% demo of FS constructions
% Jonathan (Y) Stein

% resolution and number of terms
t = (1:1024)/512;
N=15;
close all

% triangular wave
scrsz = get(0,'ScreenSize');
figure(1); set(1, 'Position', [  1 1 scrsz(3)/2 scrsz(4)] );  
figure(2); set(2, 'Position', [ scrsz(3)/2 1 scrsz(3)/2 scrsz(4)] );
y = zeros(size(t));
for i = 1:N
  j = 2*i-1;
  x = cos(2*pi*j*t)/(j*j) ;
  y = y + x;
  figure(1); hold on ; plot ( t, x ) ; 
  title([ '\Sigma_{odd k}  cos(2 \pi k t) / k^2       ' num2str(i) ]);
  figure(2); plot ( t, y ) ;
  if i==N
      title('triangle wave') ;
  end
  pause ;
end
close all

% sawtooth wave
figure(1); set(1, 'Position', [  1 1 scrsz(3)/2 scrsz(4)] );  
figure(2); set(2, 'Position', [ scrsz(3)/2 1 scrsz(3)/2 scrsz(4)] );
y = zeros(size(t));
for i = 1:N
  x = sin(2*pi*i*t)/i ;
  y = y + x;
  figure(1); hold on ; plot ( t, x ) ; 
  title([ '\Sigma_k  sin(2 \pi k t) / k       ' num2str(i) ]);
  figure(2); plot ( t, y ) ;
  if i==N
      title('sawtooth') ;
  end
  pause ;
end
close all

% square wave
%figure(1); set(1, 'Position', [  5 295 500 395]);  
%figure(2); set(2, 'Position', [520 295 500 395]); 
figure(1); set(1, 'Position', [  1 1 scrsz(3)/2 scrsz(4)] );  
figure(2); set(2, 'Position', [ scrsz(3)/2 1 scrsz(3)/2 scrsz(4)] );
y = zeros(size(t));
for i = 1:N
  j = 2*i-1;
  x = sin(2*pi*j*t)/j ;
  y = y + x;
  figure(1); hold on; plot ( t, x ) ;
  title([ '\Sigma_{odd k}  sin(2 \pi k t) / k       ' num2str(i) ]);
  figure(2); plot ( t, y ) ;
  if i==N
      title('square wave') ;
  end
  pause ;
end
close all

% impulse
figure(1); set(1, 'Position', [  1 1 scrsz(3)/2 scrsz(4)] );  
figure(2); set(2, 'Position', [ scrsz(3)/2 1 scrsz(3)/2 scrsz(4)] );
title('impulse'); 
y = zeros(size(t));
for i = 1:N
  i
  x = cos(2*pi*i*t) ;
  y = y + x;
  figure(1); hold on ; plot ( t, x ) ;
  title([ '\Sigma_k  cos(2 \pi k t)       ' num2str(i) ]);
  figure(2); plot ( t, y )
  if i==N
      title('impulse') ;
  end
  pause
end