Difference between revisions of "HW4.1 Josh Long ECE301Fall2008mboutin" - Rhea

Latest revision as of 11:03, 16 September 2013

Example of Computation of Fourier series of a CT SIGNAL

A practice problem on "Signals and Systems"

The Signal

mmm lets randomly take...

$ \sin4\pi t + \cos3\pi t + e^{j2\pi t} $

The Coefficients

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

$ a_k=\frac{1}{T} \int_0^Tx(t)e^{-jk\omega_ot}dt $

Going to conver the equation into signal that is all in exponentials.

$ \frac{1}{2j}(e^{j4\pi t}-e^{-j4\pi t}) + \frac{1}{2}(e^{j3\pi t} + e^{-j3\pi t}) + e^{j2\pi t} $

The terms come out to be

$ 4, -4, 3, -3, and 2 $

$ a_4 = \frac{1}{2j} $ $ a_-4 = \frac{1}{2j} $ $ a_3 = \frac{1}{2} $ $ a_-3 = \frac{1}{2} $ $ a_2 = 1 $

$ a_k = 0, k \ne 4, -4, 3, -3, 2 $

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