Nyquist & Sampling Rate Calculator — aliasing and filter design

Minimum sample rate, alias frequencies and anti-alias filter requirements for a given signal.

Example: At 48 kHz sampling, 1 kHz is captured correctly — 24× oversampled against a 24 kHz Nyquist limit.

Formula

f_Nyquist = f_s / 2    f_alias = |f − n × f_s|

Worked example

At 48 kHz sampling, 1 kHz is captured correctly — 24× oversampled against a 24 kHz Nyquist limit.

  1. f_Nyquist = f_s / 2

    48 kHz / 2

    24 kHz

    The highest frequency that can be represented unambiguously.

  2. f_alias = |f − n × f_s|

    |1 kHz − 0 × 48 kHz|

    1 kHz

    Below Nyquist, so this equals the original frequency.

Frequently asked questions

What is the Nyquist frequency?

Half the sample rate — the highest frequency a sampled system can represent unambiguously. At 48 kHz sampling that is 24 kHz. Anything above it does not simply disappear; it folds back down into the band as a false signal.

What happens to a signal above the Nyquist frequency?

It aliases: it appears at |f − n × f_s| for whichever multiple of the sample rate is nearest. A 30 kHz tone sampled at 48 kHz shows up as 18 kHz, and nothing downstream can tell it apart from a genuine 18 kHz signal.

Can I remove aliasing in software?

No. This is the one problem digital processing genuinely cannot fix. Once a frequency has folded down it occupies the same bins as real signal, and the information distinguishing them is gone. The filter has to be in front of the converter.

Why sample well above twice the highest frequency?

To give the anti-alias filter somewhere to roll off. Sampling at exactly twice satisfies the theorem in principle but leaves zero transition band, demanding an impossible brick-wall filter. Oversampling widens that band so a practical filter will do.

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