Question

For the signal f(t) = 3 sin 8πt + 6 sin 12πt + sin 14πt, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is -----------.

Answer 1

Concept:

Nyquist rate is the minimum rate at which a signal can be sampled without introducing errors, which is twice the highest frequency present in the signal.

Nyquist rate = 2 × highest frequency present in the signal

fs = 2fm

The condition on the sampling interval is: fs > 2fm

Calculation:Ts<12Tm

f(t) = 3 sin 8πt + 6 sin 12πt + sin 14πt

Nyquist criteria says that

Sampling frequency, f_s > 2f _max

f_max  →  maximum frequency of message signal.

Maximum frequency is given signal, ω_max = 14 π

⇒  f_max = 7

∴ sampling frequency, f_s > 2 × 7

f_s > 14

∴ minimum sampling frequency is 14 Hz