A system has a sampling rate of 50,000 samples per second. The maximum frequency of the signal it can acquire to reconstruct is

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 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 f_s = 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