Question

Find the Nyquist rate and Nyquist interval of sinc[t].

(a) 1 Hz, 1 sec

(b) 2 Hz, 2 sec

(c) \(\frac{1}{2}\) Hz, 2 sec

(d) 2 Hz, \(\frac{1}{2}\)sec

I have been asked this question by my college professor while I was bunking the class.

My question is based upon Sampling topic in division Sampling Theorem of Signals and Systems

Answer 1

The correct choice is (a) 1 Hz, 1 sec

Explanation: We know that sinc[t] ↔ G2π(ω)

Here ωm = 2π

2πfm = π

∴  2fm = 1

Nyquist rate, Fs = 2fm = 1 Hz

Nyquist interval, T = \(\frac{1}{2f_m}\) = 1 sec.