The spectrum X(ω) for a real bandpass signal x(t) is shown in Fig. P3.3-4. (a) Determine the permissible ranges of the sampling frequency Fs that allow the original signal to be recovered from its...

(a) Determine the permissible ranges of the sampling frequency Fs that allow the original signal to be recovered from its samples.

(b) Sketch X(ω), the spectrum of the sampled signal, for the sampling frequencies F_s
= 5, 6, and 10 kHz. Can we reconstruct x(t) using these sampling rates? How?

(c) What happens if the sampling rate F_s
is slightly below 5 kHz? What if F_s
is just above 6 kHz? How about the case when F_s
is just below 10 kHz?

(d) Consider the sampling rates F_s
= 5.5 and 11 kHz. Determine what happens for both sampling rates, and state, with reasons, which rate is preferable.