How Do You Compute the DFT of Periodic Signals?

AI Thread Summary
To compute the discrete Fourier transform (DFT) of periodic signals, specific sequences need to be analyzed. For the first case, where x[n] = δ[n], the DFT results in a constant value across all frequencies. In the second case, x[n] = μ[n] - μ[n - K] leads to a DFT that reflects the difference of two step functions, which can be computed using properties of the DFT. The third case, x[n] = cos((2*pi*M*n)/N), results in a DFT that reveals the frequency components of the cosine function. Resources like Wikipedia provide foundational information on DFT that can assist in solving these problems.
ankh
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Homework Statement


Find the discrete Fourier transform X[k] = DFTn {x[n]} of the following
periodic sequences x[n] = x[n - N] with period N:

(a) For n = 0 . . .N - 1 we have x[n] =\delta[n].
(b) For n = 0 . . .N - 1 we have x[n] = \mu[n] -\mu[n - K] with K < N.
(c) x[n] = cos( (2*pi*M*n)/N ).

Homework Equations


We don't have a book for my digital processing class and i missed couple of classes so i have no idea how to start these problems. A little hint or a link to a good tutorial/source would be greatly appreciated.

The Attempt at a Solution

 
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