Consider the signal x(t) = 3 cos(6πt) + sin(18πt) + 2 cos[(28 − ϵ)πt], where ϵ is a very small number → 0. (a) Sketch X(ω), the spectrum of x(t). Determine the minimum sampling rate required to be...

(a) Sketch X(ω), the spectrum of x(t). Determine the minimum sampling rate required to be able to reconstruct x(t) from these samples.

(b) Does the minimum sampling rate of part (a) change if ϵ = 0? Explain.

(c) Sketch the spectrum of the sampled signal when the sampling rate is 25% above the Nyquist rate (show the spectrum over the frequency range ±50 Hz only). How would you reconstruct x(t) from these samples?