Revision as of 11:22, 25 September 2008 by Zcurosh (Talk)

Define a periodic DT signal

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

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

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