% fig30
clear;clc;close all;
N=512;
K=75;

z=zeros(1,N);
z(1,[1:64])=1-([0:63]/64);
z(1,[257:320])=1-([0:63]/64);
subplot(221);plot(z);axis([0 512 -0.2 1.2]);
title('Original Signal: page248 Frazier');

% Fourier compression
% Case K=75
z_hat=fft(z);
zz=fliplr(sort(abs(z_hat)));

thres=zz(1,K);

for k=1:N,
   if (abs(z_hat(k))<thres)
      z_hat(k)=0;
   end;   
end;   

w1=ifft(z_hat);

% Case K=200
z_hat=fft(z);
zz=fliplr(sort(abs(z_hat)));

thres=zz(1,200);

for k=1:N,
   if (abs(z_hat(k))<thres)
      z_hat(k)=0;
   end;   
end;   

w3=ifft(z_hat);


% Wavelet compression (db6)
[c,l] = wavedec(z,4,'db6');
zz=fliplr(sort(abs(c)));

thres=zz(1,K);

for k=1:N,
   if (abs(c(k))<thres)
      c(k)=0;
   end;   
end;

w2 = waverec(c,l,'db6');

% Plotting
subplot(222);plot(real(w1));axis([0 512 -0.2 1.2]);
title('Fourier compression,K=75');
subplot(223);plot(real(w3));axis([0 512 -0.2 1.2]);
title('Fourier compression,K=200');
subplot(224);plot(w2);axis([0 512 -0.2 1.2]);
title('D6 wavelet compression,K=75');