Difference between revisions of "HW4.1 Justin Kietzman ECE301Fall2008mboutin" - Rhea

Latest revision as of 09:53, 16 September 2013

Example of Computation of Fourier series of a CT SIGNAL

A practice problem on "Signals and Systems"

Useful Info

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

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

Let

$ x(t) = 2sin(2\pi t) + cos(\pi t). $

Solution

$ x(t) = 2\frac{e^{2 \pi jt}+e^{-2 \pi jt}}{2j} + \frac{e^{\pi jt}+e^{-\pi jt}}{2} $

$ x(t) = \frac{1}{j}(e^{2 \pi jt} + e^{-2 \pi jt}) + \frac{1}{2}(e^{\pi jt}+e^{-\pi jt}) $

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

$ a_2 = \frac{1}{2} $

$ \omega_0 = \frac{2\pi}{T} = \frac{2\pi}{2\pi} = 1 $

else

$ a_k = 0 $

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