Question

The Nyquist frequency for the signal x (t) = 3 cos 50πt + 10 sin 300πt – cos 100t is ___________

(a) 50 Hz

(b) 100 Hz

(c) 200 Hz

(d) 300 Hz

The question was posed to me during an interview for a job.

I'm obligated to ask this question of Discrete-Time Fourier Transform topic in section Fourier Transform of Signals and Systems

Answer 1

The correct choice is (d) 300 Hz

Explanation: We know that Nyquist frequency is twice the maximum frequency, i.e.  fs = 2 fm.

The maximum frequency present in the signal is ωm = 300 π or fm = 150 Hz. Therefore the Nyquist frequency fs = 2 fm = 300 Hz.