HW4.1 Hang Zhang ECE301Fall2008mboutin - Rhea

Example of Computation of Fourier series of a CT SIGNAL

A practice problem on "Signals and Systems"

Periodic CT Signal

$ x(t) = \frac{4\pi}{3} + \frac{1}{2}sin(1000\pi t) - cos(1000\pi t) \ $

Rewritten in $ e^{jw_0} $ Form

$ x(t) = \frac{4\pi}{3} + \frac{1}{j2000}(e^{j1000\pi t}+e^{j-1000\pi t}) - \frac{1}{j1000}(e^{j1000\pi t}-e^{j-1000\pi t}) $

Fourier Series Coefficients

$ a_0 = \frac{4\pi}{3} $

$ a_1 = \frac{1}{1000} $

$ w_0 = 1000\pi\ $

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