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Aliasing Frequency Calculator

Enter the signal frequency and sample rate to get the aliased frequency and Nyquist frequency.

Result

14,100.00 Hz
22,050.00 Hz

How it is calculated

The engine finds the closest multiple of the sample rate to the signal frequency and measures the distance to it: falias = |f − round(f / fs) · fs|. Here f is the true frequency and fs the sampling rate, both in Hz. The result always lies between 0 and fs/2, the Nyquist frequency, which is also shown. A signal below the Nyquist frequency comes out unchanged. A signal above it is folded back to a lower frequency. The sample rate must be above zero and the frequency cannot be negative. The tool describes an ideal sampler with no anti-aliasing filter.

Worked example

A 30,000 Hz tone is sampled at 44,100 Hz, so the Nyquist frequency is 44,100 / 2 = 22,050 Hz. The tone is above that limit. The ratio 30,000 / 44,100 ≈ 0.68 rounds to 1, so the nearest multiple of the sample rate is 44,100. The alias is |30,000 − 44,100|, which the tool shows as 14,100.00 Hz. After sampling, the tone looks like one at 14.1 kHz, well inside the audible range.

Try this example →

Common mistakes

  • Expecting an alias for every input. A frequency below half the sample rate is returned as it is, with no folding.
  • Confusing the sample rate with the Nyquist frequency. The sample rate is the larger number; Nyquist is half of it.
  • Entering kHz in one field and Hz in the other. Both must be in Hz.
  • Treating the alias as a filter result. The alias is where the unwanted tone appears; once it is in the sampled data it cannot be removed, so the filter must come before the converter.
  • Treating a tone exactly at Nyquist as safe. A frequency exactly half the sample rate is the limit and can be captured with a phase and amplitude that depend on the sampling instants.

About this calculator

The Nyquist-Shannon sampling theorem states that a signal must be sampled at more than twice its highest frequency component (the Nyquist frequency, half the sample rate) to be reconstructed without distortion. When a signal is sampled below that rate, its true frequency gets misrepresented as a lower, “folded” frequency — this is aliasing, calculated by reflecting the signal frequency around multiples of the Nyquist frequency until it lands within the valid range.

Aliasing shows up as jagged edges in undersampled images, the classic “wagon-wheel effect” where spinning wheels appear to rotate backward on video, and false low-frequency tones in poorly filtered audio digitization. Audio engineers, DSP designers, and anyone building an analog-to-digital conversion pipeline use this calculation to choose a sample rate — or design an anti-aliasing filter — that avoids letting high frequencies masquerade as false low ones.

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