File:Square wave summation animation.gif

English: The animation shows the square wave being constructed. The blue curve is the summation of the previous frequencies while the red curve is the frequency that is currently added.

freq = 1/(2*pi); x = 0:0.01:2*pi; figure(1) filename = 'image.gif'; flag_first = 1 map = @(x) -2*x.^3+3*x.^2 % maps [0,1] to [0,1] for n = 1:8

   s = @(x,k) bsxfun(@rdivide,sin(bsxfun(@times,2*pi*(2*k-1)*freq,x)),(2*k-1));
   f = @(x,t) 4/pi * (sum(s(x,[1:n-1]'),1) + t*sin(2*pi*(2*n-1)*x*freq)/(2*n-1));
   for t = map(linspace(0,1,18-n))
       clf
       hold on
       plot(x,f(x,t))
       plot(x,t*4/pi*sin(2*pi*(2*n-1)*x*freq)/(2*n-1),'r-')
       axis([0,2*pi,-1.5,1.5]);
       text(-0.2,1.5,['f = ',num2str(2*n-1)])
       set(gcf,'color',[1 1 1]);
       axis off
       hold off
       drawnow
       frame = getframe(1);
       im = frame2im(frame);
       [imind,cm] = rgb2ind(im,256);
       if flag_first == 1;
           imwrite(imind,cm,filename,'gif', 'Loopcount',inf, 'DelayTime',0.1);
           flag_first = 0;
       else
           imwrite(imind,cm,filename,'gif','WriteMode','append','DelayTime',0.1);
       end
   end

end