A system has a sampling rate of 50,000 samples per second. The ma
| A system has a sampling rate of 50,000 samples per second. The maximum frequency of the signal it can acquire to reconstruct is
A. 25 kHz
B. 50 kHz
C. 100 kHz
D. 10 kHz
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Nyquist Sampling Theorem:
A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to the twice the highest frequency component of the message signal, i.e.
fs ≥ 2fm
Therefore when we want to convert continuous signals to discrete signals, the sampling must be done at the Nyquist rate.
Application:
Given fs = 50 k
We can write:
\(50k \ge 2 \times f_m\)
\({f_m} \leq 25k\)
∴ The maximum frequency of the signal it can acquire to reconstruct is 25 kHz