Frequency-domain sampling the signal x(n) = a|n|, -1 < a < 1 has a Fourier transform X() = 1 a2/1 2a cos +

Frequency-domain sampling the signal x(n) = a|n|, -1 < a < 1 has a Fourier transform X(ω) = 1 – a2/1 – 2a cosω + a2
(a) Plot X(ω) for 0 ≤ ω ≤ 2π, a = 0.8. Reconstruct and plot X(ω) from its samples X(2πk/N), 0 ≤ k ≤ N – 1 for:
(b) N = 20
(c) N = 100
(d) Compare the spectra obtained in parts (b) and (c) with the original spectrum X(ω) and explain the differences.
(e) Illustrate the time-domain aliasing when N = 20.