Question

(TCO 1) A signal given by 15 Cos (20t) 20 Sin (40t) is sampled at a rate of 15 Hz. Is the Nyquist theorem violated

Answer 1

Fs = 15 Hz > 12.7322 Hz

Hence, Nyquist theorem is NOT violated

Explanation:

Given that;

a signal given by 15cos(20t) + 20sin(40t)

sampled at a rate of 15 Hz

Is the Nyquist theorem violated?

so;

from 15cos(20t) + 20sin(40t)

Freq F1 = 20/2π Hz

F1 = 3.1830 Hz

and

Freq F2 = 40/2π

F2 = 6.3661 Hz

Now, Nyquist's rate FN ≥ 2 × F_max

FN ≥ 2 × 6.3661

FN ≥ 12.7322 Hz

Now our given signal was sampled at a rate of 15 Hz

so, Fs = 15 Hz > 12.7322 Hz

Hence, Nyquist theorem is NOT violated