clear all
clc
syms t n aSym(n) bSym(n) x(t) f(t)
tStart = -pi;
tStop = pi;
To = 10*pi;
f(t) = 1;
wo = 2*pi/To;
x(t) = f(t) *(heaviside(t-tStart)-heaviside(t-tStop));
a0 = (int(x(t),t,tStart,tStop)/To)/(2*pi)
aSym(n)  = simplify(int(x(t)*cos(n*wo*t),t,tStart,tStop)/(To/2))
bSym(n)  = simplify(int(x(t)*sin(n*wo*t),t,tStart,tStop)/(To/2))

nMax = 20;
n = 1:nMax;
a = eval(aSym(n));
b = eval(bSym(n));

figure
subplot(3,1,1)
stem(n,a)
ylabel('a(n)');
subplot(3,1,2);
stem(n,b)
ylabel('b(n)');

xApprox = a0;
for m = 1:nMax
    xApprox = xApprox + a(m)*cos(m*wo*t) + b(m)*sin(m*wo*t);
end
t = -20*pi:0.1:20*pi;

xCalc = eval(xApprox);
subplot(3,1,3);
plot(t,xCalc)
grid on
ylabel('x(t)')