Question: Consider the real finite-length sequence x[n] shown in Figure. (a) Sketch the finite-length sequence y[n] whose six-point DFT is? Y[k] = W 6 4k X[k],

Consider the real finite-length sequence x[n] shown in Figure.

x [n] 2 -2 -1 0 1 2 3 4 5 6

(a) Sketch the finite-length sequence y[n] whose six-point DFT is?

Y[k] = W64k X[k],

where X[k] is the six-point DFT of x[n].

(b) Sketch the finite-length sequence w[n] whose six-point DFT is?

W[k] = Re{X [k]}.

(c) Sketch the finite-length sequence q[n] whose three-point DFT is

Q[k] = X[2k], ? ? ? ? ? ? ? k = 0, 1, 2.

x [n] 2 -2 -1 0 1 2 3 4 5 6

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