% C. Talarico
% file: fourierseries.m

clear all; close all; clc;

syms t n;

A = 3;
T = 4;
w0 = 2*pi/T;
n = 1:20;

a0 = (1/T)*int(A,t,0,T/2);
an = (2/T)*int(A*cos(n*w0*t),t,0,T/2);
bn = (2/T)*int(A*sin(n*w0*t),t,0,T/2);
a0 = double(vpa(a0));
an = double(vpa(an));
bn = double(vpa(bn));

t=-6:1e-6:6;
x = [-6 -4 -4 -2 -2 0 0 2 2 4 4 6];
y = [0 0 A A 0 0 A A 0 0 A A];
ylim ([-1 4]);
f = a0;
figure(1)
for n = 1:1;
f = f+an(n)*cos(w0*n.*t)+bn(n)*sin(w0*n.*t);
hold on;
plot(x,y,'-',t,f,'-r')
xlabel ('t', 'fontsize',16,'fontname', 'Helvetics');
ylabel ('f(t)','fontsize',16,'fontname', 'Helvetica');
ax = gca;
set(ax,'fontsize',14,'fontname', 'Monospace');
title('f(t) approximation for n = 1', 'fontsize',16,'fontname', ...
    'Monospace','fontweight','Bold');
end

f = a0;
figure(2)
for n = 1:3;
f = f+an(n)*cos(w0*n.*t)+bn(n)*sin(w0*n.*t);
end
plot(x,y,'-',t,f,'-r');
xlabel ('t', 'fontsize',16,'fontname', 'Monospace');
ylabel ('f(t)','fontsize',16,'fontname', 'Monospace');
ax = gca;
set(ax,'fontsize',14,'fontname', 'Monospace');
title('f(t) approximation for n = 3', 'fontsize',18,'fontname', ...
    'Monospace');

f = a0;
figure(3)
for n = 1:20;
f = f+an(n)*cos(w0*n.*t)+bn(n)*sin(w0*n.*t);
end
plot(x,y,'-',t,f,'-r')
xlabel ('t', 'fontsize',16,'fontname', 'Monospace');
ylabel ('f( t )','fontsize',16,'fontname', 'Monospace');
ax = gca;
set(ax,'fontsize',14,'fontname', 'Monospace');
title('f(t) approximation for n = 20', 'fontsize',16,'fontname', ...
    'Monospace','fontweight','Bold');