Example of a periodic CT signal
The following is a periodic signal:
$ \,x(t)=(1+j)cos(\pi t)+sin(2\pi t) $
Using Eulers formula, we can interpret this function in terms of exponentials which can then be used to compute the $ a_k $ values for a Fourier series:
$ \,x(t)=(1+j)\frac {e^{j\pi t}+e^{-j \pi t}}{2} + \frac {e^{j2 \pi t}-e^{-j2 \pi t}}{2j} $
$ x(t)=\sum^{\infty}_{k = -\infty} a_k e^{jk\omega_0 t}\, $
