Example of Computation of Fourier series of a CT SIGNAL

A practice problem on "Signals and Systems"


Define a periodic CT signal and compute its Fourier series coefficients.

For CT,

$ x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t} $

where

$ a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt $.

Let the signal be

y(t) = 2*sin(2t)+2*cos(4t)

$ y(t) = 2(\frac{e^{j2t} - e^{-j2t}}{2j}) + 2(\frac{e^{2j2t} + e^{-2j2t}}{2}) \! $

$ a_1 = a_-1 = (\frac{1}{j}) $

$ a_2 = a_-2 = 1 $

a_k = 0 elsewhere


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Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood