Page 137 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

3. Numerical Linear Algebra 125

14.1.2 M-file for haar forward and inverse transformation

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haartrans.m

i=0:1/511:1;
a=sin(2*pi*i)+sin(2*pi*100*i);
plot(a)
figure
s=length(i);
for i=1:1:log2(s)
temp=createhaarmatrix(length(a))*a';
temp=reshape(temp,2,length(temp)/2);
approx{i}=temp(1,:);
det{i}=temp(2,:);
a=approx{i};
end
for k=1:1:(length(approx)-1)
subplot((length(approx)-1),1,k)
plot(approx{k})
title(strcat('approx',num2str(k)))
end
subplot(
figure
for k=1:1:(length(approx)-1)
subplot((length(approx)-1),1,k)
plot(det{k})
title(strcat('detail',num2str(k)))
end
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createhaarmatrix.m

function [res]=createhaarmatrix(m)
temp1=[ones(1,m/2);(-1)*ones(1,m/2)];
temp1=reshape(temp1,1,size(temp1,1)*size(temp1,2));
d1=temp1.*(1/2);
temp2=[ones(1,m/2);zeros(1,m/2)];
temp2=reshape(temp2,1,size(temp2,1)*size(temp2,2));
d2=(1/2)*temp2(1:1:length(temp2)-1);
res=diag(d1)+diag(d2,1)+diag(d2,-1);