Question

Calculate the Nyquist rate for the signal x(t) = 12cos50πt + 7 cos75π t – 13 cos100πt.

(a) 300 Hz

(b) 600 Hz

(c) 100 Hz

(d) 150 Hz

The question was posed to me during an online interview.

This question is from Coherent Detection of DSBSC Waves topic in chapter Double Sideband Suppressed Carrier Modulation of Analog Communications

Answer 1

Right answer is (c) 100 Hz

To explain I would say: On comparing with general Equation, Acosωt and substituting ω = 2×π× f. We have f1 = 25 Hz, f2 = 37.5Hz, f3 = 100π/2π  = 50Hz.

Taking the maximum modulating frequency, fmax = 50Hz

Nyquist rate = 2 × fmax  = 2 × 50 = 100 Hz.