What is the Nyquist sampling theorem?

The Nyquist-Shannon theorem states that to perfectly reconstruct a band-limited signal, you must sample it at a rate at least twice its highest frequency component (fs ≥ 2 × f_max). The minimum rate 2 × f_max is called the Nyquist rate.

Aliasing occurs when a signal is sampled below its Nyquist rate. Frequency components above fs/2 fold back into the spectrum and appear as lower-frequency imposters, corrupting the reconstructed signal. An anti-aliasing low-pass filter before the ADC prevents this.

What is the Nyquist frequency vs. Nyquist rate?

The Nyquist rate is the minimum sample rate needed to capture a signal: 2 × f_max. The Nyquist frequency (also called the folding frequency) is half the sample rate, fs/2 — the highest frequency a given sample rate can represent without aliasing.

Why do real systems sample faster than the Nyquist minimum?

In practice, real-world filters cannot perfectly remove all energy above f_max, so engineers add a guard band by sampling at 4× to 10× the maximum signal frequency. Audio CDs sample at 44.1 kHz for 20 kHz audio — a factor of about 2.2×.

Does this apply to images and video?

Yes. The theorem generalizes to 2D (images) and time (video). Spatial aliasing causes moiré patterns; temporal aliasing (strobing) makes spinning wheels appear to turn backward. Anti-aliasing filters or supersampling techniques address both.

Nyquist Sampling Rate Calculator

Enter a signal frequency to get the minimum sample rate, or enter a sample rate to find the maximum recoverable frequency — with aliasing explained.

Mode

Signal Frequency (f_max)

Presets

Result

Enter a value and click Calculate.

Aliasing — What Happens Below the Nyquist Rate

When sampling rate fs < 2 × f_max, frequency components above fs/2 fold back into the spectrum. A 1.2 kHz tone sampled at 2 kHz (Nyquist: 1 kHz) reappears as a false 0.8 kHz tone — an alias.

An anti-aliasing filter (low-pass, cutoff at fs/2) placed before the ADC eliminates this by removing energy above the Nyquist frequency before sampling occurs.

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Summary

The Nyquist Sampling Rate Calculator applies the Nyquist-Shannon theorem to compute the minimum sample rate required to faithfully capture a signal (fs_min = 2 × f_max), or the maximum recoverable frequency for a given sample rate (f_max = fs / 2). Enter a frequency or sample rate in Hz, kHz, or MHz and the result updates instantly. Presets for common systems — CD audio, telephony, and RF — give real-world reference points. The aliasing explainer shows what happens when sampling falls short of the Nyquist rate.

How it works

Choose a mode: "Frequency → Sample Rate" to find the minimum sampling rate, or "Sample Rate → Max Frequency" to find the Nyquist frequency.
Enter the signal frequency or sample rate value and select the unit (Hz, kHz, MHz).
The result and Nyquist frequency appear instantly.
Read the aliasing section to understand what happens when sampling below the Nyquist rate.
Use the presets (audio CD, telephone, Wi-Fi, etc.) as reference starting points.

Use cases

Determine the correct ADC sample rate when digitizing an analog signal.
Verify that an audio system samples fast enough for the frequency range it must capture.
Understand why aliasing artifacts appear in under-sampled signals.
Teaching the Nyquist-Shannon sampling theorem in DSP or communications courses.
Check sample-rate requirements for RF, radar, or sensor data acquisition.
Reverse-calculate the maximum signal frequency a given sample rate can reconstruct.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu