Question

Find the Nyquist rate and Nyquist interval for the signal f(t)=\(\frac{sin⁡500πt}{πt}\).

(a) 500 Hz, 2 sec

(b) 500 Hz, 2 msec

(c) 2 Hz, 500 sec

(d) 2 Hz, 500 msec

This question was posed to me in an interview for job.

Question is from Sampling in chapter Sampling Theorem of Signals and Systems

Answer 1

Correct choice is (b) 500 Hz, 2 msec

Easy explanation: Given f(t) = \(\frac{sin⁡500πt}{πt}\)

Frequency, ωm = 500π

2πfm = 500π

2fm = 500 Hz

Nyquist rate, Fs = 2fm = 500 Hz

Nyquist interval, T = \(\frac{1}{2f_m} = \frac{1}{500}\) = 2 msec.