信号处理+盲源分离+FastICA算法仿真

function [unmixingMatrix,separationSignal] = FastICA(mixedSignal) % FastICA算法 % % Input : % * mixedSignal: 混合信号构成的矩阵，即观测信号 % % Output : % * unmixingMatrix： is an n x m estimate of the mixing matrix % * separationSignal: estimate of the source signals MixedS = mixedSignal; MixedS_bak=MixedS; %%%%%%%%%%%%%%%%%%%%%%%%%% 标准化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % MixedS_mean=zeros(2,1); % for i=1:2 % MixedS_mean(i)=mean(MixedS(i,:)); % end % 计算MixedS的均值 % % for i=1:2 % for j=1:size(MixedS,1) % MixedS(i,j)=MixedS(i,j)-MixedS_mean(i); % end % end %%%%%%%%%%%%%%%%%%%%%%%%%%% 白化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MixedS_cov=cov(MixedS'); % cov为求协方差的函数 [E,D]=eig(MixedS_cov); % 对信号矩阵的协方差函数进行特征值分解 Q=inv(sqrt(D))*(E)'; % Q为白化矩阵 MixedS_white=Q*MixedS; % MixedS_white为白化后的信号矩阵 IsI=cov(MixedS_white'); % IsI应为单位阵 %%%%%%%%%%%%%%%%%%%%%%%%　FASTICA算法 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X=MixedS_white; % 以下算法将对X进行操作 [VariableNum,SampleNum]=size(X); numofIC=VariableNum; % 在此应用中，独立元个数等于变量个数 B=zeros(numofIC,VariableNum); % 初始化列向量w的寄存矩阵,B=[b1 b2 ... bd] for r=1:numofIC i=1;maxIterationsNum=1000; % 设置最大迭代次数（即对于每个独立分量而言迭代均不超过此次数） IterationsNum=0; b=rand(numofIC,1)-.5; % 随机设置b初值 b=b/norm(b); % 对b标准化 norm(b):向量元素平方和开根号 while i<=maxIterationsNum+1 if i == maxIterationsNum % 循环结束处理 fprintf('\n第%d分量在%d次迭代内并不收敛。', r,maxIterationsNum); break; end bOld=b; a2=1; u=1; t=X'*b; g=t.*exp(-a2*t.^2/2); dg=(1-a2*t.^2).*exp(-a2*t.^2/2); b=((1-u)*t'*g*b+u*X*g)/SampleNum-mean(dg)*b; % 核心公式 b=b-B*B'*b; % 对b正交化 b=b/norm(b); if abs(abs(b'*bOld)-1)<1e-9 % 如果收敛，则 B(:,r)=b; % 保存所得向量b break; end i=i+1; end end for k=1:numofIC W(:,k)=B(:,k)/5^k; % 得到解混矩阵W end %%%%%%%%%%%%%%%%%%%%%%%%%% 进行解混合 %%%%%%%%%%%%%%%%%%%%%%%%% ICAedS=W'*Q*MixedS_bak; % 计算ICA后的矩阵 unmixingMatrix = W; %解混矩阵 separationSignal = ICAedS; %分离后的信号 end