Illustrate the discrete-time fourier transform

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Reference no: EM131674613

Question 1:

A certain analog signal xa (t) has the following real Fourier transform:

                1, |Ω|≤8Π
Xa(jΩ) =
                0, otherwise

(a) Illustrate Xa(jΩ)

(b) Carefully illustrate the discrete-time Fourier transform of the discrete-time signal x(n) define by x(n) = xa(nT) for the case T = 1/16sec and T = 1/4 sec.

(c) Is xa(t)band limited? If so, find the Nyquist rate. If not, tell why not.

Question 2:

Let x[n], 0 ≤ n ≤ N - 1 be an even-length sequence with an N-point DFT X[k], 0 ≤ k ≤ N - 1. Determine the N-point DFTs of the following length-N sequences in terms of X[k]:

(a) u[n] = x[n] - x[n - N/2]

(b) y[n] = x[n] + x[n - N/2]

(c) y[n] = (-1)nx[n]

Reference no: EM131674613

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