# Figura 7.1
close all;
for M=3:10
  N=2^M;
  k = 3;
  Ek = shift([1 zeros(1,N-1)],k);
  Fk = ifft(Ek);
  plot(linspace(0,1,N),real(Fk),linspace(0,1,N),imag(Fk));
  axis([0 1 -1.1*max(real(Fk)) 1.1*max(real(Fk))]);
  drawnow;
  pause(1);
endfor

# Outra visualização: funções básicas de Fourier
close all;
for k=1:64
  Ek = shift([1 zeros(1,N-1)],k);
  Fk = ifft(Ek);
  plot(linspace(0,1,N),real(Fk),linspace(0,1,N),imag(Fk));
  axis([0 1 -1.1*max(real(Fk)) 1.1*max(real(Fk))]);
  title(sprintf("%da funcao basica de Fourier",k));
  drawnow;
  pause(0.5);
endfor


# Figura 7.2
close all;
for M=3:10
  N=2^M;
  k=6;
  Ek = shift([1 zeros(1,N-1)],k);
%  F = "Haar";
%  F = "Le Gall 5/3";
  F = "Daubechies 4-tap";
  Fk=idwt(Ek,M,F);
  plot(linspace(0,1,N),Fk);
  axis([0 1 -1.1*max(Fk) 1.1*max(Fk)]);
  drawnow;
  pause(1);
endfor

# Outra visualização: funções básicas
close all;
for k=1:64
  Ek = shift([1 zeros(1,N-1)],k);
%  F = "Haar";
%  F = "Le Gall 5/3";
  F = "Daubechies 4-tap";
  Fk=idwt(Ek,M,F);
  plot(linspace(0,1,N),Fk);
  axis([-0.1 1.1 -1.1*max(Fk) 1.1*max(Fk)]);
  title(sprintf("%da funcao basica de %s",k,F));
  drawnow;
  pause(1);
endfor


# Figura 7.3
close all;
for M=3:10
  N=2^M;
  #x=idwt(shift([1 zeros(1,N-1)],7),M,"Daubechies 4-tap");
  x = invfullwave(shift([1 zeros(1,N-1)],7),M-2,"d4");
  plot(linspace(0,1,N),x);
  axis([0 1 -1.1*max(x) 1.1*max(x)]);
  drawnow;
  pause(0.5);
endfor

# Outra visualização: funções básicas
close all;
for j=1:64
  x=idwt(shift([1 zeros(1,N-1)],j-1),M,"Daubechies 4-tap");
  #x = invfullwave(shift([1 zeros(1,N-1)],j-1),M-2,"d4");
  plot(linspace(0,1,N),x);
  axis([0 1 -1.1*max(x) 1.1*max(x)]);
  title(sprintf("j=%d",j-1));
  drawnow;
  pause(0.5);
endfor



# Repetindo a idéia para os filtros Le Gall 5/3
close all;
for M=3:10
  N=2^M;
  x=idwt(shift([1 zeros(1,N-1)],7),M-2,"Le Gall 5/3");
  plot(linspace(0,1,N),x);
  axis([0 1 -1.1*max(x) 1.1*max(x)]);
  drawnow;
  pause(0.5);
endfor

# Outra visualização: funções básicas
close all;
for j=1:64
  x=idwt(shift([1 zeros(1,N-1)],j-1),M-2,"Le Gall 5/3");
  plot(linspace(0,1,N),x);
  axis([0 1 -1.1*max(x) 1.1*max(x)]);
  title(sprintf("j=%d",j-1));
  drawnow;
  pause(0.5);
endfor



# Exemplo 7.1, Figuras 7.7 e 7.8
close all;
N=2^12;
t = linspace(0,1,N);
f = t.*(1-t).*(2-t);
figure(1);
plot(t,f);
axis([0 1 0 0.5]);
title("Funcao original");

close all;
f0 = (1/N)*sum(f)*ones(1,N);;
plot(t,f0);
axis([0 1 0 0.5]);
title("Aproximacao f_0");

close all;
K=8;
for k=0:K
  for n=0:(2^k-1)
    psikn = zeros(1,N);
    psikn((N*n/(2^k)+1):(N*(n+1/2)/(2^k))) = 2^(k/2);
    psikn((N*(n+1/2)/(2^k)+1):(N*(n+1)/(2^k))) = -2^(k/2);
    ckn = (1/N)*sum(f.*psikn);
    f0 += ckn*psikn;
  endfor;
  plot(t,f0);
  axis([0 1 0 0.5]);
  title(sprintf("Aproximacao f_%d",k+1));
  pause(0.5);
endfor


c0 = 1+sqrt(3); c1 = 3+sqrt(3); c2 = 3-sqrt(3); c3 = 1-sqrt(3);
c = (1/(4*sqrt(2)))*[ c0 c1 c2 c3 ];

[phi,psi,t] = dyadicortho(c,10);
figure(1);
plot(t,phi);
figure(2);
plot(t,psi);

l = [ -1/8 1/4 3/4 1/4 -1/8 ];
#h = [ -1/2 1 -1/2 ];
[phi,psi,t] = dyadicortho(l,10);
figure(1);
plot(t,phi);
figure(2);
plot(t,psi);