Hi Faisal
Running the code:
syms n t
T = 2;
w = 2*pi/T;
% Exponential Fourier series
C(n) = (1/T)*(int(4*exp(-1i*w*n*t),t,0,1)+int(-4*exp(-1i*w*n*t),t,1,2));
C0 = limit(C(n),n,0); % C(0)
Harmonics = [C0 C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12)];
%fprintf('First 13 Harmonics:\n')
%disp(Harmonics)
% f(t) using Fourier Series representation
f(t) = symsum(C(n)*exp(1i*w*n*t),n,-100,-1)+C0+symsum(C(n)*exp(1i*w*n*t),n,1,100);
fplot(t,f(t),[0 5])
xlabel('t')
ylabel('f(t)')
title('f(t) using Fourier Series Coefficients')
grid on
The code returns a square wave, but doesn't seem to be the signal in the problem:
the max and min are +-4, but should be +-1
the fundamental period is 4, but it should be 8.
the switch from high to low should be at t = 2, not t = 1.
I suggest you revisit the code, define T0 and T1 as variables and assign to them the given values, and then carefully rewrite C(n) using T0 and T1 as needed using the definition of x(t). Better yet, consider defining x(t) as an expression defined in the problem, and then use x(t) in expression for C(n). To that end, have a look at the function
doc rectangularPulse
