a. The highest frequency in the spectrum X (ω) (Fig. P8.1-8a) of a bandpass signal x (t) is 30 Hz. Hence, the minimum sampling frequency needed to sample x (t) is 60 Hz. Show the spectrum of the signal sampled at a rate of 60 Hz. Can you reconstruct x (t) from these samples? How?
b. A certain busy student looks at X (ω), concludes that its bandwidth is really 10 Hz, and decides that the sampling rate 20 Hz is adequate for sampling x (t). Sketch the spectrum of the signal sampled at a rate of 20 Hz. Can she reconstruct x (t) from these samples?
c. The same student, using the same reasoning, looks at Y (ω) in Fig. P8.1-8b, the spectrum of another bandpass signal y (t), and concludes that she can use sampling rate of 20 Hz to sample y (t). Sketch the spectrum of the signal y (t) sampled at a rate of 20 Hz. Can she reconstruct y (t) from these samples?