Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
CT Periodic Signal :
$ x(t) = \cos(2\pi t) + \sin(3\pi t)\, $
$ = \frac{e^{2j\pi t}}{2} + \frac{e^{-2j\pi t}}{2} + \frac{e^{3j\pi t}}{2j} - \frac{e^{-3j\pi t}}{2j} \, $
$ \omega_o \, $ = $ \pi \, $
Coefficients of signal:
$ a_2 = \frac{1}{2}\, $
$ a_{-2} = \frac{1}{2}\, $
$ a_{3} = \frac{1}{2j}\, $
$ a_{-3} = -\frac{1}{2j}\, $
Since
$ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $ where
$ a_2 = a_{-2} = \frac{1}{2}\, $
$ a_{3} = -a_{-3}\, $
$ a_k = 0 , k \neq 2,-2,3,-3\, $
Reference -* HW4.1 Wei Jian Chan_ECE301Fall2008mboutin
