for M=[5 10 20 40 80 160]
  t=0:0.001:2*pi;
  e=exp(1);
  N=length(t);
  x=zeros(1,N);
  x(1:N/2)=1;
  xa=zeros(1,N);
  for k=-M:M
      if (k==0)
          a=0.5;
      elseif (floor(k/2)*2==k)
          a=0;
      else
          a=-i/(pi*k);
      end
      xa=xa+a*e.^(i*t*k);
  end;
  xa=real(xa);
  max(xa)
  figure
  plot(t,x,t,xa)
  axis([0,2*pi,-0.2,1.2]);
  title(strcat('Partial sum of Fourier series M = '...
      ,int2str(M)),'FontName', 'Arial CE');
  xlabel('t');ylabel('x(t), x_a(t)');
end;