%
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% Optical Imaging and Spectroscopy
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% David J. Brady
% Duke University
% www.opticalimaging.org
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% Figure 10.43
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%
%
figure(1);
set(gcf,'color','white');
colormap gray;
Hl=toeplitz([1, zeros(1,127)],[1 1 1 1 0 0 0 0,zeros(1,128-8)])/4;
[al bl cl]=svd(Hl);
%subplot(1,2,1);plot(diag(bl),'-k');axis([0 128 0 1]);
%title('Singular value spectra'); hold on;
l1=diag(bl);
Hl=toeplitz([1, zeros(1,127)],[1 1 0 0 0 1 0 1,zeros(1,128-8)])/4;
[al bl cl]=svd(Hl);
subplot(1,2,1);plot(diag(bl),'-k');
l2=diag(bl);
Hl=toeplitz([1, zeros(1,127)],[1 1 1 0 0 1 0 0,zeros(1,128-8)])/4;
[al bl cl]=svd(Hl);
subplot(1,2,1);plot(diag(bl),'-k');
l3=diag(bl);
Hl=kron(eye(32),(1+hadamard(4))/8);
[al bl cl]=svd(Hl);
%subplot(1,2,1);plot(diag(bl),'-k');
l4=diag(bl);
x=1:128;
subplot(1,2,1);
plot(x,l1,'-k',x,l2,'--k',x,l3,'-.k',x,l4,':k');
axis([0 128 0 1]);
title('Singular value spectra');
legend('11110000','11000101','11100100','Hadamard');
subplot(1,2,2);imagesc(cl);
title('Hadamard singular vectors');