CN102281045A - Method for constructing subband self-adapting filter - Google Patents

Abstract

The invention is suitable for the field of signal processing and provides a method for constructing a subband self-adapting filter. The method comprises the steps of: carrying out two-stage decomposition and self-adaptive filtration on input signals; carrying out two-stage subband decomposition on desired signals; and updating a filtration regulating coefficient subjected to self-adaptive filtration at the next time according to a filtration regulating coefficient for carrying out self-adaptive filtration on the input signals and the difference of the obtained output signals subjected to the self-adaptive filtration and the desired signals subjected to the two-stage decomposition. In the embodiment of the invention, the filtration regulating coefficient subjected to self-adaptive filtration at the next time can be updated according to the filtration regulating coefficient for carrying out self-adaptive filtration on the input signals and the difference of the obtained output signals subjected to the self-adaptive filtration and the desired signals subjected to the two-stage decomposition, the method for constructing the subband self-adaptive filter is realized, convergence rate can be further improved and computation complexity is reduced.

Description

A kind of structure sub-band adaptive filtered method

Technical field

The invention belongs to the signal processing field, relate in particular to a kind of structure sub-band adaptive filtered method.

Background technology

Sef-adapting filter can be applied to many fields, for example System Discrimination, channel equalization, echo elimination, wave beam formation etc.Under the situation of not knowing any priori of environment, the general method that makes up sef-adapting filter is that initial filter coefficient is set to any condition earlier, upgrade filter coefficient according to input signal and desired signal length by length then, to obtain the optimal filter coefficients setting.Because the simplicity and the robustness that realize make up sef-adapting filter and adopt lowest mean square (Least mean square, LMS) algorithm renewal filter coefficient often.But employing LMS algorithm more line filter coefficient can produce the slow problem of convergence rate, and under coloured input, for example voice signal especially when the exponent number of sef-adapting filter to be made up is very long, then needs higher computing cost.A good method that improves convergence rate and reduction computing cost is to make up the sub-band adaptive filter, input signal is resolved into a plurality of subband signals, on each subband, carry out adaptive-filtering respectively, so just can improve convergence rate to the colourful signal albefaction of input.

The existing heterogeneous decomposition sub-band adaptive Filter Structures that makes up as shown in Figure 1.By bank of filters input signal is carried out N ' sub-band division doubly, coloured input signal is cut apart by frequency band, be equivalent to input signal has been carried out albefaction, can reduce the correlation of input signal, the convergence of raising adaptive algorithm.And, input signal is carried out N ' doubly extract, can reduce the data rate of subband, thereby reduce the computing cost when upgrading adaptive filter coefficient.In addition, by the heterogeneous decomposition of the sef-adapting filter for the treatment of structure, can reduce exponent number, the raising convergence rate of sef-adapting filter; For finite impulse response, can also keep rebuilding fully finite impulse response (FIR) (Finite Impulse Response, the FIR) system on any rank.In a word, than full band structure, the sub-band adaptive filter of heterogeneous decomposition has potential rapid convergence.

But, since the sub-band adaptive filter of this structure only the antithetical phrase band carried out the one-level decomposition, in order to obtain convergence rate faster, then sub band number just need increase, the filter length in the bank of filters also will correspondingly increase.Like this, the needed computing cost of sub-band division has also just increased greatly, and this just need compromise in computational complexity and convergence rate.

Summary of the invention

The purpose of the embodiment of the invention is intended to solve the problem that the existing sub-band adaptive filter that makes up heterogeneous decomposition need be traded off in computational complexity and convergence rate, a kind of method that makes up the sub-band adaptive filter is provided, can further improves convergence rate, reduce computational complexity.

The embodiment of the invention is achieved in that a kind of method that makes up the sub-band adaptive filter, comprises the steps:

Input signal is carried out two-stage to be decomposed and adaptive-filtering;

Desired signal is carried out the two-stage sub-band division;

Adjust coefficient according to the current filtering that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

In embodiments of the present invention, according to the current filtering adjustment coefficient that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal and two-stage are decomposed behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly and is adjusted coefficient, realized a kind of method that makes up the sub-band adaptive filter, can further improve convergence rate, reduce computational complexity.

Description of drawings

Fig. 1 is the sub-band adaptive Filter Structures schematic diagram of the heterogeneous decomposition that provides of prior art;

Fig. 2 is the realization flow figure of the structure sub-band adaptive filtered method that provides of the embodiment of the invention;

Fig. 3 be the embodiment of the invention provide input signal is carried out the structural representation of two-stage sub-band division and adaptive-filtering;

Fig. 4 is the structure chart to the two-stage sub-band division of desired signal that the embodiment of the invention provides;

Fig. 5 is the whole model framework chart of the System Discrimination that provides of the embodiment of the invention.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer,, the present invention is further elaborated below in conjunction with drawings and Examples.Should be appreciated that specific embodiment described herein only in order to explanation the present invention, and be not used in qualification the present invention.

In embodiments of the present invention, according to the current filtering adjustment coefficient that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal and two-stage are decomposed behind the adaptive-filtering that obtains upgrades next filtering of carrying out adaptive-filtering constantly and adjusts coefficient, realized a kind of method that makes up the sub-band adaptive filter.

Fig. 2 shows the realization flow of the structure sub-band adaptive filtered method that the embodiment of the invention provides, and details are as follows:

In step S201, input signal is carried out two-stage decompose and adaptive-filtering;

In step S202, desired signal is carried out the two-stage sub-band division;

In step S203, adjust coefficient according to the current filtering that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

In embodiments of the present invention, adopt structure shown in Figure 3 that input signal is carried out two-stage sub-band division and adaptive-filtering.Particularly, step S201 comprises:

Step S2011 carries out N first order sub-band division and N doubly with input signal and doubly extracts;

Step S2012 carries out the first order subband signal that obtains M second level sub-band division doubly respectively;

Step S2013 carries out adaptive-filtering to each second level subband signal respectively and M doubly extracts, and obtains second level output signal.

Accordingly, adopt structure shown in Figure 4 that desired signal is carried out the two-stage sub-band division, the first order is N times, and the second level is M times, can obtain N*M subband desired signal.Step S202 is:

Desired signal is carried out N times and M two-stage sub-band division doubly.

Further, in step S203, adjust coefficient according to the current filtering that each second level subband signal is carried out adaptive-filtering, and the difference of the second level desired signal after the two-stage decomposition that obtains among each second level output signal that obtains among the step S2013 and the corresponding step S202 is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

Below, corresponding diagram 3,4 describes the process of structure sub-band adaptive filtered method provided by the invention.

In step S2011, earlier input signal u (n) is passed through first order N path filter group H successively ₀(z), H ₁(z) ..., H _N-1(z) filtering, and carry out a z of chronomere ^-1Time-delay; Then, respectively the first order subband signal that obtains being carried out N doubly extracts.In step S2012, the first order subband signal that will carry out after N doubly extracts passes through second level M path filter group H ' respectively ₀(z), H ' ₁(z) ..., H ' _M-1(z) filtering can obtain N * N * M second level subband signal x _0,0(k), x _0,1(k) ... x _{0, N-1}(k), x _1,0(k), x _1,1(k) ... x _{1, N-1}(k) ... x _{NM-1, N-1}(k), also be the input signal vector of N * N * M sef-adapting filter.In step S2013, respectively with each second level subband signal by sef-adapting filter group w ₀(k), w ₁(k) ..., w _N-1(k) carry out adaptive-filtering, obtain second level subband output signal; Again each second level subband output signal is carried out M and doubly extract, obtain second level output signal y ₀(k), y ₁(k) ..., y _NM-1(k).In step S202, adopt structure shown in Figure 4 that desired signal d (n) is carried out the two-stage sub-band division: earlier desired signal d (n) to be passed through first order N path filter group H successively ₀(z), H ₁(z) ..., H _N-1(z) filtering is carried out N again and is extracted; Then, again the first order desired signal that obtains is passed through second level M path filter group H ' ₀(z), H ' ₁(z) ..., H ' _M-1(z) filtering is carried out M again and is extracted, and obtains the second level desired signal d after two-stage is decomposed ₀(k), d ₁(k) ..., d _NM-1(k).With each second level output letter work y ₀(k), y ₁(k) ..., y _NM-1(k) with corresponding second level desired signal d ₀(k), d ₁(k) ..., d _NM-1(k) difference e ₀(k), e ₁(k) ..., e _NM-1(k) as error signal.According to current time, promptly k carries out the filtering of the sef-adapting filter group of adaptive-filtering and adjusts coefficient w constantly ₀(k), w ₁(k) ..., w _N-1And the error signal e that obtains (k), ₀(k), e ₁(k) ..., e _NM-1(k) upgrade next constantly, promptly k+1 constantly, carry out adaptive-filtering the sef-adapting filter group filtering adjust coefficient w ₀(k+1), w ₁(k+1) ..., w _N-1(k+1).

Here, dual stage filter group H ₀(z), H ₁(z) ..., H _N-1(z) and H ' ₀(z), H ' ₁(z) ..., H ' _M-1(z) all use the cosine-modulation bank of filters of the better performances can satisfy complete recondition.In the superincumbent parametric representation, n represents the data rate of input signal, and k represents the input signal of each subband correspondence and the data rate of output signal, k=n/N.

Particularly, above each second level subband signal is carried out the sef-adapting filter group w of adaptive-filtering ₀(k), w ₁(k) ..., w _N-1(k) be equivalent to the heterogeneous N of being decomposed into of a full band filter w (z) sub-filter is obtained, full band filter w (z) carried out the N phase decomposition undertaken by following formula:

$W\left(z\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{z}^{-j}{w}_j\left(z^N\right)---\left(1\right)$

Each second level subband signal carries out the second level output signal y that obtains behind the adaptive-filtering _i(k) be:

$y_i\left(k\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{w}_j^T\left(k\right)x_{\mathrm{ij}}\left(k\right)---\left(2\right)$

Wherein, i=0,1 ..., NM-1, subscript T represent that adaptive-filtering is adjusted coefficient matrix wj (k) asks transposition.

Subband error signal e _i(k) be:

e _i(k)＝d _i(k)-y _i(k) (3)

In embodiments of the present invention, based on the minimise interference principle, the update algorithm of coefficient is adjusted in the filtering of calculating sef-adapting filter.The minimise interference principle is when twice iteration, when meeting the expectation signal bondage, guarantees the variable quantity f minimum of total adaptive-filtering adjustment coefficient.Here, the variable quantity f of total adaptive-filtering adjustment coefficient is defined as:

$f=\underset{j=0}{\overset{j=N-1}{\mathrm{\Σ}}}{\left|\right|w_j(k+1)-w_j\left(k\right)\left|\right|}^2---\left(4\right)$

Constraints is:

$d_i\left(k\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{w}_j^T(k+1)x_{\mathrm{ij}}\left(k\right)---\left(5\right)$

for?i＝0，1，...，NM

Wherein, i=0,1 ..., NM-1.

The minimise interference principle can be expressed as: when formula is met, make (4) formula minimum in (5).So, use lagrange's method of multipliers, can construct cost function J (k), that is:

$J\left(k\right)=f+\underset{i=0}{\overset{i=\mathrm{NM}-1}{\mathrm{\Σ}}}{\mathrm{\λ}}_i[d_i\left(k\right)-\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{w}_j^T(k+1)x_{\mathrm{ij}}\left(k\right)]---\left(6\right)$

Calculate the partial derivative of following formula, and to make it be zero, the update calculation formula of coefficient is adjusted in the filtering that can obtain sef-adapting filter, that is, and and order

$\frac{\∂J\left(k\right)}{\∂w_j(k+1)}=0,$ for?j＝0，1，2...N-1

Calculating following formula can get:

$w_j(k+1)=w_j\left(k\right)+\frac{1}{2}\underset{i=0}{\overset{i=\mathrm{NM}-1}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{x}_{\mathrm{ij}}\left(k\right)---\left(7\right)$

Ask parameter lambda below _i, at first, (7) formula is updated to constraints (5) formula:

$d_l\left(k\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{[w_j\left(k\right)+\frac{1}{2}\underset{i=0}{\overset{i=2M-1}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{x}_{\mathrm{ij}}\left(k\right)]}^T{x}_{\mathrm{lj}}\left(k\right)---\left(8\right)$

In conjunction with following formula and (2) formula, can get:

$e_l\left(k\right)=\frac{1}{2}\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{i=2M-1}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{x}_{\mathrm{ij}}^T\left(k\right)x_{\mathrm{lj}}\left(k\right)---\left(9\right)$

Because the sef-adapting filter group not have very big aliasing, the cross-correlation of its output signal will be far smaller than its auto-correlation, so when i ≠ 1,

$x_{\mathrm{ij}}^T\left(k\right)x_{\mathrm{lj}}\left(k\right)=0---\left(10\right)$

The result of following formula is updated to (9), can solves parameter lambda _i

${\mathrm{\λ}}_i=\frac{{2e}_i\left(k\right)}{\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{\left|\right|x_{\mathrm{il}}\left(k\right)\left|\right|}^2}---\left(11\right)$

Following formula substitution as a result (7) formula, the update calculation formula that can obtain the filtering adjustment coefficient vector of final sef-adapting filter is again:

$w_j(k+1)=w_j\left(k\right)+\mathrm{\μ}\underset{i=0}{\overset{i=\mathrm{NM}-1}{\mathrm{\Σ}}}\frac{x_{\mathrm{ij}}\left(k\right)e_i\left(k\right)}{\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}{\left|\right|x_{\mathrm{il}}\left(k\right)\left|\right|}^2}---\left(12\right)$

Wherein, μ is positive step parameter, by adding positive step-size parameter mu, is carved into next coefficient constantly in the time of can avoiding from one and produces too big change.

This formula (12) is among the step S203 according to the current filtering that input signal is carried out adaptive-filtering and adjusts coefficient, and the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded the computing formula of next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

Below, prove the convergence of algorithm condition, i.e. the magnitude range of positive step-size parameter mu.The model framework chart of realizing System Discrimination as shown in Figure 5, input signal is u (n), and input signal u (n) is obtained desired signal d (n) after by unknown system S (z), the The noise that v (n) is subjected to when observing d (n).Here, v (n) is modeled as additive white noise.The structure sub-band adaptive filtered method that provides by the embodiment of the invention comes desired signal d (n) is carried out the two-stage sub-band division and input signal u (n) is carried out sub-band adaptive filtering.

Equally, the heterogeneous decomposition of definition unknown system S (z) is as follows, is decomposed into N part s unknown system S (z) is also heterogeneous _jThe length of setting unknown system is L, then its heterogeneous decomposition component s _jLength be L/N.

$S\left(z\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{S}_j\left(z^N\right)---\left(13\right)$

Defining filtering that k carries out sub-band adaptive filtering constantly adjusts the error vector of coefficient and is:

ε _j(k)＝s _j-w _j(k) (14)

Wherein, j=0,1 ..., N-1.

Total coefficient of mean square deviation (mean-square deviation, MSD) c (k) is,

$c\left(k\right)=E[\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}{\left|\right|{\mathrm{\ϵ}}_j\left(k\right)\left|\right|}^2---\left(15\right)$

Wherein, E represents to ask expectation, be here to all sub-band adaptive filter filtering adjust coefficient error vector inner product square and ask expectation, in order to the statistical value of the size of representing whole coefficient error vector.

Make system's convergence, then coefficient of mean square deviation c (k) will constantly reduce, that is:

c(k+1)-c(k)＜0 (16)

In order to find the solution following formula, coefficient update equation (12) substitution (14), substitution again (15), the span that can try to achieve step-size parameter mu is:

$0<\mathrm{\&mu;}<\frac{2\underset{i=0}{\overset{2M-1}{\mathrm{\&Sigma;}}}E\left[\frac{e_i\left(k\right)\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_j^T\left(k\right)x_{\mathrm{ij}}\left(k\right)}{\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|\right|x_{\mathrm{ij}}\left(k\right)\left|\right|}^2}\right]}{\underset{i=0}{\overset{2M-1}{\mathrm{\&Sigma;}}}E\left[\frac{e_i^2\left(k\right)}{\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|\right|x_{\mathrm{ij}}\left(k\right)\left|\right|}^2}\right]}---\left(17\right)$

When noiseless is disturbed, can obtain:

$\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}_j^T\left(k\right)x_{\mathrm{ij}}\left(k\right)=\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{s}_1{x}_{\mathrm{ij}}\left(k\right)-\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{w}_j\left(k\right)x_{\mathrm{ij}}\left(k\right)$

With following formula substitution (17) formula, the form that can obtain simplifying:

0＜μ＜2 (18)

Therefore, adjust in the computing formula (12) of coefficient vector in the filtering of above-mentioned renewal sef-adapting filter, μ gets the arbitrary value between (0,2).

Certainly, according to different application scenarios, can also be entirely with coefficient vector, according to the principle of heterogeneous decomposition, conversely can be according to N heterogeneous component in the hope of full band coefficient vector,

$W\left(z\right)=\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{z}^{-j}{W}_j\left(2^N\right)$

Below, the complexity that can decompose the adaptive-filtering structure that adopts the secondary decomposition, consider the multiplication number of times of each input sample, comprise sub-band division to input signal and desired signal, to the filtering of input signal, to the integration of each second level subband output signal, and five parts of coefficient calculations are adjusted in the filtering of adaptive-filtering.

Suppose the cosine filter group H among Fig. 3,4 ₀(z), H ₁(z) ..., H _N-1(z) and H ' ₀(z), H ' ₁(z) ..., H ' _M-1(z) in, the length of filter is the multiple of sub band number, supposes that sub band number is m, and then the length of filter is F _m=8m.Like this, the computation complexity that can obtain total is:

P _new＝3L+N+3NF _N+(NM+M+1)F _M

And the adaptive-filtering structure to using one-level to decompose, its complexity is:

P _old＝3L+N′+3N′F _N′

Shown in the following Table I, L is entirely with the length of sef-adapting filter; The structure that is to use one-level 4 sub-band division of (4,1) representative, N=4; The structure that (2,2) representative uses two-stage to decompose, the first order is the N=2 sub-band division, the second level also is the M=2 sub-band division.As shown in Table 1, adopt two-stage to decompose, under the situation of same sub-band number, identical, the needed amount of calculation of convergence rate is littler.

(N，M)	L＝128	L＝1024
			(2，2)	593	3281
(4，1)	772	3460

Table 1

In embodiments of the present invention, according to the current filtering adjustment coefficient that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal and two-stage are decomposed behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly and is adjusted coefficient, realized a kind of method that makes up the sub-band adaptive filter, can further improve convergence rate, reduce computational complexity.

One of ordinary skill in the art will appreciate that, realize that all or part of step in the foregoing description method is to instruct relevant hardware to finish by program, described program can be in being stored in a computer read/write memory medium, described storage medium, as ROM/RAM, disk, CD etc., this program is used for carrying out following steps:

Input signal is carried out two-stage to be decomposed and adaptive-filtering;

Desired signal is carried out the two-stage sub-band division;

Adjust coefficient according to the current filtering that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

The above only is preferred embodiment of the present invention, not in order to restriction the present invention, all any modifications of being done within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. a method that makes up the sub-band adaptive filter is characterized in that, described method comprises the steps:

Input signal is carried out two-stage to be decomposed and adaptive-filtering;

Desired signal is carried out the two-stage sub-band division;

Adjust coefficient according to the current filtering that input signal is carried out adaptive-filtering, and the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

2. the method for claim 1 is characterized in that, describedly input signal is carried out two-stage is decomposed and the step of adaptive-filtering comprises:

Input signal is carried out N first order sub-band division and N doubly doubly to be extracted;

Respectively the first order subband signal that obtains is carried out M second level sub-band division doubly;

Respectively each second level subband signal is carried out adaptive-filtering and M doubly extracts, obtain second level output signal.

3. method as claimed in claim 2 is characterized in that, the described step that desired signal is carried out the two-stage sub-band division is specially:

Desired signal is carried out N times and M two-stage sub-band division doubly.

4. method as claimed in claim 3, it is characterized in that, describedly adjust coefficient, and the step that the difference of the desired signal after output signal is decomposed with two-stage behind the adaptive-filtering that obtains is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient is specially according to the current filtering that input signal is carried out adaptive-filtering:

Adjust coefficient according to the current filtering that each second level subband signal is carried out adaptive-filtering, and the difference of the second level desired signal after each second level output signal that obtains and the corresponding two-stage decomposition is upgraded next filtering of carrying out adaptive-filtering constantly adjustment coefficient.

5. method as claimed in claim 4, it is characterized in that, according to the current filtering adjustment coefficient that each second level subband signal is carried out adaptive-filtering, and each second level output signal that obtains and the difference of second level desired signal after corresponding two-stage is decomposed adopt following formula to upgrade filtering and adjust coefficient when upgrading next filtering of carrying out adaptive-filtering constantly and adjusting coefficient:

$w_j(k+1)=w_j\left(k\right)+\mathrm{\&mu;}\underset{i=0}{\overset{i=\mathrm{NM}-1}{\mathrm{\&Sigma;}}}\frac{x_{\mathrm{ij}}\left(k\right)e_i\left(k\right)}{\underset{l=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|\right|x_{\mathrm{il}}\left(k\right)\left|\right|}^2};$

Wherein, w _j(k+1) coefficient, w are adjusted in expression k+1 filtering constantly _j(k) coefficient, x are adjusted in expression k filtering constantly _Ij(k) expression k second level subband signal constantly, e _i(k) expression subband error signal, i.e. the difference of second level output signal and corresponding second level desired signal, μ is positive step parameter.

6. method as claimed in claim 5 is characterized in that, described μ gets the arbitrary value between (0,2).

7. as each described method of claim 1 to 6, it is characterized in that, adopt the cosine-modulation bank of filters that input signal is carried out two-stage and decompose.

Images