(Solution) - Frequency analysis of amplitude modulated discrete time signal -(2025 Original AI-Free Solution)

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Frequency analysis of amplitude-modulated discrete-time signal the discrete-time signal
x(n) = cos2?f1n + cos2?f2n
Where f1 = 1/18 and f2 = 5/128, modulates the amplitude of the carrier
x0(n) = cos2?f0n
Where f0 = 50/128. The resulting amplitude-modulated signal is
xam(n) = x(n)cos2?f0n
(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.