Question

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

(a) 2 Hz, 2 sec

(b) 1 Hz, 1 sec

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

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

The question was asked during an internship interview.

The doubt is from Sampling topic in portion Sampling Theorem of Signals and Systems

Answer 1

Right choice is (b) 1 Hz, 1 sec

For explanation I would say: Nyquist rate and Nyquist interval are independent of Amplitude (magnitude scaling). But time scaling will change the rate.

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.

∴Fs = 1 Hz, T = 1 sec.