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+% C-FICA algorithm - time-domain Convolutive extension of FastICA - v1.2
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+%
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+% J. Thomas, Y. Deville and S. Hosseini
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+% "Time-domain fast fixed-point algorithms for convolutive ICA",
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+% IEEE Signal Processing Letters, vol. 13, no. 4, pp. 228-231, April 2006.
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+%
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+%
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+% [Sc,sc,Isc,y,fe,fc,te,tc]=cfica(x,non-lin,epsi,Re,[we1 we2],Rc,[wc1 wc2],itermax,initializ,verbose)
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+%
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+% Inputs (place the deconvolution parameters before the recoloration ones
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+% themselves before iter_max)
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+%
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+% x : observation vector
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+% non-lin : 'k'->kurtosis, 'g'->Gaussian, 't'->tanh default 'g'
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+% initializ : 'i' for initialization with unit filters optional
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+% epsi : stopping criterion (between 0 and 1) default 10^-12
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+% Re : order of the extraction filters default 80
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+% [we1 we2] : extraction time window optional
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+% Rc : order of the recoloration filters default 3R1
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+% [wc1 wc2] : recoloration time window optional
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+% itermax : maximum number of iteration default 10000
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+% verbose : 'v' for verbose optional
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+%
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+% Outputs
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+%
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+% Sc : most powerful contributions for each estimated source
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+% sc : estimated source contributions (tensor N*N*nb_samples)
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+% Isc : indices of the most powerful contributions
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+% y : N-1 estimated innovation processes (matrix (N-1)*nb_samples)
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+% fe : extraction filters
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+% fc : recoloration filters
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+% te : times of extraction
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+% tc : times of recoloration
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+% -------------------------------------------------------------------------
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+% History of the software:
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+% V1.1: original software written by J. Thomas
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+%
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+% V1.2: Error messages appeared with recent releases of Matlab in the function
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+% conv_mix_nc. This version corrects them.
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+% Author: Matthieu PUIGT Contact: matthieu.puigt@lisic.univ-littoral.fr
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+%
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+% -------------------------------------------------------------------------
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+
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+
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+
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+function [Sc,sc,Isc,y,fe,fc,te,tc]=cfica(x,varargin)
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+
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+% N: number of observations, n: number of samples
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+[N,n]=size(x);
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+
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+% centering of the observations
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+x=x-mean(x,2)*ones(1,n);
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+
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+% ordering of the input arguments
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+[criterion,initializ,epsi,Re,we1,we2,Rc,wc1,wc2,iter_max,verbose]=args(varargin,n);
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+
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+% R1 non-causal filter coefficients
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+% R2 strictly causal filter coefficients
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+R1=floor(Re/2);Rc1=floor(Rc/2);
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+clear Re Rc
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+R2=R1;Rc2=Rc1;
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+
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+% unit filter
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+id=[zeros(1,R1),1,zeros(1,R2)];
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+
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+% deflated observation vector
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+x_def=x;
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+for r=1:N-1
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+
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+if verbose,fprintf('convolutive sphering %d .. \n',r),end
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+tic
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+
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+% creation of a multi-delayed observation vector
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+for k=1:N-r+1
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+ for i=-R1:R2
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+ x_tilde((R1+R2+1)*(k-1)+i+1+R1,:)=x_def(k,we1-i:we2-i);
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+ end
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+end
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+
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+% whitening process
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+[x_prime,B]=white(x_tilde,we2-we1+1);
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+clear x_tilde;
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+
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+% initialization of the extraction process
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+if initializ
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+ id1=id(ones(1,N-r+1),:);
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+ id1=reshape(id1',1,(N-r+1)*(R1+R2+1));
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+ fe0=id1*B^-1;
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+else
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+ fe0=ones(1,(N-r+1)*(R1+R2+1))*B^-1;
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+end
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+
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+if verbose,fprintf('fixed-point extraction %d .. \n',r),end
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+% extraction of a non-Gaussian innovation process
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+[fe{r},iter]=extract(x_prime,fe0,criterion,epsi,iter_max);
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+
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+te(r)=toc;
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+clear x_prime;
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+
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+fe{r}=fe{r}*B;
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+
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+% reshaping of the extraction vector
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+fe{r}=reshape1(fe{r},[1,N-r+1,R1+R2+1],[3 2 1]);
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+
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+% application of the extraction filters
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+y(r,:)=conv_mix_nc(fe{r},x_def(1:N-r+1,:),R1);
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+
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+
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+for k=1:N
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+
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+% coloration of the r^th source for the r^th sensor
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+if verbose,fprintf('recoloration process %d-%d .. \n',k,r),end
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+tic
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+[sc(k,r,:),fc{k,r}]=color(y(r,:),x(k,:),wc1,wc2,Rc1,Rc2);
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+tc(k,r)=toc;
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+
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+end
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+
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+% removing of the last estimated contributions from the sensors
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+for t=1:N
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+ s0(1,:)=sc(t,r,:);
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+ x_def(t,:)=x_def(t,:)-s0;
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+end
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+clear s0;
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+
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+end
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+
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+% the last contributions corresponding to the N^th source
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+sc(:,N,:)=x_def;
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+
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+% identification of the most powerful contribution
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+[M,Isc]=max(mean(sc.^2,3));
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+
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+% output signals
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+for k=1:N
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+ Sc(k,:)=sc(Isc(k),k,:);
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+end
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+
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+%-----------------------------------------
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+function [x_prime,B]=white(x_tilde,n)
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+
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+% eigendecomposition of xxt
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+[E,D]=eig(x_tilde*x_tilde');
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+
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+% computation of whitening matrix
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+sqD=sqrt(n)*D^(-1/2);
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+B=sqD*E';
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+
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+% whitening process
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+x_prime=B*x_tilde;
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+
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+%------------------------------------------------------------
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+function [w,iter]=extract(x_prime,w,criterion,epsi,iter_max)
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+
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+[N,n]=size(x_prime);
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+
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+% extraction vector normalization
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+w=w./norm(w);
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+
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+test=1;iter=0;
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+while test>epsi & iter<iter_max
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+
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+ y=w*x_prime;
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+
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+ switch criterion
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+ case 'k'
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+ % kurtosis fixed-point iteration
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+ w1=1/n*(y.^3)*x_prime'-3*w;
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+ case 'g'
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+ % Gaussian negentropic fixed-point iteration
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+ gauss_y=exp(-y.^2/2);
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+ w1=1/n*(y.*gauss_y)*x_prime' - 1/n*sum(((1-y.^2).*gauss_y))*w;
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+ case 't'
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+ % hyperbolic-tangent negentropic fixed-point iteration
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+ tanh_y=tanh(y);
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+ w1=1/n*tanh_y*x_prime' - 1/n*sum(1-tanh_y.^2)*w;
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+ end
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+
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+ % vector normalization
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+ w1=w1./norm(w1);
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+
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+ % computation of the stopping criterion
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+ test=min([abs(w1-w) abs(w1+w)]);
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+ w=w1;
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+
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+ iter=iter+1;
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+end
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+
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+%-------------------------------------------------------
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+function [sc,c]=color(y,x,w1,w2,R1,R2)
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+
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+n=w2-w1+1;
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+
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+% computation of the autocorrelation matrix of y
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+y2=y(w1+R1:w2+R1);
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+for r=-R1:R2
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+ y1=y(w1-r:w2-r);
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+ Ry1(r+R1+1)=1/n*y1*y2';
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+end
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+
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+for r1=-R1:R2
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+ for r2=-R1:R2
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+ Ry(r1+R1+1,r2+R1+1)=Ry1(abs(r2-r1)+1);
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+ end
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+ % computation of the intercorrelation vector of y and x
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+ y1=y(w1-r1:w2-r1);
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+ ryx(r1+R1+1)=1/n*y1*(x(w1:w2))';
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+end
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+
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+% computation of the wiener filter
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+c=Ry^(-1)*ryx';
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+
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+% non-causal filtering process
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+sc=filter_nc(c,y,R1);
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+
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+%-------------------------------------------------
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+function x=conv_mix_nc(A,s,R1);
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+% R1 non-causal coefficients
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+% R2 strictly causal coefficients
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+
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+R2=size(A,3)-R1-1;
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+
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+for i=1:size(A,1)
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+ x(i,:)=zeros(1,size(s,2)+R1+R2);
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+ for j=1:size(s,1)
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+ x(i,:)=x(i,:)+conv(reshape(A(i,j,:),size(A,3),1,1),s(j,:));
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+ end
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+end
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+
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+% removing of the out samples
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+x=x(:,1+R1:end-R2);
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+
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+%-------------------------------------------------
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+function s=filter_nc(h,e,R1);
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+
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+R2=length(h)-R1-1;
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+
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+% convolution process
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+s=conv(h,e);
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+
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+% removing of the out samples
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+s=s(1+R1:end-R2);
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+
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+%---------------------------------------------------
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+function w1=reshape1(w,dims,order)
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+
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+% ordering of the tensor dimensions
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+dims1=dims(order);
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+
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+% reshaping of the vector w
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+w1=reshape(w,dims1);
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+
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+% re-ordering of the tensor
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+w1=ipermute(w1,order);
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+
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+%-----------------------------------------------------
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+function [criterion,initializ,epsi,Re,we1,we2,Rc,wc1,wc2,iter_max,verbose]=args(varargin,n)
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+
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+% ordering of the input arguments
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+
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+for i=1:length(varargin)
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+ if length(varargin{i})==1
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+ switch varargin{i}
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+ case {'k','g','t'},criterion=varargin{i};
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+ case 'i',initializ=1;
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+ case 'v',verbose=1;
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+ otherwise
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+ if varargin{i}<1 & varargin{i}>0,epsi=varargin{i};
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+ else,if ~exist('Re'),Re=varargin{i};
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+ else,if ~exist('Rc'),Rc=varargin{i};
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+ else iter_max=varargin{i};end,end,end
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+ end
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+ else,if ~exist('we1'),we1=varargin{i}(1);we2=varargin{i}(2);
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+ else,wc1=varargin{i}(1);wc2=varargin{i}(2);end
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+ end
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+end
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+
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+if ~exist('criterion'), criterion='g';end
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+if ~exist('initializ'), initializ=0;end
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+if ~exist('epsi'), epsi=1e-12;end
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+if ~exist('Re'), Re=80;end
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+if ~exist('we1'), we1=Re+1;we2=n-Re-1;end
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+if ~exist('Rc'), Rc=2*Re;end
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+if ~exist('wc1'), wc1=Rc+1;wc2=n-Rc-1;end
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+if ~exist('iter_max'), iter_max=1e4;end
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+if ~exist('verbose'), verbose=0; end
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+
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+if verbose,criterion,initializ,epsi,Re,extr_window=[we1,we2],Rc,col_window=[wc1,wc2],iter_max,verbose,end
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