Answer:
Fs = 15 Hz > 12.7322 Hz
Hence, Nyquist theorem is NOT violated
Step-by-step 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
