% programita para la serie de senos y cosenos de f(x) = x
% -L \le x \le L
close all
L = 1;
letra=18;

prefix='heaviside';
efe = inline('(x>0)');

a0 = 1/2;

margen = 0.1;

for N = [1 3 5 15]

  n=[1:N];
  a = zeros(1,N);
  b = 1/pi./n .* (1-(-1).^n);

  x = [-L:0.01:L];
  npix = pi*(n'*x)/L;
  fap = a0 + a * cos(npix) + b * sin(npix);

  f = efe(x);

  M = max([f fap]);
  m = min([f fap]);
  plot([-3*L 3*L],[0 0],'b',[0 0],[m M],'b') % ejes
  hold on

  plot(x,f,'r','LineWidth',2)
  plot(x,fap,'m','LineWidth',2)
  
  %title(sprintf('N = %d   error = %.8f',N,max(abs(f-fap))))
  axis([-L-margen L+margen m-margen M+margen])
  set(gca,'FontSize', letra)
  filename=sprintf('fourier-%s-N=%02d',prefix,N); 
  print('-dpng',filename)
  print('-depsc2',filename)
  hold off
  pause
end

pause
ff = f;
xx = x;
xx1 = xx(1:100);
xx2 = xx(102:201);
ff1 = zeros(size(xx1));
ff2 = ones(size(xx2));
plot([-3*L 3*L],[0 0],'b',[0 0],[m M],'b') % ejes
hold on
plot(xx1,ff1,'m','LineWidth',2)
plot(xx2,ff2,'m','LineWidth',2)

plot([-L 0 L], [1/2 1/2 1/2], 'mo', 'MarkerEdgeColor','m','MarkerFaceColor','m', ...
	'MarkerSize', 10)
plot([-L L],[0 0],'b', [0 0],[m M],'b');
axis([-L-margen L+margen m-margen M+margen])
set(gca,'FontSize', letra)
filename=sprintf('fourier-%s-N=inf',prefix);
print('-dpng',filename)
print('-depsc2',filename)
hold off
pause

for N = [15]

  n=[1:N];
  a = zeros(1,N);
  b = 1/pi./n .* (1-(-1).^n);

  x = [-3*L:0.01:3*L];
  npix = pi*(n'*x)/L;
  fap = a0 + a * cos(npix) + b * sin(npix);

  f = efe(x);

  M = max([f fap]);
  m = min([f fap]);
  
  plot([-3*L 3*L],[0 0],'b',[0 0],[m M],'b') % ejes
  hold on
  plot(x,f,'r','LineWidth',2)
  plot(x,fap,'m','LineWidth',2)
  axis([-3*L-margen 3*L+margen m-margen M+margen])
  set(gca,'FontSize', letra)
  filename=sprintf('fourier-%s-N=%02d-3L',prefix,N);
  print('-dpng',filename)
  print('-depsc2',filename)
  hold off
  pause
end

pause

plot([-3*L 3*L],[0 0],'b',[0 0],[m M],'b') % ejes
hold on
plot(xx1-2*L,ff1,'m','LineWidth',2)
plot(xx2-2*L,ff2,'m','LineWidth',2)
plot(xx1,ff1,'m','LineWidth',2)
plot(xx2,ff2,'m','LineWidth',2)
plot(xx1+2*L,ff1,'m','LineWidth',2)
plot(xx2+2*L,ff2,'m','LineWidth',2)
plot([-3*L -2*L -L 0 L 2*L 3*L], ones(1,7)/2, 'mo', 'MarkerEdgeColor','m','MarkerFaceColor','m', ...
	'MarkerSize', 10)

axis([-3*L-margen 3*L+margen m-margen M+margen])

set(gca,'FontSize', letra)
filename=sprintf('fourier-%s-N=inf-3L',prefix);
print('-dpng',filename)
print('-depsc2',filename)