Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Define a periodic CT signal and compute its Fourier series coefficients.
For CT,
$ x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t} $
where
$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $.
Let the signal be
y(t) = 2*sin(2t)+2*cos(4t)
$ y(t) = 2(\frac{e^{j2t} - e^{-j2t}}{2j}) + 2(\frac{e^{2j2t} + e^{-2j2t}}{2}) \! $
$ a_1 = a_-1 = (\frac{1}{j}) $
$ a_2 = a_-2 = 1 $
a_k = 0 elsewhere
