Difference between revisions of "HW4.2 Zachary Curosh ECE301Fall2008mboutin" - Rhea

Revision as of 10:35, 25 September 2008

Define a Periodic DT Signal and Compute the Fourier Series Coefficients

I am going to choose a sine signal, since there have been many cosines done already.

DT signal: $ x[n] = 2\sin(\pi n + \frac{\pi}{2}) + 4\sin(\frac{\pi}{2} n + \pi)\, $

Now, each sine has its own period, and the fundamental period of the function is the greater of the separate periods.

$ N_2sin = \frac{2\pi}{\pi} k = \frac{2}{1} k $

$ N_4sin = \frac{2\pi}{\frac{\pi}{2}} k = \frac{2}{\frac{1}{2}} k $

Take $ k = 1\, $,

$ N_2sin = 2\, $

$ N_4sin = 4\, $, so the overall fundamental period is

$ N = 4\, $

In order to find the coefficients, we must first calculate the values of $ x[n]\, $ for four consecutive integer values of $ n\, $. By plugging values of $ n\, $ into the given signal, we find that

$ x[0] = 2\, $

$ x[1] = -6\, $

$ x[2] = 2\, $

$ x[3] = 2\, $

$ x[4] = 2\, $

$ x[5] = -6\, $

$ x[6] = 2\, $

$ x[7] = 2\, $

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