自适应滤波：维纳滤波器——GSC算法及语音增强

【读书笔记04】

1）背景介绍；

2）广义旁瓣相消（Generalized Sidelobe Cancellation, GSC）理论推导；

3）GSC应用——语音阵列信号增强；

${{\bf{C}}^H}{\bf{w}} = {\bf{g}}$

A-理论介绍

• 如果A是满列秩（N>=M）对于符合LA=I的矩阵解为：${\bf{L}} = {\left( {{{\bf{A}}^H}{\bf{A}}} \right)^{ - 1}}{{\bf{A}}^H}$;
• 如果A是满行秩（N<=M）对于符合AR=I的矩阵解为：${\bf{R}} = {{\bf{A}}^H}{\left( {{{\bf{A}}}{\bf{A}^H}} \right)^{ - 1}}$.

${{\bf{w}}_q} = {\bf{C}}{\left( {{{\bf{C}}^H}{\bf{C}}} \right)^{ - 1}}{\bf{g}}$

${{\bf{w}}_{re}} = {\bf{w}} - {{\bf{w}}_q}$

${\bf{C}}_a^H{\bf{C}} = {\bf{0}}$

重新给出推导的结果：

${\bf{w}} = {{\bf{w}}_q} - {{\bf{C}}_a}{{\bf{w}}_a}$       s.t. ${{\bf{C}}_a}{{\bf{w}}_q} = {\bf{0}}$

B-阻塞矩阵的选取

MMI_define_var(Xf1,Xf2);
%initialization
W1 = [0 0 0 0.1 0 0 0.2 ];
W2 = [0 2 0 0 0.2 0 0.1 ];
[Wa1,Wa2]=MMI_EstimateWa([W1 W2]');

function MMI_define_var(Xf1,Xf2)

global Wq B covX1X1 covX2X2  covX1X2  len;

Wq=[1 1 1 1 1 1 1 1]'*1/8;
B=[1 -1 0 0 0 0 0 0 ;0 1 -1 0 0 0 0 0 ;0 0 1 -1 0 0 0 0 ;0 0 0 1 -1 0 0 0 ;0 0 0 0 1 -1 0 0 ;0 0 0 0 0 1 -1 0 ;0 0 0 0 0 0 1 -1 ]';

[~,len]=size(Xf2);
XfMean1=mean(Xf1.');
XfMean2=mean(Xf2.');
for i=1:8
Xf1(i,:)=Xf1(i,:)-XfMean1(i);
Xf2(i,:)=Xf2(i,:)-XfMean2(i);
end

covX1X1=Xf1*Xf1'/len;
covX2X2=Xf2*Xf2'/len;
covX1X2=Xf1*Xf2'/len;
MMI_EstimateWa实现参数估计:
function [Wa1 Wa2]=MMI_EstimateWa(W)
%obtain the Wa
ww=[real(W)' imag(W)']';

options = optimset('LargeScale','off','display','off');
[X,fval] = fminunc('MMI_real_imag_objfun',ww,options);
X_real=X(1:14);
X_imag=X(15:28);
Wa1_real=X_real(1:7);
Wa1_imag=X_imag(1:7);
Wa2_real=X_real(8:14);
Wa2_imag=X_imag(8:14);

Wa1=Wa1_real+sqrt(-1)*Wa1_imag;
Wa2=Wa2_real+sqrt(-1)*Wa2_imag;
end


• K. Kumatani, T. Gehrig, U. Mayer, E. Stoimenov, J. McDonough and M. WÖlfel, "Adaptive Beamforming With a Minimum Mutual Information Criterion," in IEEE Transactions on Audio, Speech, and Language Processing, vol. 15, no. 8, pp. 2527-2541, Nov. 2007.
• Simon Haykin 《Adaptive Filter Theory Fourth Edition》.
posted @ 2017-03-26 09:20  桂。  阅读(9244)  评论(2编辑  收藏  举报