Nyquist Sampling Rate

Formula

Description

The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a band-limited signal, the sampling rate must be at least twice the highest frequency component in the signal. Sampling below this rate causes aliasing, where high-frequency components fold back into the sampled bandwidth as spurious lower-frequency signals that cannot be removed. This is why audio CDs sample at 44.1 kHz (just over 2 × 20 kHz human hearing limit) and why anti-aliasing filters are placed before ADC inputs to remove frequencies above fs/2.

Variables

• fs_min — Minimum sampling frequency (Hz)
• fmax — Maximum signal frequency (Hz)

Practical Notes

In practice, sample at 2.5-10x the maximum frequency to ease anti-aliasing filter requirements and improve reconstruction quality. Oversampling (sampling much faster than Nyquist) trades speed for resolution and simplifies analog filter design. Sigma-delta ADCs exploit extreme oversampling (64-256x) followed by digital decimation filtering.