% demo of FS constructions

% Jonathan (Y) Stein

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

% get Chinese gong sound from toolbox demos
load('\matlab\toolbox\matlab\sounds\gong.mat');
gong=y;


% sawtooth wave
figure(1); set(1, 'Position', [  5 200 390 350]); title('sawtooth'); 
figure(2); set(2, 'Position', [400 200 390 350]); 
'SUM_i  sin(2 pi i t) / i'
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 ) ; 
  figure(2); plot ( t, y ) ;
  i
  pause ;
end
sound(gong,8192);
pause;

% square wave
figure(3); set(3, 'Position', [  5 200 390 350]); title('square wave'); 
figure(4); set(4, 'Position', [400 200 390 350]); 
'SUM_{odd i}  sin(2 pi i t) / i'
y = zeros(size(t));
for i = 1:N
  j = 2*i-1;
  x = sin(2*pi*j*t)/j ;
  y = y + x;
  figure(3); hold on; plot ( t, x ) ;
  figure(4); plot ( t, y ) ;
  i
  pause ;
end
sound(gong,8192);
pause;

% triangular wave
figure(5); set(5, 'Position', [  5 200 390 350]); title('triangle wave'); 
figure(6); set(6, 'Position', [400 200 390 350]); 
'SUM_{odd i}  cos(2 pi i t) / i^2'
y = zeros(size(t));
for i = 1:N
  j = 2*i-1;
  x = cos(2*pi*j*t)/(j*j) ;
  y = y + x;
  figure(5); hold on ; plot ( t, x ) ; 
  figure(6); plot ( t, y ) ;
  i
  pause ;
end
sound(gong,8192);
pause;

% impulse
figure(7); set(7, 'Position', [  5 200 390 350]); title('impulse'); 
figure(8); set(8, 'Position', [400 200 390 350]); 
'SUM_i  cos(2 pi i t)'
y = zeros(size(t));
for i = 1:N
  i
  x = cos(2*pi*i*t) ;
  y = y + x;
  figure(7); hold on ; plot ( t, x ) ;
  figure(8); plot ( t, y )
  pause
end
sound(gong,8192);