% Periodic Fourier series, -2 < x < 2 
% Step function at x = 1

format compact;

NptsX=2000;          % number of x pts
Nf=5;              % number of Fourier terms
x=linspace(-5,5,NptsX);

fs=8;
figure(1)
clf

a0=1/4;
a=zeros(1,Nf);
b=zeros(1,Nf);
f=a0*ones(1,NptsX);

for n=1:Nf
    a(n)= -sin(n*pi/2)/(n*pi); % Fourier cosine coefficients
    b(n)=(cos(n*pi/2)-cos(n*pi))/(n*pi);  % Fourier sine coefficients
    fn=a(n)*cos((n*pi*x)/2) + b(n)*sin((n*pi*x)/2);  % Fourier function(n)
    f=f+fn;
end
set(gca,'FontSize',[fs]);
plot(x,f,'b-');
hold on
plot([-5,1],[0,0],'r-');
plot([1,5],[1,1],'r-');
xlabel('x','Fontsize',fs); ylabel('f(x)','Fontsize',fs); axis on; grid;