# Frequency analysis of amplitude-modulated discrete-time signal the discrete-time signal x(n) = cos2 f 1 n + cos2 f 2 n Where f 1 = 1/18 and f 2 = 5/128, modulates the amplitude of the carrier x 0 (n) = cos2 f 0 n Where f 0 = 50/128. The resulting amplitude-modulated signal is x am (n) = x(n)cos2 f

Frequency analysis of amplitude-modulated discrete-time signal the discrete-time signal

x(n) = cos2π*f _{1}*n + cos2π

*f*n

_{2}Where *f _{1}* = 1/18 and

*f*= 5/128, modulates the amplitude of the carrier

_{2}x_{0}(n) = cos2π*f _{0}*n

Where *f _{0}* = 50/128. The resulting amplitude-modulated signal is

x_{am}(n) = x(n)cos2π*f _{0}*n

(a) Sketch the signals x(n), x_{0}(n), and x_{am}(n), 0 ≤ n ≤ 255.

(b) Compute and sketch the 128-point DFT of the signal x_{am}(n). 0 ≤ n ≤ 127.

(c) Compute and sketch the 128-point DFT of the signal x_{am}(n). 0 ≤ n ≤ 99.

(d) Compute and sketch the 128-point DFT of the signal x_{am}(n). 0 ≤ n ≤ 179.

(e) Explain the results obtained in parts (b) through (d), by deriving the spectrum of the amplitude-modulated signal and comparing it with the experimental results.

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## Digital Signal Processing

3rd Edition

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

**ISBN:** ?978-0133737622