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| − | == Define a | + | == 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. | I am going to choose a sine signal, since there have been many cosines done already. | ||
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<math>N_4sin = 4\,</math>, so the overall fundamental period is | <math>N_4sin = 4\,</math>, so the overall fundamental period is | ||
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<math>N = 4\,</math> | <math>N = 4\,</math> | ||
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| + | In order to find the coefficients, we must first calculate the values of <math>x[n]\,</math> for four consecutive integer values of <math>n\,</math> | ||
Revision as of 11:24, 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 + \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\, $
In order to find the coefficients, we must first calculate the values of $ x[n]\, $ for four consecutive integer values of $ n\, $
