Difference between revisions of "HW4.1 Naman Anand Verma ECE301Fall2008mboutin" - Rhea

Latest revision as of 10:09, 16 September 2013

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

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