Question

Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz,

a. Sketch the spectrum of the sampled signal up to 20 kHz;

b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal

; c. Determine the frequency/frequencies of aliasing noise

. Q2) Given an analog signal x(t) whose frequency content is given by

?(?) = { 4 |?| ≤ 3 ?? 1 3 < |?| ≤ 5 ?? 0 ??ℎ??????

a) Draw X(f).

b) Draw the spectrum of the sampled signal xs(t) and of the recovered signal y(t) for the following cases. Assume that the signal is recovered from the samples with a low pass filter with a cutoff frequency of 5 Hz. Draw the spectrum from 0 until 20 Hz.

i) Sampling rate is 12 Hz.

ii) Sampling rate is 10 Hz.

iii) Sampling rate is 9 Hz.

c) Comment on the results of parts b (i), (ii), and (iii).