CN101086730A - Convolution mixed blind separation frequency domain method based on non continuous smoothness - Google Patents

Abstract

The invention relates to a convolution mixing blind frequency domain method. It makes short time Fourier transformation of convolution mixing signal to change the transformation coefficient into uncontinual multi instant short time Fourier transformation coefficient smoothness. It uses similar united diagonalization for the instant mixing bland separation to acquire the mixing matrix and separation signal for each frequency plate. It uses the real part of the separation signal adjusting the sequence of the mixing hybrid matrix vector, to generate separate filter matrix of the mixed matrix. It generates separation signal through separation filter matrix to complete convolution blind separation. It is helpful to reduce STFT coefficient instant mixing and error between mixing signal STFT to improve the separation feature. Besides, it reduces computation quantity compared to traditional mixed matrix vector sequence adjustment.

Description

Convolution mixed blind separation frequency domain method based on non continuous smoothness

Technical field

The present invention relates to a kind of convolution mixed blind separation frequency domain method based on non continuous smoothness, specifically by a kind of discontinuous level and smooth method of short time discrete Fourier transform coefficient (STFT) of carving for a long time, reduce the instantaneous mixing of source signal STFT and the error between convolution mixed signal STFT, improved the separating effect of the blind separation of convolution mixing frequency domain.In addition, with respect to the order method of adjustment of the column vector of hybrid matrix on each frequency chip of tradition, the present invention proposes a kind of method of adjustment of simplification, has reduced significantly and has adjusted required operand.

Background technology

With respect to instantaneous mixing, convolution is mixed more complicated, also more is close to the hybrid mode of signal in the actual environment.At present, the convolution mixed blind separation problem has attracted numerous researchers, and the convolution mixed blind separation algorithm that is proposed in recent years roughly is divided into two classes: time domain approach and frequency domain method.Time domain approach generally meets the large-scale hybrid matrix of certain form by setting, convolution is mixed change single instantaneous mixing based on this large-scale hybrid matrix into, but complex calculations and store requirement accordingly make it be not easy to be generalized to the multichannel convolution and mix.And on frequency domain, convolution is mixed plural instantaneous mixing on each frequency chip of degenerating, and can use for reference numerous ripe relatively blind separation algorithms of instantaneous mixing, so frequency domain method receives more and more the concern.

Yet, because the branch frame of STFT is equivalent to the sectional convolution of realizing source signal and wave filter, and there is error between linear convolution and cyclic convolution during sectional convolution, therefore on each frequency chip, the STFT coefficient that the instantaneous mixing of source signal STFT coefficient and out of true equal convolution mixed signal, instantaneous mixing on each frequency chip also just becomes is with instantaneous mixing under the condition of making an uproar, be to have error between the instantaneous mixing of source signal STFT coefficient and convolution mixed signal STFT coefficient, thereby influenced the separation accuracy that existing frequency domain convolution mixes blind separation algorithm.Because error signal can not appear in the convolution mixed signal, therefore this error can only reduce and can not be eliminated.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, proposed a kind of based on the discontinuous level and smooth convolution mixing blind separation method in frequency domain of short time discrete Fourier transform coefficient of carving for a long time, this method helps to reduce the instantaneous mixing of source signal STFT coefficient and the error between convolution mixed signal STFT coefficient, thereby promotes separating property.In addition, with respect to the order method of adjustment of the column vector of hybrid matrix on each frequency chip of tradition, the present invention proposes a kind of method of adjustment of simplification, has reduced significantly and has adjusted required operand.

The present invention is achieved through the following technical solutions, and concrete step is as follows:

A kind of convolution is mixed blind separation method in frequency domain, is used to reduce the instantaneous mixing of source signal STFT and the error between convolution mixed signal STFT, improves the separating effect that convolution is mixed the blind separation of frequency domain, it is characterized in that concrete steps are as follows:

(1) to convolution mixed signal X _i(n) do frame length and move branch frame, and ask each frame X into o for the T frame _i(l) (i=1,2 ..., T point short time discrete Fourier transform D),

And vector sequence $\stackrel{\‾}{X}(w_k,l)={[{\stackrel{\‾}{X}}_1(w_k,l),...,{\stackrel{\‾}{X}}_D(w_k,l)]}^{\′},$ W wherein _k=2 π k/T, k ∈ [0, T-1], i ∈ 1,2 ..., D), l represents the sequence number of frame;

(2) at each frequency chip w _kOn, generate

The discontinuous level and smooth result of short time discrete Fourier transform coefficient that carves for a long time $E\left(\stackrel{\‾}{X}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{X}(w_k,l+p\·T),$ Wherein be the P smoothing factor, T is aforesaid minute frame frame length;

(3) utilize

Carry out frequency chip w _kOn the blind separation of instantaneous mixing, obtain frequency chip w _kOn the estimated value of hybrid matrix

And separation signal $E\left(\stackrel{\‾}{S}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{S}(w_k,l+\mathrm{\β}\·p);$

(4) by gathering independently principle, foundation

Adjust on each frequency chip

Corresponding relation between column vector generates real Thereby overcome the probabilistic disunity of order on the different frequency sheet;

(5) to adjusted

w _k=2 π k/T, k[0, T-1], utilize contrary short time discrete Fourier transform to generate contrary compound filter (be separation filter, convolution mixed signal is imported separation filter) array and generate final convolution composite liberation signal.

The discontinuous short time discrete Fourier transform coefficient of carving for a long time of convolution mixed signal that to the effect that utilizes of the present invention smoothly replaces short time discrete Fourier transform, carries out convolution and mixes the blind separation of frequency domain.The feature of error between linear convolution and cyclic convolution when its purpose is to utilize sectional convolution, reduce the error between instantaneous mixing of source signal short time discrete Fourier transform and convolution mixed signal short time discrete Fourier transform, and then promote the separating property that convolution is mixed the blind separation of frequency domain.

Description of drawings

Fig. 1 is to use the system works flow process figure of the inventive method.

Embodiment

A preferred embodiment of the present invention is:

Referring to Fig. 1, the concrete operations step that this convolution is mixed blind separation method in frequency domain is as follows:

(1) establishing frame length is T, and frame moves and is o, and α=T-o is then to convolution mixed signal X _i(n) (i=1,2 ..., D) behind the branch frame, l (l 〉=0) frame constitutes vector X _i(l)=[X _i(l α) ..., X _i(l α+T-1)].X _i(l) T point short time discrete Fourier transform is at frequency chip w _kLast coefficient is ${\stackrel{\‾}{X}}_i(w_k,l)={\mathrm{\Σ}}_{m=0}^{T-1}{X}_i(m+l(T-o))\exp (-\sqrt{(-1)}2\mathrm{km\π}/M),$ And have $\stackrel{\‾}{X}(w_k,l)={[{\stackrel{\‾}{X}}_1(w_k,l),...,{\stackrel{\‾}{X}}_D(w_k,l)]}^{\′},$ W wherein _k=2 π k/T, k ∈ [0, T-1].

(2) at each frequency chip w _kOn, generate

The discontinuous level and smooth back of the short time discrete Fourier transform coefficient result that carves for a long time $E\left(\stackrel{\‾}{X}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{X}(w_k,l+p\·T),$ Wherein P is called as smoothing factor, characterizes the number that participates in level and smooth discontinuous STFT coefficient, and the experience value of P is 100～1000 a integer.

(3) at frequency chip w _kOn, right

The blind separation of instantaneous mixing of adopting associating approximate diagonalization (JADE:JointApproximate diagonalization estimation) method to carry out obtains frequency chip w _kOn the estimated value of hybrid matrix

And separation signal $E\left(\stackrel{\‾}{S}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{S}(w_k,l+p\·T).$ The diagonalizable specific implementation of approximate associating is as follows:

A) generate

Whitened signal

$E_w\left(\stackrel{\‾}{X}(w_k,l)\right)=U^{-0.5}E\left(\stackrel{\‾}{X}(w_k,l)\right),$ Wherein $U=\mathrm{Cov}(E\left(\stackrel{\‾}{X}(w_k,l)\right),E\left(\stackrel{\‾}{X}(w_k,l)\right)).$

B) generate The non-zero propagation covariance matrix of second order $R\left(\mathrm{\τ}\right)=\mathrm{Cov}(E\left(\stackrel{\‾}{X}(w_k,l)\right),E\left(\stackrel{\‾}{X}(w_k,l+\mathrm{\τ})\right)),$ τ＝1，2，…，M。The experience value of M is the integer more than 10.

C) when D=2, establish $R\left(\mathrm{\τ}\right)=\left[\begin{array}{cc}a\left(\mathrm{\τ}\right)& b\left(\mathrm{\τ}\right)\\ c\left(\mathrm{\τ}\right)& d\left(\mathrm{\τ}\right)\end{array}\right],$ g(τ)＝[a(τ)-d(τ)，b(τ)-c(τ)，j(c(τ)-b(τ)]′，

G＝[g(1)，g(2)，…，g(M)]′。With matrix G ^HThe real part of each element of G constitutes real number matrix Real (G ^HG), to Real (G ^HG) do eigen value decomposition, ask the latent vector v=[v of its mould dominant eigenvalue correspondence ₁, v ₂, v ₃V must be the unit column vector of 3 dimensions when] ' (JADE algorithm guaranteed D=2), and generator matrix $V=0.5\·\left[\begin{array}{cc}2\·\sqrt{(1-v_1)/2}& -(v_2+j\·v_3)/\sqrt{(1-v_1)/2}\\ (v_2-j\·v_3)/\sqrt{(1-v_1)/2}& 2\·\sqrt{(1-v_1)/2}\end{array}\right],$ When then the two-way convolution mixed blind separates 2 * 2

Be V.

D) when D＞2 (participate in mixed signal way that convolution mixed blind separates more than 2), it is capable to each D * D matrix R (τ) gets α, β, four elements of α, β row intersection location constitute 2 * 2 by diagonalizable matrix (1≤α≤D wherein, α≤β≤D), utilize c) in method be similar to the associating diagonalization, acquisition 2 * 2 matrix V.Generate the unit matrix of D * D then, (α, α), (α, β), (β is α) with (β, the β) element of position form matrix T to the unit matrix that V (1,1), V (1,2), V (2,1) and V (2,2) are replaced respectively again _q, 1≤q≤D (D-1)/2 wherein, D * D when then the multichannel convolution mixed blind separates

For: $\stackrel{\widehat{\‾}}{H}\left(w_k\right)={\mathrm{\Π}}_{q=1}^{D\·(D-1)/2}{T}_q.$

(4) by gathering independently principle, foundation

Adjust on each frequency chip Corresponding relation between column vector generates real $\stackrel{\‾}{H}\left(w_k\right)(0\≤q\≤T-1),$ Thereby overcome the probabilistic disunity of order on the different frequency sheet:

A) with vector

In the real part of each element constitute vector $Y(w_k,l)={[{\stackrel{\‾}{Y}}_1(w_k,l),...,{\stackrel{\‾}{Y}}_D(w_k,l)]}^{\′},$ Make again that the reference frequency sheet is w _r=0, k frequency chip w then _kGo up with

(i=1 ..., D) Dui Ying output sequence is ${\stackrel{\‾}{O}}_i(w_k,l)={\stackrel{\‾}{Y}}_{\mathrm{\σ}(i,k)}(w_k,l),$ Wherein ${\stackrel{\‾}{O}}_i(w_r,l)={\stackrel{\‾}{Y}}_i(w_r,l),$ $\mathrm{\σ}(i,k)=\underset{j=\mathrm{1,2},...,D}{\arg \max }\left(\right|\mathrm{Exp}\left\{\right[{\stackrel{\‾}{O}}_i(w_r,l)-\mathrm{Exp}\left({\stackrel{\‾}{O}}_i(w_r,l)\right)\left]\right[{\stackrel{\‾}{O}}_j(w_k,l)-\mathrm{Exp}\left({\stackrel{\‾}{O}}_j(w_k,l)\right){]}^{*}\left\}\right|),$ Exp represents to peek and hopes in term.

B) the unit matrix I of generation D * D, adjustment matrix Λ _kReally

Wherein Λ (:, i)=I (:, σ (i, k)), $\stackrel{\‾}{H}\left(w_k\right)=\stackrel{\widehat{\‾}}{H}\left(w_k\right)\·{\mathrm{\Λ}}_k.$

(5) to adjusted

(w _k=2 π k/T, k ∈ [0, T-1]), utilize inverse fourier transform to generate contrary compound filter (separation filter) array, convolution mixed signal is imported separation filter) the final convolution composite liberation signal of array generation:

A) get $\stackrel{\‾}{W}\left(w_k\right)={\stackrel{\‾}{H}}^{-1}\left(w_k\right),$ From convolution mixed signal X _iTo separation signal Y _g(the separation filter w between the 1≤i≤D, 1≤g≤D) _IgPulse shock response be: $w_{\mathrm{ig}}=\mathrm{IFFT}\left(\right[\stackrel{\‾}{W}\left(w_1\right)(i,g),...,\stackrel{\‾}{W}\left(w_k\right)(i,g),...\stackrel{\‾}{,W}\left(w_T\right)(i,g){]}^{\′}),$ Wherein IFFT represents inverse fourier transform,

Representing matrix

Element at the capable g row of i.

B) with convolution mixed signal vector X (n)=[X ₁(n) ..., X _D(n)] ' generate separation signal vector Z (n)=[Z by the separation filter array ₁(n) ..., Z _D(n)] ', make [Z ₁(n) ..., Z _D(n)] ' as source signal [S ₁(n) ..., S _D(n)] estimation ' (uncertainty of existence order and amplitude).That is:

$Z\left(n\right)=(W*X)\left(n\right)={\mathrm{\Σ}}_{\mathrm{\τ}=0}^{T-1}W\left(\mathrm{\τ}\right)X(n-\mathrm{\τ})$

Wherein W (τ) (i, j)=w _Ij(τ) (τ=0 ..., M-1).

Claims (4)

1. the convolution based on non continuous smoothness is mixed blind separation method in frequency domain, is used to reduce the instantaneous mixing of source signal STFT and the error between convolution mixed signal STFT, improves the separating effect that convolution is mixed the blind separation of frequency domain, it is characterized in that concrete steps are as follows:

(1) to convolution mixed signal X _i(n) do frame length and move branch frame, and ask each frame X into o for the T frame _i(l) (i=1,2 ..., T point short time discrete Fourier transform D),

And vector sequence $\stackrel{\‾}{X}(w_k,l)={[{\stackrel{\‾}{X}}_1(w_k,l),...,{\stackrel{\‾}{X}}_D(w_k,l)]}^{\′},$ W wherein _k=2 π k/T, k ∈ [0, T-1], i ∈ 1,2 ..., D}, l represent the sequence number of frame;

(2) at each frequency chip w _kOn, generate

The discontinuous level and smooth result of short time discrete Fourier transform coefficient that carves for a long time $E\left(\stackrel{\‾}{X}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{X}(w_k,l+p\·T),$ Wherein be the P smoothing factor, T is aforesaid minute frame frame length.

(3) utilize

Carry out frequency chip w _kOn the blind separation of instantaneous mixing, obtain frequency chip w _kOn the estimated value of hybrid matrix

And separation signal $E\left(\stackrel{\‾}{S}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{S}(w_k,l+\mathrm{\β}\·p);$

(4) by gathering independently principle, foundation

Adjust on each frequency chip

Corresponding relation between column vector generates real $\stackrel{\‾}{H}\left(w_k\right)(0\≤q\≤T-1),$ Thereby overcome the probabilistic disunity of order on the different frequency sheet:

A) with vector

In the real part of each element constitute vector $Y(w_k,l)={[{\stackrel{\‾}{Y}}_1(w_k,l),...,{\stackrel{\‾}{Y}}_D(w_k,l)]}^{\′},$ Make again that the reference frequency sheet is w _r=0, k frequency chip w then _kGo up with ${\stackrel{\‾}{Y}}_i(w_r,l)(i=1,...,D)$ Corresponding output sequence is ${\stackrel{\‾}{O}}_i(w_k,l)={\stackrel{\‾}{Y}}_{\mathrm{\σ}(i,k)}(w_k,l),$ Wherein ${\stackrel{\‾}{O}}_i(w_r,l)={\stackrel{\‾}{Y}}_i(w_r,l),$ $\mathrm{\σ}(i,k)=\underset{j=\mathrm{1,2},...,D}{\arg \max }\left(\right|\mathrm{Exp}\left\{\right[{\stackrel{\‾}{O}}_i(w_r,l)-\mathrm{Exp}\left({\stackrel{\‾}{O}}_i(w_r,l)\right)\left]{[{\stackrel{\‾}{O}}_j(w_k,l)-\mathrm{Exp}\left({\stackrel{\‾}{O}}_j(w_k,l)\right)]}^{*}\right\}\left|\right),$ Exp represents to peek and hopes in term;

B) the unit matrix I of generation D * D, adjustment matrix Λ _kReally

Wherein Λ (:, i)=I (:, σ (i, k)), $\stackrel{\‾}{H}\left(w_k\right)=\stackrel{\widehat{\‾}}{H}\left(w_k\right)\·{\mathrm{\Λ}}_k;$

(5) to adjusted w _k=2 π k/T, k ∈ [0, T-1] utilizes contrary short time discrete Fourier transform to generate contrary compound filter array and generates final convolution composite liberation signal.

2. convolution according to claim 1 is mixed blind separation method in frequency domain, it is characterized in that, described step (3) is utilized

Carry out frequency chip w _kOn the blind separation of instantaneous mixing, but not usually frequency domain convolution to mix blind separation used Itself.

3. convolution according to claim 1 is mixed blind separation method in frequency domain, it is characterized in that, utilizes in the described step (3) $E\left(\stackrel{\‾}{X}(w_k,l)\right)=\frac{1}{P}{\mathrm{\Σ}}_{p=0}^{P-1}\stackrel{\‾}{X}(w_k,l+p\·T)$ Carry out the blind separation of instantaneous mixing on the frequency chip wk, when the big more then this method of smoothing factor P high more with respect to the separation accuracy of common frequency domain convolution mixings blind separating method lifting.

4. convolution according to claim 1 is mixed blind separation method in frequency domain, it is characterized in that, only adopt the real part of instantaneous composite liberation signal on each frequency chip to replace instantaneous composite liberation signal itself (plural number) in traditional method of adjustment in the described step (4).Because multiplication cross between 4 real imaginary parts of the needs of the multiplication between plural number, and the present invention adopts the method formula only to need 2 reals to multiply each other, traditional relatively method of adjustment, institute of the present invention employing method significantly reduce operand (operand only for traditional method of adjustment 1/4), and more meet reference signal The condition that only contains real part.