Question

Find the Nyquist rate and Nyquist interval for the signal f(t) = -10 sin ⁡40πt  cos ⁡300πt.

(a) 40 Hz, 40 sec

(b) 340 Hz, 340 sec

(c) 300 Hz, 300 sec

(d) 340 Hz, \(\frac{1}{340}\) sec

I have been asked this question in exam.

Query is from Sampling in section Sampling Theorem of Signals and Systems

Answer 1

Correct answer is (d) 340 Hz, \(\frac{1}{340}\) sec

To elaborate: sin ⁡40πt has highest frequency ωm1 = 40π

cos⁡300πt has highest frequency ωm2 = 300π

As we know, multiplication in time domain is equivalent to convolution in frequency domain, the convoluted spectra will have highest frequency component ωm = ωm1 + ωm2 = 40π + 300π

ωm = 340π

2πfm = 340π

2fm = 340

Nyquist rate, Fs = 2fm = 340 Hz

Nyquist interval, T = \(\frac{1}{F_s} =\frac{1}{340}\) sec.