Nyquist Sampling Rate Calculator
Verify that a sample rate satisfies the Nyquist-Shannon criterion (f<sub>s</sub> ≥ 2·f<sub>max</sub>), calculate aliased frequency when undersampling occurs, and determine oversampling ratio for headroom in anti-alias filter design.
How to Use
- Enter your sampling rate f<sub>s</sub> in Hz, kHz, MHz, or GHz.
- Enter the signal frequency f<sub>sig</sub> you intend to capture.
- The tool reports Nyquist frequency (f<sub>s</sub>/2), oversampling ratio, status (OK / aliased), and the frequency at which an aliased signal would appear.
Show Work
Formulas
History of the Nyquist-Shannon Theorem
Harry Nyquist (Swedish-born Bell Labs engineer) published his seminal paper "Certain Topics in Telegraph Transmission Theory" in 1928, where he derived the minimum pulse rate needed to transmit information through a bandlimited channel — directly leading to the sampling theorem. Claude Shannon\'s 1949 paper "Communication in the Presence of Noise" completed the formulation, combining Nyquist\'s work with information theory to prove that any signal bandlimited to B Hz can be exactly reconstructed from samples at rate fs > 2B.
Vladimir Kotelnikov (USSR, 1933) and Edmund Whittaker (UK, 1915) had derived equivalent results independently, which is why the theorem is sometimes called the Whittaker-Nyquist-Kotelnikov-Shannon theorem in European literature. The "2×" rule is sometimes called the Nyquist rate or Nyquist frequency depending on context — Nyquist rate is the minimum sampling rate (2B), Nyquist frequency is the highest signal frequency representable at a given sample rate (fs/2).
Practical application of the theorem drives every digital audio, video, and communication system today. CD audio\'s 44.1 kHz sample rate reflects the theorem applied to 20 kHz human hearing with 10% margin; every cellular modem, WiFi radio, oscilloscope, and seismograph designs its anti-alias filter at fs/2 with filter skirts falling into the stopband by the next octave. The math is 100 years old and completely unchanged.
About This Calculator
Enter a sample rate and signal frequency. The tool reports the Nyquist frequency (fs/2), oversampling ratio relative to 2×fsignal, pass/fail status, and — if the signal is above Nyquist — the frequency at which the alias would appear in the baseband.
Useful for: verifying ADC configuration meets signal-bandwidth requirements, designing anti-alias filters (the passband must end before fs/2 with enough stopband attenuation), and diagnosing unexpected spectral artifacts (if you see a line at an unexpected frequency, check whether it matches an alias of a known out-of-band signal). Everything runs client-side.
Frequently Asked Questions
Why exactly 2× the highest frequency?
Harry Nyquist (1928) and Claude Shannon (1949) proved that any band-limited signal containing no frequencies above B can be perfectly reconstructed from samples taken at rate f<sub>s</sub> > 2B. At exactly 2B the reconstruction is mathematically possible but requires an ideal brick-wall filter; practical systems use f<sub>s</sub> = 2.2B to 4B to allow realizable anti-alias filters.
What happens if I undersample?
High-frequency components fold back into the baseband as aliases. A 15 kHz signal sampled at 10 kHz folds to 5 kHz — indistinguishable from a real 5 kHz signal once digitized. This is why every quality ADC has an anti-alias low-pass filter in front of it, cutting off frequencies above f<sub>s</sub>/2 before sampling.
Why do many ADCs oversample 4–16×?
A realizable anti-alias filter can\'t transition instantly from passband to stopband. Sampling at 2× forces a filter with brick-wall response at f<sub>s</sub>/2 — impossible. Sampling at 4–16× gives the filter a gentle transition band, moving the filter implementation cost from the analog domain to the (much cheaper) digital domain via decimation.
What is intentional undersampling?
In software-defined radio and some instrumentation, signals in higher Nyquist zones are deliberately sampled below 2× their frequency. The aliases fold into the first Nyquist zone where they can be processed digitally. Requires a tight bandpass anti-alias filter around the target zone — you\'re using aliasing as a mixer.
Does Nyquist apply to all signals?
Strictly it applies to band-limited signals (those with a finite maximum frequency). Real-world signals always have some energy above any given frequency (thermal noise, etc.), so "band-limited" means "energy above f<sub>max</sub> is below the ADC noise floor." The AAF enforces this by definition.
Common Use Cases
Audio ADC Setup
Capturing 20 kHz audio bandwidth requires f<sub>s</sub> > 40 kHz. CD audio uses 44.1 kHz (2.2× oversampling); pro audio often uses 96 or 192 kHz for slower AAF roll-off and higher effective resolution.
Oscilloscope Bandwidth Check
A 100 MHz scope with 400 Msps sample rate gives 2× Nyquist at claimed bandwidth — real scopes typically provide 5× oversampling (500 Msps or more at 100 MHz bandwidth).
SDR Direct Sampling
An Ettus N200 sampling at 100 Msps can directly capture any signal up to 50 MHz without frequency conversion — the entire HF band lives in its first Nyquist zone.
Bandpass Undersampling
A 170 MHz signal sampled at 50 Msps aliases to 20 MHz in the digital domain (170 − 3·50). With a bandpass filter around 170 MHz, this is functional — and simpler than a frequency-translation receiver.
Data Logger Frequency Range
A 1 ksps temperature logger cannot detect or respond to signals above 500 Hz — AC line noise at 60 Hz is well below Nyquist, so it appears correctly; a 1 kHz switching noise component would alias and distort the DC reading.
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