close all
clear all 
clc

Tp = 3; % period
om0 = 2*pi/Tp; % omega0
T = 0.001; % sampling spacing
N = 100; % number of Fourier coefficients

t = 0:T:Tp;
s = signal(t);
figure
plot(t,s)
grid
xlabel('t')
ylabel('s(t)')
hold on

% numerical coefficients
for M = [1e3,1e4]
    tfs = zeros(size(t)); % truncated Fourier series
    nT = (0:M-1)*Tp/M;
    snT = signal(nT);
    for k = -N:N % cicle on coefficients
        bk = sum(snT.*exp(-1i*k*om0*nT))/M;
        tfs = tfs +  bk*exp(1i*k*om0*t);
    end
    tfs = real(tfs); % prevent numerical errors
    plot(t,tfs)
end
legend('signal','M=1000','M=10000')
title('approx truncated Fourier series')

% printing figure in png format
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 4.5])
print -dpng homework2.png -r100

function s = signal(t)
t1 = mod(t,3); 
s = t1.*(t1<1) + (t1>=1).*(t1<2);
end