Each part of this problem may be solved independently. All parts use the signal x[n] giv...

Each part of this problem may be solved independently. All parts use the signal x[n] given by

x[n] = 3δ[n] − δ[n − 1] + 2δ[n − 3] + δ[n − 4] − δ[n − 6].

(a) Let X(e^jω) be the DTFT of x[n]. Define

Plot the signal r[n] which is the four-point inverse DFT of R[k].

(b) Let X[k] be the eight-point DFT of x[n], and let H[k] be the eight-point DFT of the

impulse response h[n] given by h[n] = δ[n] − δ[n − 4].

Define Y [k] = X[k]H[k] for 0 ≤ k ≤ 7. Plot y[n], the eight-point DFT of Y [k].