Difference between revisions of "HW4.1 Wei Jian Chan ECE301Fall2008mboutin" - Rhea

Revision as of 09:23, 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(3\pi t) + \sin(4\pi t)\, $

$ x(t) = \cos(3\pi t) + \sin(4\pi t)\, $

$ = \frac{e^{3j\pi t}}{2} + \frac{e^{-3j\pi t}}{2} + \frac{e^{4j\pi t}}{2j} - \frac{e^{-4j\pi t}}{2j} \, $

I take $ \omega_o \, $ as $ \pi \, $ since both functions have a period based on it.

The following is the coefficient of the signal:

$ a_3 = \frac{1}{2}\, $

$ a_{-3} = \frac{1}{2}\, $

$ a_{4} = \frac{1}{2j}\, $

$ a_{-4} = -\frac{1}{2j}\, $

We can write the function in the following illiterations:

$ x(t) = \sum^{\infty}_{k = -\infty} a_k e^{jk\pi t}\, $ where

$ a_3 = a_{-3} = \frac{1}{2}\, $

$ a_{4} = \frac{1}{2j} = -a_{-4}\, $

$ a_k = 0 , k \neq 3,-3,4,-4\, $

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