As per Nyquist theorem, to reproduce the original analog signal one necessary…
2022
As per Nyquist theorem, to reproduce the original analog signal one necessary condition is that the sampling rate be at least ……… the highest frequency present in the original signal.
- A.
twice
- B.
equal to
- C.
half of
- D.
four times
Attempted by 360 students.
Show answer & explanation
Correct answer: A
If a continuous-time (analog) signal contains frequency components only up to a maximum frequency fₘₐₓ, then perfect reconstruction from samples requires:
fₛ ≥ 2fₘₐₓ
where fₛ is the sampling frequency.
If fₛ < 2fₘₐₓ, the replicated spectra overlap. This is aliasing, and the original signal cannot be uniquely recovered.
If fₛ ≥ 2fₘₐₓ, the spectra remain separate and an ideal low-pass filter can reconstruct the original signal.