%%
%% Code for demos presented in lecture 3
%% 


%%
%% Variable shape signal experiment
%%
MAX_SIG_LEN = 32;
MAX_JITTER = 14;
BLIP_LENGTH = 2;
N = 400;
S = zeros(N,MAX_SIG_LEN);

for EE=1:N,
   %% Generate signal
   xx = round(MAX_JITTER*rand(1,2))+[1 MAX_SIG_LEN-MAX_JITTER];
   S(EE,xx(1)+[1:BLIP_LENGTH])=-1-rand;
   S(EE,xx(2)-[1:BLIP_LENGTH])=+1+rand;
   %S(EE,:) = S(EE,:) - mean(S(EE,:));
end;

for i=1:16,
   figure(5);
   subplot(4,4,i);
   plot(S(i,:));
end;

%MS = mean(S);
%S = S - ones(N,1)*MS;


[U,SS,V] = svd(S'*S);

figure(6); sval = diag(SS); semilogy(sval(1:16),'.','MarkerSize',15);
   
for i=1:16,
   figure(7);
   subplot(4,4,i);
   plot(U(:,i));
end;


%% Projection of signals onto new base
for EE=1:N,
   c1(EE) = S(EE,:) * U(:,1);
   c2(EE) = S(EE,:) * U(:,2);
end;
figure(8); plot(c1,c2,'.','MarkerSize',15);
xlabel('1st component'); ylabel('2nd component');
title(['The ' num2str(N) ' sample signals projected onto the reduced base']);