Last updated: 2026-07-02

Nyquist Sampling Rate

Turning a continuous signal into a stream of numbers means measuring its amplitude at regular intervals. How often those measurements must be taken is not a matter of taste: the Nyquist-Shannon sampling theorem fixes a hard lower bound. Sample fast enough and the original signal can be reconstructed exactly; sample too slowly and high frequencies masquerade as low ones, a distortion called aliasing that cannot be removed afterward.

The two Nyquist quantities

Two related numbers come out of the theorem. The Nyquist rate is a property of the signal — the minimum sampling rate you must use — and equals twice the highest frequency present:

The Nyquist frequency is a property of the sampler — the highest frequency a given sampling rate can represent — and equals half the sampling rate:

Aliasing is avoided precisely when the sampling rate is at least the Nyquist rate, which is the same as saying the signal's highest frequency stays at or below the Nyquist frequency:

Worked example

Suppose a signal contains frequencies up to $f_{max} = 20\ \text{kHz}$ — a common model for the upper limit of human hearing. The minimum sampling rate is:

Now check a CD, which samples at $f_s = 44.1\ \text{kHz}$. Its Nyquist frequency is:

Because $44.1\ \text{kHz} \ge 40\ \text{kHz}$ (equivalently $20\ \text{kHz} \le 22.05\ \text{kHz}$), the 20 kHz signal is captured without aliasing, with 2.05 kHz of margin above the audible limit. If instead the signal reached 25 kHz, its Nyquist rate would be 50 kHz, above 44.1 kHz — sampling at CD rate would fold that 25 kHz content down to a false $44.1 - 25 = 19.1\ \text{kHz}$ tone.

What aliasing does

When a frequency exceeds the Nyquist frequency, sampling cannot tell it apart from a lower frequency. A component at $f$ above $f_c$ appears at the mirror image $f_s - f$ (for the first fold), landing inside the represented band as a tone that was never in the original. Because two different input frequencies then map to the same samples, the process is irreversible: no later filtering can separate the real content from the alias. The standard defense is an anti-aliasing filter — an analog low-pass filter applied before sampling that removes everything above the Nyquist frequency, so nothing is left to fold back.

Common sampling rates

Why 44.1 kHz for audio

If human hearing stops near 20 kHz, why not sample at exactly 40 kHz? Real anti-aliasing filters cannot cut off instantly at the Nyquist frequency; they need a transition band over which they roll off. Choosing 44.1 kHz places the Nyquist frequency at 22.05 kHz, leaving roughly 2 kHz of room above the audible range for the filter to attenuate ultrasonic content before it can alias. The specific value 44,100 also arose from early digital recorders that stored audio on video tape, where it divided evenly into the line and frame rates of both PAL and NTSC formats.

Related estimates

Once a sampling rate and bit depth are chosen, the storage cost follows directly — see the Audio File Size Calculator. For lossy media where a target data rate is set instead, the Video Bitrate & File Size Calculator works the size out from the bitrate.