Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Equations
Fourier series of x(t):
$ x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t} $
Signal Coefficients:
$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $
From Phil Cannon
Input Signal
$ x(t)=cos(3*pi*t)cos(6*pi*t)\! $
$ x(t)=[1/2*e^{j*2*pi*t}+1/2*e^{-j*2*pi*t}]*[1/2*e^{j*4*pi*t}+1/2*e^{-j*4*pi*t}] $
$ =1/4*e^{j6pit}+1/4*e^{-j2pit}+1/4*e^{j2pit}+1/4*e^{-j6pit} $
The fundamental frequency is 2*pi
a3=1/4
a-1=1/4
a1=1/4
a3=1/4
all other ak=0
