%例程6－9  方波信號的離散小波變換
% e.g.6-9.m for example6-9;
%test the function of wavedec.
 
clear all;
t=0:.01*pi:10*pi;
x=square(t,80);
X=x+randn(size(x))/10;
subplot(5,2,1:2); plot(t,X);
xlabel('Time t');
axis([0 11*pi  -2 2]);
ylabel('Amplitude X');
title('Original signal ')
 
% Perform decomposition at level 3 of X using sym8. 
wname='sym8';
[c,l] = wavedec(X,3,wname);
%At level 1
ca1=appcoef(c,l,wname,1); %1-D approximation coefficients
cd1=detcoef(c,l,1);    %1-D detail coefficients
subplot(523); plot(ca1); title('Approx. coef. at level 1'); 
subplot(524); plot(cd1); title('Detail coef. at level 1');
%At level 2
ca2=appcoef(c,l,wname,2);
cd2=detcoef(c,l,2);
subplot(525); plot(ca2); title('Approx. coef. at level 2'); 
subplot(526); plot(cd2); title('Detail coef. at level 2');
%At level 3
ca3=appcoef(c,l,wname,3);
cd3=detcoef(c,l,3);
subplot(527); plot(ca1); title('Approx. coef. at level 3'); 
subplot(528); plot(cd1); title('Detail coef. at level 3');
% Reconstruct approximation at level 3 from the wavelet decomposition structure [c,l].
ra3 = wrcoef('a',c,l,'sym8',3);
subplot(5,2,9:10); plot(ra3); 
title('Reconstruct signal form approximation at level 5:ra3');