PROBLEM 2

PART 2: Use wavekit to do transformation and compare

>> function wavekitHaar(f)

[h, g]=wavecoef('Haar');
w = fwt1(f,h,g)

end;

>> x1=[1 0 0 0 0 0 0 0]
x1 =
     1     0     0     0     0     0     0     0
>> wavekitHaar(x1)
w =
    0.3536
    0.3536
    0.5000
         0
    0.7071
         0
         0
         0
>> x2=[1 1 1 1 1 1 1 1]
x2 =
     1     1     1     1     1     1     1     1
>> wavekitHaar(x2)
w =
    2.8284
         0
         0
         0
         0
         0
         0
         0
>> x3=[1 -1 1 -1 1 -1 1 -1];
>> wavekitHaar(x3)
w =
         0
         0
         0
         0
    1.4142
    1.4142
    1.4142
    1.4142
>> x4=[1 1 1 1 -1 -1 -1 -1];
>> wavekitHaar(x4)
w =
         0
    2.8284
         0
         0
         0
         0
         0
         0


PART 3:


%function to compare fft and fwt1 for Hallelujah

function chrpcomp

t = 0 : 65536;
[h,g] = wavecoef('coi', 24);

load('handel.mat')
hallelujah=y(1:65536);

chrpcomf
fixpos

subplot(241); title('Hallelujah');
subplot(242); title('Fourier transform');
subplot(243); title('Wavelet basis');
subplot(244); title('Best wavelet packet basis');
drawnow

watchon;

subplot(241); 
plot(1:65536,hallelujah);
axis square
title('Hallelujah'), xlabel('time')
drawnow

subplot(242); 
plot(1:65536,fft(hallelujah)); 
axis square
title('Fourier transform'), xlabel('frequency')
drawnow

subplot(243);
w1 = wpa1(hallelujah,h,g);
phasepln(wavbasis(w1),h,g)
title('Wavelet basis'), xlabel('time'), ylabel('frequency')
drawnow

subplot(244);
phasepln(bestbase(w1),h,g)
title('Best wavelet packet basis'), xlabel('time'), ylabel('frequency')
drawnow

watchoff;

set(gcf, 'handlevisibility', 'callback')