Nyquist Frequency & Aliasing Calculator

How it works

Nyquist frequency f_N = f_s ÷ 2 · minimum sampling rate = 2 × f_max · alias frequency = |f − f_s × round(f ÷ f_s)| · Nyquist zone = ⌊f ÷ f_N⌋ + 1 · oversampling ratio = f_s ÷ (2 f)

The Nyquist–Shannon sampling theorem says a signal can be rebuilt from its samples only if it contains no frequencies at or above half the sampling rate, the Nyquist frequency. Anything higher folds back (aliases) into the 0 to f_N band and becomes indistinguishable from a real low-frequency tone, which is why ADCs sit behind an anti-aliasing low-pass filter. In practice designers sample at 2.2 to 10 times the highest frequency of interest so the filter has room to roll off.

Worked example

Audio sampled at 44.1 kHz has a Nyquist frequency of 22.05 kHz. A 30 kHz tone is above it, so it needs at least 60 kHz sampling; at 44.1 kHz it folds to |30 − 44.1| = 14.1 kHz, an audible alias in Nyquist zone 2. The sampling period is 22.68 µs.

Sources: Analog Devices — MT-002: What the Nyquist Criterion Means to Your Sampled Data System Design · Wikipedia — Nyquist–Shannon sampling theorem

Frequently asked questions