邢台网站制作公司哪家专业,线上营销的方式,百度产品大全入口,辽宁鲲鹏建设集团网站JADE算法原理
JADE 算法首先通过去均值预白化等预处理过程得到解相关的混合信号#xff0c;预处理后的信号构建的协方差矩阵变为单位阵#xff0c;为后续的联合对角化奠定基础#xff1b;其次#xff0c;通过建立四阶累积量矩阵#xff0c;利用高阶累积量的统计独立性等性…JADE算法原理
JADE 算法首先通过去均值预白化等预处理过程得到解相关的混合信号预处理后的信号构建的协方差矩阵变为单位阵为后续的联合对角化奠定基础其次通过建立四阶累积量矩阵利用高阶累积量的统计独立性等性质从白化后的传感器混合(观测)信号中得到待分解的特征矩阵最后通过特征矩阵联合对角化和Givens 旋转得到酉矩阵U从而获得盲源分离算法中混合矩阵A 的有效估计进而分离出需要的目标信号。 JADE算法的流程图如下 #mermaid-svg-x8bQJoI1wwM8UpvT {font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;fill:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .error-icon{fill:#552222;}#mermaid-svg-x8bQJoI1wwM8UpvT .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-x8bQJoI1wwM8UpvT .edge-thickness-normal{stroke-width:2px;}#mermaid-svg-x8bQJoI1wwM8UpvT .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-x8bQJoI1wwM8UpvT .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-x8bQJoI1wwM8UpvT .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-x8bQJoI1wwM8UpvT .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-x8bQJoI1wwM8UpvT .marker{fill:#333333;stroke:#333333;}#mermaid-svg-x8bQJoI1wwM8UpvT .marker.cross{stroke:#333333;}#mermaid-svg-x8bQJoI1wwM8UpvT svg{font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-x8bQJoI1wwM8UpvT .label{font-family:"trebuchet ms",verdana,arial,sans-serif;color:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .cluster-label text{fill:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .cluster-label span{color:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .label text,#mermaid-svg-x8bQJoI1wwM8UpvT span{fill:#333;color:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .node rect,#mermaid-svg-x8bQJoI1wwM8UpvT .node circle,#mermaid-svg-x8bQJoI1wwM8UpvT .node ellipse,#mermaid-svg-x8bQJoI1wwM8UpvT .node polygon,#mermaid-svg-x8bQJoI1wwM8UpvT .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-x8bQJoI1wwM8UpvT .node .label{text-align:center;}#mermaid-svg-x8bQJoI1wwM8UpvT .node.clickable{cursor:pointer;}#mermaid-svg-x8bQJoI1wwM8UpvT .arrowheadPath{fill:#333333;}#mermaid-svg-x8bQJoI1wwM8UpvT .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-x8bQJoI1wwM8UpvT .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-x8bQJoI1wwM8UpvT .edgeLabel{background-color:#e8e8e8;text-align:center;}#mermaid-svg-x8bQJoI1wwM8UpvT .edgeLabel rect{opacity:0.5;background-color:#e8e8e8;fill:#e8e8e8;}#mermaid-svg-x8bQJoI1wwM8UpvT .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-x8bQJoI1wwM8UpvT .cluster text{fill:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT .cluster span{color:#333;}#mermaid-svg-x8bQJoI1wwM8UpvT div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:"trebuchet ms",verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-x8bQJoI1wwM8UpvT :root{--mermaid-font-family:"trebuchet ms",verdana,arial,sans-serif;} 混合信号 白化 四阶累计量矩阵 特征矩阵联合对角化和Givens旋转 得到酉矩阵 解混合 源信号 下面是JADE算法的公式推导从论文中截的图
JADE仿真程序
JADE算法的函数
function [A,S]jade(X,m)
% Source separation of complex signals with JADE.
% Jade performs Source Separation in the following sense:
% X is an n x T data matrix assumed modelled as X A S N where
%
% o A is an unknown n x m matrix with full rank.
% o S is a m x T data matrix (source signals) with the properties
% a) for each t, the components of S(:,t) are statistically
% independent
% b) for each p, the S(p,:) is the realization of a zero-mean
% source signal.
% c) At most one of these processes has a vanishing 4th-order
% cumulant.
% o N is a n x T matrix. It is a realization of a spatially white
% Gaussian noise, i.e. Cov(X) sigma*eye(n) with unknown variance
% sigma. This is probably better than no modeling at all...
%
% Jade performs source separation via a
% Joint Approximate Diagonalization of Eigen-matrices.
%
% THIS VERSION ASSUMES ZERO-MEAN SIGNALS
%
% Input :
% * X: Each column of X is a sample from the n sensors
% * m: m is an optional argument for the number of sources.
% If ommited, JADE assumes as many sources as sensors.
%
% Output :
% * A is an n x m estimate of the mixing matrix
% * S is an m x T naive (ie pinv(A)*X) estimate of the source signals
[n,T] size(X); %% source detection not implemented yet !
if nargin1, mn ; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A few parameters that could be adjusted
nem m; % number of eigen-matrices to be diagonalized
seuil 1/sqrt(T)/100;% a statistical threshold for stopping joint diag %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% whitening
%
if mn, %assumes white noise [U,D] eig((X*X)/T); [puiss,k]sort(diag(D)); ibl sqrt(puiss(n-m1:n)-mean(puiss(1:n-m))); bl ones(m,1) ./ ibl ; W diag(bl)*U(1:n,k(n-m1:n)); IW U(1:n,k(n-m1:n))*diag(ibl);
else %assumes no noise IW sqrtm((X*X)/T); W inv(IW);
end;
Y W*X; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Cumulant estimation R (Y*Y )/T ;
C (Y*Y.)/T ; Yl zeros(1,T);
Ykl zeros(1,T);
Yjkl zeros(1,T); Q zeros(m*m*m*m,1) ;
index 1; for lx 1:m ; Yl Y(lx,:);
for kx 1:m ; Ykl Yl.*conj(Y(kx,:));
for jx 1:m ; Yjkl Ykl.*conj(Y(jx,:));
for ix 1:m ; Q(index) ... (Yjkl * Y(ix,:).)/T - R(ix,jx)*R(lx,kx) - R(ix,kx)*R(lx,jx) - C(ix,lx)*conj(C(jx,kx)) ; index index 1 ;
end ;
end ;
end ;
end %% If you prefer to use more memory and less CPU, you may prefer this
%% code (due to J. Galy of ENSICA) for the estimation the cumulants
%ones_m ones(m,1) ;
%T1 kron(ones_m,Y);
%T2 kron(Y,ones_m);
%TT (T1.* conj(T2)) ;
%TS (T1 * T2.)/T ;
%R (Y*Y)/T ;
%Q (TT*TT)/T - kron(R,ones(m)).*kron(ones(m),conj(R)) - R(:)*R(:) - TS.*TS ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%computation and reshaping of the significant eigen matrices [U,D] eig(reshape(Q,m*m,m*m));
[la,K] sort(abs(diag(D))); %% reshaping the most (there are nem of them) significant eigenmatrice
M zeros(m,nem*m); % array to hold the significant eigen-matrices
Z zeros(m) ; % buffer
h m*m;
for u1:m:nem*m, Z(:) U(:,K(h)); M(:,u:um-1) la(h)*Z; h h-1;
end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% joint approximate diagonalization of the eigen-matrices %% Better declare the variables used in the loop :
B [ 1 0 0 ; 0 1 1 ; 0 -i i ] ;
Bt B ;
Ip zeros(1,nem) ;
Iq zeros(1,nem) ;
g zeros(3,nem) ;
G zeros(2,2) ;
vcp zeros(3,3);
D zeros(3,3);
la zeros(3,1);
K zeros(3,3);
angles zeros(3,1);
pair zeros(1,2);
c 0 ;
s 0 ; %init;
encore 1;
V eye(m); % Main loop
while encore, encore0; for p1:m-1, for qp1:m, Ip p:m:nem*m ; Iq q:m:nem*m ; % Computing the Givens angles g [ M(p,Ip)-M(q,Iq) ; M(p,Iq) ; M(q,Ip) ] ; [vcp,D] eig(real(B*(g*g)*Bt)); [la, K] sort(diag(D)); angles vcp(:,K(3)); if angles(1)0 , angles -angles ; end ; c sqrt(0.5angles(1)/2); s 0.5*(angles(2)-j*angles(3))/c; if abs(s)seuil, %%% updates matrices M and V by a Givens rotation encore 1 ; pair [p;q] ; G [ c -conj(s) ; s c ] ; V(:,pair) V(:,pair)*G ; M(pair,:) G * M(pair,:) ; M(:,[Ip Iq]) [ c*M(:,Ip)s*M(:,Iq) -conj(s)*M(:,Ip)c*M(:,Iq) ] ; end%% if end%% q loop end%% p loop
end%% while %%%estimation of the mixing matrix and signal separation
A IW*V;
S V*Y ; return ; 主程序
%% JADE算法仿真
% 输入信号为两段语音混合矩阵为随机数构成
% 采用基于四阶累计量的特征矩阵联合近似对角化JADE算法对两段语音进行分离并绘制了源信号、混合信号和分离信号
% Author:huasir 2023.9.19 Beijing
close all,clear all;clc;
%%
% 读取语音文件输入源信号 %
%%
[S1,fs1] audioread(E:\sound1.wav); % 读取原始语音信号需要将两个语音文件放置在相应目录下
[S2,fs2] audioread(E:\ICA\sound2.wav);
figure;
subplot(3,2,1),plot(S1),title(输入信号1); %绘制源信号
subplot(3,2,2),plot(S2),title(输入信号2);
s1 S1; %一行代表一个信号
s2 S2;
S[s1;s2]; % 将其组成矩阵
%%
% 对源信号进行混合得到观测信号 %
%%
Sweight rand(size(S,1)); %由随机数构成混合矩阵
MixedSSweight*S; % 将混合矩阵重新排列
subplot(3,2,3),plot(MixedS(1,:)),title(混合信号1); %绘制混合信号
subplot(3,2,4),plot(MixedS(2,:)),title(混合信号2);
%%
% 采用JADE算法进行盲源分离得到源信号的估计 %
%%
[Ae,Se]jade(MixedS,2); %Ae为估计的混合矩阵Se为估计的源信号
% 将混合矩阵重新排列并输出
subplot(3,2,5),plot(Se(1,:)),title(JADE解混信号1);
subplot(3,2,6),plot(Se(2,:)),title(JADE解混信号2);
%%
% 源信号、混合信号以及解混合之后的信号的播放 %
%%
% sound(S1,8000); %播放输入信号1
% sound(S2,8000); %播放输入信号2
% sound(MixedS(1,:),8000); %播放混合信号1
% sound(MixedS(2,:),8000); %播放混合信号2
% sound(Se(1,:),8000); %播放分离信号1
% sound(Se(2,:),8000); %播放分离信号2
fprintf(混合矩阵为\n); % 输出混合矩阵以及估计的混合矩阵
disp(Sweight);
fprintf(估计的混合矩阵为\n);
disp(Ae);然后对其进行混合混合后调用JADE函数进行解混合最后对解混合的信号进行绘制并进行读取。 可以听到两段录音的内容不一样音调也不用它们满足不相关性因此能够很好的分离。由下图可以看出分离后的信号的幅度和真实信号有所不同并且排序也不同这是盲分离算法本身的局限性即幅度模糊性和排序模糊性。但是一般情况下信号的信息保存在波形的变化中人们对于其绝对幅度并不敏感。 结果如下图 图1. JADE算法分离结果 在主程序中首先是读取语音文件语音文件由以下链接给出当然也可以自己生成源信号。
链接https://pan.baidu.com/s/1DwnZqDBc1sogERcq7RrVqA 提取码ngk1
