# 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) = cos2πf1n + cos2πf2n

Where f1 = 1/18 and f2 = 5/128, modulates the amplitude of the carrier

x0(n) = cos2πf0n

Where f0 = 50/128. The resulting amplitude-modulated signal is

xam(n) = x(n)cos2πf0n

(a) Sketch the signals x(n), x0(n), and xam(n), 0 ≤ n ≤ 255.

(b) Compute and sketch the 128-point DFT of the signal xam(n). 0 ≤ n ≤ 127.

(c) Compute and sketch the 128-point DFT of the signal xam(n). 0 ≤ n ≤ 99.

(d) Compute and sketch the 128-point DFT of the signal xam(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.