Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Definition of Periodic CT Signal
x(t) is periodic if there existes T>0 such that x(t)=x(T+t)
Example
Let's look at: $ x(t)=3*cos(3t) $, we know that the fudamental period of x(t) is
$ w_0=2\pi/T=3 $
$ x(t)=3cos(3t) $
$ =\frac{3}{2}[(e^{j3t})+(e^{-j3t})] $
$ =\frac{3}{2}(e^{j3t})+\frac{3}{2}(e^{-j3t}) $
so we can see that when k=1, $ a_1=\frac{3}{2} $, and when k=-1,$ a_{-1}=\frac{3}{2} $
others are all zero
