II) to Dolby-AC3 conversion, in FIGS. 10 (for a short window) and 13 ( for a long window), and more generally (in other cases of conversion in particular) to one of FIGS. 4 to 6.

In this respect, the present invention also aims at this second computer program. It also relates to a conversion device between different subband domains, for example for transcoding, or else coding or decoding involving a cascade of filter banks (such as those defined in the MPEG AAC + SBR standard, called also "HE-AAC", MPEG Surround or MPEG Enhanced Low Delay AAC) having a memory in which this second program is stored, the transcoding device then comprising a processor for executing the instructions of the second program.

Of course, the present invention is not limited to the embodiments described above; it extends to other variants. For example, it appears in the treatment described above that the nature of the modulation transforms (cosine, sine, or other) does not influence the determination of the conversion matrix T '(z). Therefore, the treatment in the sense of the invention applies to any type of transform (cosine, sine, or other).

Moreover, the advantages obtained in the case of a conversion from MPEG-1/2 (LI & II) coding to Dolby AC-3 coding are linked, as we have seen, only to the fact that There is an advantageous relationship between the coefficients L and M and in no way to the very nature of the codings. It will therefore be understood that these advantageous results are directly transferable to any other type of conversion to transforms where L and M satisfy the same relations.

Claims

A method implemented by computer resources for processing data by passing between different subband domains, consisting in compacting in the same process the application of a first vector (X (z)) having a first number L of respective subband components, to a synthesis filterbank, then to an analysis filter bank, to obtain a second vector (Y (z)) having a second number of respective subband M components, the method being of the type comprising the following steps, after determining a third number K, the least common multiple between the first number L and the second number M: a) if the third number K is different from the first number L, setting blocks by serial / parallel conversion of the first vector to obtain p ₂ polyphase component vectors, with p ₂ - K / L, b) application of a chosen matrix filtering, involving a conversion matrix, square and of dimensions 2K x 2K, to said p ₂ polyphase component vectors to obtain p _γ polyphase component vectors of the second vector, with

characterized in that said bank of synthesis filters and said bank of analysis filters implement modulated transforms and each result from the modulation of a prototype filter by a modulation matrix, and in that: - before step a), the first vector (X (z)) is first applied to the transpose of the modulation matrix (D ^) of the synthesis filter bank, after step c), the second vector (Y (z)) results from the application of the modulation matrix (C _h ) of the analysis filter bank, and said square matrix T '(z) is expressed as a function of:

2. Method according to claim 1, characterized in that it comprises a preliminary step of off-line construction of said conversion matrix T '(z), in that said conversion matrix T' (z) includes sub-blocks

each comprising at least portions of anti-diagonals of null elements, and in that, at the previous step, one searches in each sub-block at least

a portion of remaining anti-diagonal with at least some of the elements are non-zero.

3. The method according to claim 2, wherein the second number L is a multiple of the first number M (M = pL), characterized in that the conversion matrix comprises

P = M IL sub-blocks, with j between 0 and p -1, each of dimensions

2M x IL, and in that, for each sub-block A ^ (z), we search for anti-diagonal portions whose index u = k + 1, where k is a line index and / is a subscript column of the sub-block, check a relation of type: u = aL - \ (TU), where a is an integer

between 1 and 2/7 + 1, these anti-diagonal portions being the only ones likely to comprise non-zero elements.

4. Method according to claim 3, characterized in that, if the integer p = MIL is even such that p = 2p '(T13), we search for anti-diagonal portions of index u = aL -1 where the integer a is such that the sum a + j is an even integer (T14), these portions of anti-diagonals being the only ones likely to comprise non-zero elements, and in that the non-zero elements of a sub-block A are given

(S16, S17) by:

where: - z ^x is an advance or a delay according to the sign of x,

G _x is a component of index x, for a polyphase decomposition of order 2M, of the prototype filter of the analysis bench, and

K _xy is a component of index j, for a polyphase decomposition of order p, of the index component x, for a polyphase decomposition of order 2L, of the prototype filter of the synthesis bench.

5. Method according to claim 3, characterized in that if the integer p = MIL is odd such that p = 2p '+ 1, the parity of the sum a + j is taken into account according to different intervals in which may be situated this sum a + j (T 15), to search for portions of anti-diagonals that may contain non-zero elements, and in that the non-zero elements of a sub-block are given

(S16, S17) by:

or: z ^x is an advance or a delay according to the sign of x,

K _xy is a component of index y, for a polyphase decomposition of order p, of the index component x, for a polyphase decomposition of order IL, of the prototype filter of the synthesis bench, the notation means that the sum a + j is a pair, and the notation

+ 1 means that the sum a + j is odd.

6. The method according to claim 2, wherein the first number M is a multiple of the second number L (L - pM), characterized in that the conversion matrix comprises p = LIM sub-blocks.

, with i between 0 and p -1, each of dimensions 2M x IL, and in that for each sub-block

, we look for the portions of anti-diagonals whose index u = k + l, where k is a line index and / is a column index of the sub-block

, check a relation of the type: u = aM -1 (T21), where a is an integer between 1 and 2/7 + 1, these portions of anti-diagonals being the only ones likely to comprise non-zero elements.

7. Method according to claim 6, characterized in that if the integer p = LI M is even such that p = 2p '(T23), one looks for the anti-diagonal portions of index u = aM - 1 where the integer a is such that the sum a -i is an odd relative integer (T24), these anti-diagonal portions being the only ones likely to comprise non-zero elements, and in that the non-zero elements of a sub-block are given

(S26, S27) by:

where: z ^x is an advance or a delay according to the sign of x,

G _Xιy is a component of index y, for a polyphase decomposition of order p, of the index component x, for a polyphase decomposition of order 2M, of the prototype filter of the analysis bench, and

K _x is a component of index x, for a polyphase decomposition of order IL, of the prototype filter of the synthesis bench.

8. Process according to claim 6, characterized in that if the integer p = LIM is odd such that p = 2p '+ 1, the parity of the difference i -a is taken into account at different intervals in which it can be situated. this difference i - a (T25) to identify portions of anti-diagonals alone likely to comprise non-zero elements, and in that the non-zero elements of a sub-block are given

(S26, S27) by:

or: z ^x is an advance or a delay according to the sign of x,

G _Xι y is a component of index y, for a polyphase decomposition of order p, of the index component x, for a polyphase decomposition of order 2M, of the prototype filter of the analysis bench, and

K _x is a component of index x, for a polyphase decomposition of order IL, of the prototype filter of the synthesis bench the notation means that the difference i - a is pair, and the notation

+ 1 means that the difference i - a is odd.

The method of claim 2, wherein the first number M and the second number L are not multiples of one another, so that it can be defined:

- two integers p _\ and p ₂ , prime between them and such that the third number K satisfies the relations K - p _γ M - p ₂ L,

- and a fourth number D largest common divisor of the numbers L and M and satisfying the relations M - p ₂ D and L - P ₁ D, characterized in that the conversion matrix comprises p _γ p ₂ sub-blocks, with i

between 0 and P ₁ -I and j between 0 and p ₂ - 1, each of dimensions 2M x IL, and in that for each sub-block, the anti-diagonal portions are sought.

whose index u = k + l, where k is a line index and / is a column index of the sub-block

, verify a relation of the type: u = aD -1 (T31), where a is an integer between 1 and 2 ^ p ₁ + p ₂ ) -l, these anti-diagonal portions being the only ones likely to contain non-zero elements.

10. Method according to claim 9, characterized in that it determines whether the product pφ ₂ is even or odd (T33) and, if the product pφ ₂ is even, it is determined:

if the integer /? i is even while the integer p ₂ is odd (T37), or

if the integer /? i is odd while the integer p ₂ is even (S39).

11. The method of claim 10, wherein the product pφ ₂ is odd, characterized in that one seeks the portions of anti-diagonals of index u such that u = aD - \, with the integer a verifying a relation of the type 2mp ₂ + 2rp _γ = (i + 1) p ₂ -Jp ₁ - U - Up ₁ P ₂ and such that this equation admits a triplet

{m, r, n) as a solution (T34), these portions of anti-diagonals being the only ones likely to comprise non-zero elements, with:

m and r are integers and respectively between 0 and P ₁ -I and 0 and p ₂ -l,

and n a relative integer between:

N _^ (U j; a) = -4 + [2 ( _Pl + P ₂ ) Zp ₁ P ₂ + B (i, j; a) / _Pl p ₂ ] and N _max (i, j; a) = [ B (i, j; a) / _Pl p ₂ where B {i, j; a) = (i + 1) P ₂ -Jp ₁ -a, and in that the non-zero elements (A ' ₇ (z) ) of a sub-block A ' ₇ (z) are expressed by

a relation of the type (S35, S36), where:

- z ^x is an advance or a delay according to the sign of x, G _x ^ is a component of index y, for a polyphase decomposition of order P ₁ , of the index component x, for a polyphase decomposition of order 2M, of the prototype filter of the analysis bench, and K _xy is a component of index j, for a polyphase decomposition i of order p ₂ , of the index component x, for a polyphase decomposition of order IL, of the prototype filter of the synthesis bench.

12. The method of claim 10, wherein the product pφi is even, the integer p \ being even with, while the integer p ₂ is odd,

characterized in that the anti-diagonal portions of index u are searched such that u = aD - \, with the integer a satisfying a relation of the type 2mp ₂ + 2rp _γ = (i + V) P ₂ -Jp ₁ - Cc - np _γ p ₂ and such that this equation admits a triplet

(m, r, n) as solution (T38), these portions of anti-diagonals being the only ones likely to comprise non-zero elements, with: - m ti r integers and understood respectively between 0 and

and 0 and p ₂ - \, - and n a relative integer between:

N _101n (UjIa) = -4 + [2 (P ₁ + P ₂ ) Zp ₁ P ₂ + B (i, JIa) Zp ₁ P ₂ ] and N _max (i, f, a) = [B (U a) Ip ₁ P ₂ where B (i, j; u) = (i + 1) p ₂ - Jp ₁ -a, and in that the non-zero elements (A '_{> y} (z)) of a sub -block A '_{> y} (z) are expressed by

a relationship of the type

(S35, S36), where:

- z ^x is an advance or a delay according to the sign of x,

G _{x ^ y} is a component of index y, for a polyphase decomposition of order p _γ , of the component of index x, for a polyphase decomposition of order 2M, of the prototype filter of the analysis bench, and

K _xy is a component of index j, for a polyphase decomposition of order p ₂ , of the component of index x, for a decompositions polyphase order IL, the prototype filter of the synthesis bench.

13. The method of claim 10, wherein the product pφ ₂ is even, the integer p _x being odd, while the integer p ₂ is even with p ₂ - 2p ' ₂ (S39), characterized in that we look for the anti-diagonal portions of index u such that u = aD-1, with the integer a satisfying a relation of the type 2mp ₂ + 2rp ₁ = (i + I) p ₂ -jp ₁ - a - Up ₁ P ₂ and such that this equation admits a triplet

{m, r, n) as a solution (T40), these anti-diagonal portions being the only ones likely to comprise non-zero elements, with: m and r being integers and included respectively between 0 and P ₁ -I and 0 and p ₂ '-l, - and n a relative integer between:

## _EQU1 ## where _n = 1 + 2 ( _{P 1} + P ₂ ) Zp ₁ P ₂ + B (i, j; a) / _P p ₂ ] and N _max {i, j; a) = [ B (i, j; a) / _Pl p ₂ where B (i, j; ά) = (i + 1) P ₂ -Jp ₁ -a, and in that the non-zero elements of a sub-block express by

a relationship of the type: where:

- z ^x is an advance or a delay according to the sign of x,

K _xy is a component of index j, for a polyphase decomposition of order p ₂ , of the component of index x, for a polyphase decomposition of order IL, of the prototype filter of the synthesis bench.

14. Method according to one of the preceding claims, wherein the second number L is a multiple of the first number M so that M = pL with /? pair such that p = 2p ', characterized in that: each component resulting from a polyphase decomposition of order p of a

input vector u '[z), modulated and resulting from step a), with y between 0 and /? - 1, is multiplied by each matrix of a set of p elementary matrices (t _u (z) t _v (z)) comprising only one non-zero element per row and / or column, said set being chosen according to the parity of the index y,

- We apply permutations, delays (z ¹ ), summations and gear ratios, chosen, the results of the products of the components u _} (z) by said elementary matrices, to obtain p sub-vectors, we group by concatenation said p sub-vectors , then the grouping is modulated by a window of the prototype filter of the analysis filter bank

(h _p (0), ..., h _p [IM-1)), to obtain a vector (v '(z)) intended to be applied to the modulation matrix (C _h ) of the filter bank of analyzing to deliver said second vector (Y (z)) after step c).

15. The method of claim 14, characterized in that the permutations, delays (z ¹ ), summations and gear ratios are optimized to minimize a number of calculations before grouping by concatenation.

16. Computer program for calculating a conversion matrix by passing between different subband domains, intended to be stored in a memory of a computing device, characterized in that it comprises instructions for the implementation of method according to one of claims 2 to 15, when they are executed by a processor of the computing device.

17. A computing device, characterized in that it comprises a memory in which is stored a computer program according to claim 16, for delivering elements of a conversion matrix by passing between different subband domains.

Computer program, intended to be stored in a memory of a conversion device between different subband domains, characterized in that it comprises instructions for implementing the method according to one of claims 1, 14 and 15, when executed by a processor of said transcoding device.

19. Device for conversion between different subband domains, characterized in that it comprises a memory in which is stored a computer program according to claim 18.