Nyquist Sampling Calculator

Compute minimum sampling rate, aliasing behavior, and a simple capture-quality assessment.

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What This Calculator Does

This calculator applies Nyquist-Shannon sampling rules to a highest-frequency component or signal bandwidth and estimates how a chosen sampling rate will alias that content back into the baseband.

It combines Highest Frequency Component, Chosen Sample Rate, Recommended Safety Factor to estimate Minimum Sampling Rate, Recommended Sampling Rate, Alias Frequency.

Formula & Method

Core equations: The minimum ideal rate is

f_s \ge 2f_{max}

. An aliased tone folds to

f_a=\left|f-f_s\cdot\mathrm{round}\left(\frac{f}{f_s}\right)\right|

within the principal sampling band.

Notation used in the formulas: $R$ = Minimum Sampling Rate; $x_{1}$ = Highest Frequency Component; $x_{2}$ = Chosen Sample Rate; $x_{3}$ = Recommended Safety Factor.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when deciding whether a sampling rate is safe, or when you need to explain why an undersampled tone appears at the wrong frequency after acquisition.

Reference Book

Signals and Systems

Alan V. Oppenheim, Alan S. Willsky, and S. Hamid Nawab · Pearson

A classic reference for convolution, Fourier analysis, Laplace transforms, z-transforms, sampling, and LTI systems.

View Book

Inputs Used

Highest Frequency Component: Used directly in the calculation.
Chosen Sample Rate: Used directly in the calculation.
Recommended Safety Factor: Used directly in the calculation.

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