# Frequency-domain sampling the signal x(n) = a|n|, -1 < a < 1 has a Fourier transform X() = 1 a2/1 2a cos + a2 (a) Plot X() for 0 2, a = 0.8. Reconstruct and plot X() from

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.

(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.

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**Related Book For**

## Digital Signal Processing

**ISBN:** ?978-0133737622

3rd Edition

**Authors:** Jonh G. Proakis, Dimitris G.Manolakis

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