Data processing method by passage between different sub-band domains

• US 20090198753A1
• Filed: 08/23/2005
• Published: 08/06/2009
• Est. Priority Date: 09/16/2004
• Status: Active Grant

• Current Assignee: Orange S.A.
• Original Assignee: Orange S.A.
• Inventors: Benjelloun Touimi, Abdellatif
• Granted Patent: US 8,639,735 B2
• Time in Patent Office: Days
• US Class Current: 708/313
• CPC Class Codes: G10L 19/0204 using subband decomposition
• CPC Class Codes: G10L 19/173 Transcoding, i.e. converting between two coded representations avoiding cascaded coding-decoding

Abstract

The invention concerns data processing by passage between different subband domains, of a first number L to a second number M of subband components. After determining a third number K, least common multiple between the first number L and the second number M: a) if K is different from L, it consists in arranging in blocs, by a serial/parallel conversion, an input vector X(z) to, obtain p₂ polyphase component vectors (p2=KL); b) applying a square matrix filtering T(z) of dimensions K×K, to the p₂ polyphase component vectors to obtain p₁ polyphase component vectors for forming an output vector Y(z), with p₁=K/M, and if the third number K is different from the second number M, providing a block arrangement by a parallel/serial conversion to obtain the output vector Y(z).

Claims

1. A method implemented by computer resources to process data by switching between different sub-band domains, consisting in compacting in one and the same processing the application of a first vector comprising:

a first number L of respective sub-band components, to a bank of synthesis filters, then to a bank of analysis filters, to obtain a second vector comprising a second number of respective sub-band components M,

wherein the method further comprises the following steps, after determination of 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, arrangement blockwise by a serial/parallel conversion of the first vector to obtain p₂ polyphase component vectors, with p₂=K/L,

b) application of a chosen matrix filtering, involving a square matrix T(z) of dimensions K×

K, to said p₂ polyphase component vectors to obtain p₁ polyphase component vectors of the second vector, with p₁=K/M, and

c) if the third number K is different from the second number M, arrangement blockwise by a parallel/serial conversion to obtain said second vector.

2. The method as claimed in claim 1, wherein the serial/parallel conversion of step a) corresponds to the application, to the first vector, of an advance z^p2−

1, followed by a chain of delays with subsampling by a factor p₂, to obtain said p₂ polyphase component vectors, corresponding to a decomposition of the order p₂, of the first vector.

3. The method as claimed in claim 1, wherein the parallel/serial conversion of step c) comprises an oversampling by a factor p₁ applied to the p₁ polyphase component vectors, corresponding to a decomposition of the order p₁, said components being intended to form the second vector.

4. The method as claimed in claim 1, wherein said square matrix T(z) results from a decimation by a factor K applied to a matrix formed of p₁×

p₂ submatrices each expressed by z<sup>lM−

jL</sup>g(z), where;

z^x denotes an advance or a delay, depending on the sign of x,

i lies between 0 and p₁−

1,

j lies between 0 and p₂−

1 and

g(z) is a matrix of dimensions M×

L resulting from the product h(z).f^T(z), where h(z) and f(z) are the vectors of the transfer functions respectively associated with the banks of analysis and synthesis filters, the notation M^T denoting the transpose of the matrix M.

5. The method as claimed in claim 4, wherein an advance z^M−

1 is moreover applied to all the p₁×

p₂ submatrices, to obtain elements of said matrix T(z) each corresponding to a causal filter and together defining a conversion system with minimal algorithmic delay.

6. The method as claimed in claim 5, wherein said elements of the matrix T(z) are expressed as a function of polyphase components to the order K of product filters G_nk(z) given by G_nk(z)=H_n(z)F_k(z), with:

n lying between 0 and M−

1 and k lying between 0 and L−

1, and

H_n(z) and F_k(z), the n^th and k^th components of the vectors of the transfer functions respectively associated with the banks of analysis and synthesis filters.

7. The method as claimed in claim 5, in which, between the bank of synthesis filters and the bank of analysis filters, there is provided moreover a supplementary filter S(z), wherein the elements of the matrix T(z) are expressed as a function of polyphase components to the order K of product filters G_nk(z) given by G_nk(z)=H_n(z)S(z)F_k(z), with:

n lying between 0 and M−

1 and k lying between 0 and L−

1, and

H_n(z) and F_k(z), the n^th and k^th components of the vectors of the transfer functions respectively associated with the banks of analysis and synthesis filters.

8. The method as claimed in claim 6, wherein the element filters T_ml(z) of the matrix T(z) are expressed by:

$T_{\mathrm{ml}}<br><br>\left(z\right)=\{\begin{array}{cc}{G}_{\mathrm{nk}}^{s_v}<br><br>\left(z\right),& \mathrm{if}<br><br><br><br>0\le <br><br>e_{\mathrm{ij}}\le <br><br>K-1,\\ z^{-1}<br><br>G_{\mathrm{nk}}^{K+e_{\mathrm{ij}}}<br><br>\left(z\right),& \mathrm{if}<br><br><br><br>e_{\mathrm{ij}}<<br><br>0,,\end{array}<br><br><br><br>\mathrm{with}<br><br><br><br>e_{\mathrm{ij}}=\left(M-1\right)+\left(\mathrm{iM}-\mathrm{jL}\right),<br><br>\mathrm{and}$

where;

in the notation G_nk^x(z), x corresponds to a polyphase component number, resulting from a decomposition to the order K of the product filter G_nk(z),

i corresponds to the integer part of the ratio m/M,

j corresponds to the integer part of the ratio l/L,

the number n is given by n=m−

iM, and

the number k is given by k=l−

jL.

9. The method as claimed in claim 8, wherein, if the second number M is a multiple of the first number L, the element filters T_ml(z) of the matrix T(z) are expressed by T_ml(z)=G_mj^(p−

k)L−

1(z), m and l lying between 0 and M−

1, and where;

p=M/L,

k is the integer part of l/L, and

the number j is given by j=l−

kL.

10. The method as claimed in claim 8, wherein, if the first number L is a multiple of the second number M, the element filters T_ml(z) of the matrix T(z) are expressed by T_ml(z)=G_il^(k+1)M−

1(z), m and l lying between 0 and L−

1, and where;

k is the integer part of m/M, and

the number i is given by i=m−

kM.

11. The method as claimed in claim 1, wherein the method further comprises:

applying a conversion system of linear periodically time varying type, and of period T defined by T=K.T_s, with T_s=T_s1/L=T_s2/M, where T_s1 and T_s2 are the respective sampling periods in the domains of the bank of synthesis filters and of the bank of analysis filters, under critical sampling.

12. The method as claimed in claim 11, wherein the method further comprises:

applying p₁ linear periodically time varying subsystems, each of period p₂.T_s1, and in periodically choosing the outputs of the successive subsystems, with a period p₁.T_s2.

13. The method as claimed in claim 12, wherein the bit rate at the input of the global conversion system is 1/T_s1, while its output bit rate is 1/T_s2, for processing input data on the fly.

14. The method as claimed in one of claims 8 and 12, wherein each subsystem, of index i lying between 0 and p₁−

1, comprises p₂ transfer matrices A_ij(z), with j lying between 0 and p₂−

1, whose elements are filters A_ij,nk(z), with n lying between 0 and M−

1 and k lying between 0 and L−

1, such that;

A_ij,nk(z)=G_nk^eij(z), if 0≦

e_ij≦

K−

1, and A_ij,nk(z)=z<sup>−

1</sup>G_{nkhu K+e}^ij(z), if e_ij<

0.

15. The method as claimed in claim 1, in which the filters of the synthesis and analysis banks have finite impulse responses, wherein said chosen matrix filtering is expressed by an overlap transform of matrix P, of dimensions NK×

K and such that;

$P=\left[\begin{array}{c}{P}_0\\ P_1\\ \mathrm{⋮<br><br>}\\ P_{N-1}\end{array}\right],$

the submatrices P_n being of dimensions K×

K and satisfying, with the matrix T(z), the relation;

$T<br><br>\left(z\right)=\underset{n=0}{\overset{N-1}{\sum <br><br>}}<br><br><br><br>P_n<br><br>z^{-n}$

where N corresponds to the maximum of the lengths of the element filters of T(z).

17. The method as claimed in claim 15, wherein the method further comprises the following steps, for a conversion between sub-band domains:

construction of a vector U[n] on the basis of p₂ first successive vectors X[k], in the sub-band domain of the bank of synthesis filters,

application to the vector U[n] of the transformed conversion matrix P, to obtain a vector W[n]=P.U[n],

addition with overlap on N successive vectors W[n−

N+1], W[n−

N+2], . . . , W[n−

1], W[n], to form a vector V[n],

arrangement in series of successive sub-vectors of the vector V[n], these sub-vectors each being of dimension corresponding to the second number M, to form said second vector.

18. The method as claimed in claim 17, wherein the method further comprises the following steps:

application of a first vector x└

k┘

, expressed in the sub-band domain of the bank of synthesis filters, to the subsystems comprising the transformed matrices B_ij, with i lying between 0 and p₁−

1 and j such that j=k mod p₂,

for each fixed i, ranging from 0 to p₁−

1;

application of a transform, of matrix B_ij, to the vector X[k] for j=k mod p₂, each matrix B_ij being expressed as follows;

B_ij=[B_ij,0^TB_ij,1^T . . . B<sub>ij,N−

1</sub>^T]^T where the elements B_ij,n are such that;

$A_{\mathrm{ij}}<br><br>\left(z\right)=\underset{n=0}{\overset{N-1}{\sum <br><br>}}<br><br>B_{\mathrm{ij},n}<br><br>z^{-n}$ $\mathrm{and}$ $P_n={\left[B_{\mathrm{ij},n}\right]}_{\underset{0\le <br><br>j\le <br><br>p_2-1}{0\le <br><br>i\le <br><br>p_1-1,}},$

for any n lying between 0 and N−

1,

summation of all the vectors resulting from the transform for j=0, . . . , p₂−

1,

addition with overlap on the vectors resulting from the summation, to construct, at the output of the subsystem of index i, a vector Y_i[n],

obtaining of a vector Y[n], at the output of the global conversion system, corresponding to the vector Y_i[n] of the subsystem of index i such that i=n mod p₁,

the notation mod n denoting the modulo of the number n.

19. The method as claimed in claim 18, wherein the matrices B_ij comprise zero blocks of dimensions L×

M such that;

for 0≦

e_ij≦

K−

1,

if 0≦

e_ij≦

r₀−

1 then;

B_ij=[B_ij,0^TB_ij,1^T . . . B<sub>ij,N−

3</sub>^TB<sub>ij,N−

2</sub>^T0<sub>L×

M</sub>]^T

if r₀≦

e_ij≦

K−

1 then;

B_ij=[B_ij,0^TB_ij,1^T . . . B<sub>ij,N−

3</sub>^T0<sub>L×

M</sub>0<sub>L×

M</sub>]^T

for e_ij<

0,

if 0≦

K+e_ij≦

r₀−

1 then;

B_ij=[0<sub>L×

M</sub>B_ij,1^T . . . B<sub>ij,N−

3</sub>^TB<sub>ij,N−

2</sub>^TB<sub>ij,N−

1</sub>^T]^T

if r₀≦

K+e_ij≦

K−

1 then;

B_ij=[0<sub>L×

M</sub>B_ij,1^T . . . B<sub>ij,N−

3</sub>^TB<sub>ij,N−

2</sub>^T0<sub>L×

M</sub>^T]^T

with;

0<sub>L×

M</sub> denoting a zero block of dimensions L×

M, and

$N=\lfloor <br><br>\frac{N_1+N_2-2}{K}\rfloor <br><br>+2,$

where;

N₁ and N₂ are the respective lengths of the filters of the synthesis bank and of the analysis bank,

the notation mod n denoting the modulo of the number n,

the notation └

x┘

denoting the integer part of the real number x.

20. The method as claimed in claim 19, wherein, if the first number M is a multiple of the second number L such that M=pL, the matrices A_ij become

$A_j$

( z ) = ∑

n = 0 N - 2 



B j , n 

z - n ,

where;

0≦

j≦

p−

1,

and B_j are the transform matrices which are expressed by;

$B_j=\{\begin{array}{cccccc}[B_{j,0}^T& B_{j,1}^T& \mathrm{\dots <br><br>}& B_{j,N-3}^T& {0_{\mathrm{LxM}}]}^T,& \mathrm{if}<br><br><br><br>0\le <br><br>j\le <br><br>j_0,\\ [B_{j,0}^T& B_{j,1}^T& \mathrm{\dots <br><br>}& B_{j,N-3}^T& {B_{j,N-2}^T]}^T,& \mathrm{if}<br><br><br><br>j_0+1\le <br><br>j\le <br><br>p-1,\end{array}$

where

$j_0=p-\lfloor <br><br>\frac{r_0+1}{L}\rfloor <br><br>,$

the notation └

x┘

denoting the integer part of the real number x.

21. The method as claimed in claim 20, wherein the method further comprises the following steps:

application of a first vector X[k], expressed in the sub-band domain of the bank of synthesis filters, to a subsystem comprising the transformed matrix B_j with j such that j=k mod p,

summation of the vectors resulting from the application of the transformed matrices B_j, for any j such that 0≦

j≦

p−

1,

obtaining of the vector Y[n], at the output of the global conversion system, by addition with overlap on the vectors resulting from said summation, the notation mod n denoting the modulo of the number n.

22. The method as claimed in claim 19, wherein, if the second number L is a multiple of the first number M such that L=pM, the matrices A_ij become

$A_i$

( z ) = ∑

n = 0 N - 2 



B i , n 

z - n ,

where;

0≦

i≦

p−

1, and

B_i are the transform matrices which are expressed by;

$B_i=\{\begin{array}{cccccc}[B_{i,0}^T& B_{i,1}^T& \mathrm{\dots <br><br>}& B_{i,N-3}^T& {B_{i,N-2}^T]}^T,& \mathrm{if}<br><br><br><br>0\le <br><br>\mathrm{<br><br>}\le <br><br>i_0,\\ [B_{i,0}^T& B_{i,1}^T& \mathrm{\dots <br><br>}& B_{i,N-3}^T& {0_{\mathrm{LxM}}]}^T,& \mathrm{if}<br><br><br><br>i_0+1\le <br><br>\mathrm{<br><br>}\le <br><br>p-1,\end{array}$

where

$i_0=\lfloor <br><br>\frac{r_0}{M}\rfloor <br><br>-1,$

the notation └

x┘

denoting the integer part of the real number x.

23. The method as claimed in claim 22, wherein the method further comprises the following steps:

application of a first vector X[k], expressed in the sub-band domain of the bank of synthesis filters, to a subsystem comprising the transfer matrix A_i(z), with 0≦

i≦

p−

1,

for any i fixed such that 0≦

i≦

p−

1, application of a transform, of matrix B_i to the vector X[k], and addition with overlap to obtain an output vector Y_i[n],

obtaining of an output vector Y[n], of the global conversion system, corresponding to the vector Y_i[n], with i such that i=n mod p,

the notation mod n denoting the modulo of the number n.

24. The method as claimed in claim 4, in which the filters of the analysis and synthesis banks are of modulated cosine and finite impulse response type, and wherein the analysis and/or synthesis filters are obtained by a cosine modulation of a low-pass prototype filter H(z),

so that the impulse responses of the analysis and/or synthesis filters, forming the vectors of the transfer functions h(z) and/or f(z), respectively, are each expressed, for a bank of filters with M bands, by:

$h_k<br><br>\left[n\right]=h<br><br>\left[n\right]<br><br>\cos <br><br>\left[\frac{\mathrm{\pi <br><br>}}{M}<br><br>\left(k+\frac{1}{2}\right)<br><br>\left(n-\frac{N-1}{2}\right)-{\mathrm{\theta <br><br>}}_k\right],<br><br>0\le <br><br>k\le <br><br>M-1,<br><br>\mathrm{and}<br><br>\text{/}<br><br>\mathrm{or}$ $f_k<br><br>\left[n\right]=h<br><br>\left[n\right]<br><br>\cos <br><br>\left[\frac{\mathrm{\pi <br><br>}}{M}<br><br>\left(k+\frac{1}{2}\right)<br><br>\left(n-\frac{N-1}{2}\right)+{\mathrm{\theta <br><br>}}_k\right],<br><br>0\le <br><br>k\le <br><br>M-1,$

where;

$-{\mathrm{\theta <br><br>}}_k=\frac{\left(2<br><br><br><br>k+1\right)<br><br>\mathrm{\Pi <br><br>}}{4},$

h[n] is the impulse response of the prototype filter, of length N,

n is such that 0≦

n≦

N−

1.

29. The method as claimed in claim 4, wherein, if provision is moreover made for a resampling by a rational factor Q/R between the bank of synthesis filters and the bank of analysis filters, the filtering matrix {circumflex over (T)}(z), of size q₁M×

q₂L, is defined by;

{circumflex over (T)}(z)=[{circumflex over (v)}(z){circumflex over (g)}(z)]|<sub>↓

K′</sub>

,

where;

ĝ

(z) is the matrix of size M×

L whose elements are given by;

Ĝ

_nk(z)=H_n(z^R)S_PB(z)F_k(z^Q), 0≦

n≦

M−

1, 0≦

k≦

L−

1,

{circumflex over (v)}(z) is the matrix whose elements are preferentially defined by;

{circumflex over (V)}_ij(Z)=z<sup>cmaxiRM−

jQL</sup>, 0≦

i≦

q₁−

1, 0≦

j≦

q₂−

1

with c_max=max {nε

N such that h≦

RM−

1 and n is divisible by gcd (L,R)},

and S_PB(z) is preferentially a low-pass filter with cutout frequency {tilde over (f)}_c=min (π

/Q,π

/R) and with passband gain Q.

30. An application of the method as claimed in claim 1, further comprising the steps of:

transcoding of a first type of compression coding/decoding to at least one second type of compression coding/decoding, wherein transcoding includes in compacting in one and the same processing the following steps;

recovering data at least partially decoded according to said first type, in the form of a first vector comprising a first number L of respective sub-band components,

applying the first vector to a bank of synthesis filters according to the first type, then to a bank of analysis filters according to the second type, and

recovering a second vector comprising a second number of respective sub-band components M and which can be applied to subsequent coding steps according to the second type.

31. A computer program product, intended to be stored in a memory of an item of equipment in a communication network, such as a server, a gateway, or else a terminal,

wherein the computer program product further comprises instructions for the implementation of all or part of the method as claimed in claim 1.

32. An item of equipment such as a server, a gateway, or else a terminal, intended for a communication network, wherein the item of equipment further comprises computer resources for the implementation of the method as claimed in claims 1.

16. (canceled)

25. (canceled)

26. (canceled)

27. (canceled)

28. (canceled)