Do not use Al or ChatGPT; I want a solution from a qualified expert. Given an analog signal X(t) = 5 cos(4000nt) +1 cos(10000πt) which is sampled at a rate of 8,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz. b. Sketch the recovered analog signal spectrum if an ideal LPF with a cutoff frequency of 4 kHz is used to recover the original signal. Then explain at which frequency that aliasing noise occurs. c. Can we recover the original spectrum in the receiver without distortion, then if not, explain at which frequency that aliasing noise occurs.

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