Nyquist-Shannon Sampling

Electrical Engineering

How It Works

The Nyquist-Shannon sampling theorem establishes the mathematical conditions under which a continuous-time analog signal can be perfectly digitized and subsequently reconstructed without information loss. A bandlimited signal with maximum frequency bandwidth B must be sampled at a rate f_s strictly greater than twice its highest frequency (the Nyquist rate f_N = 2B). If the sampling frequency falls below this critical threshold, higher frequency components overlap with baseband replicas, creating irreversible spectral distortion known as aliasing.

Governing Equation
f_s ≥ 2 · B_max   |   x(t) = ∑_{n=-∞}^{∞} x(n T_s) · sinc(π(t - n T_s) / T_s)   |   T_s = 1 / f_s