Nyquist Limit Calculator

Calculation mode Given sampling frequency Given sampling period Given maximum signal frequency

Choose what you know, then compute the Nyquist limit.

Sampling frequency

Hz kHz MHz GHz

Nyquist frequency equals half of this rate.

Sampling period

s ms us ns

Sampling frequency is 1 / T_s.

Maximum signal frequency

Hz kHz MHz GHz

Nyquist rate is at least 2 × f_max.

Oversampling factor

Use 2–8× for cleaner filtering and measurements.

Guard band (%)

Reserves margin below Nyquist for anti-alias filters.

Decimal places

Controls numeric rounding in results and exports.

Calculate Reset

This calculator follows the Nyquist sampling criterion for band-limited signals:

• Sampling frequency: fs = 1 / Ts
• Nyquist frequency: fN = fs / 2
• Nyquist rate (minimum): fs,min = 2 × fmax

For practical designs, a guard band and oversampling are included to recommend a safer sampling rate:

fs,recommended = oversample × (2 × fmax) / (1 − guard%)

1. Select the mode based on what you know: sampling frequency, sampling period, or maximum signal frequency.
2. Enter the value and choose the correct unit (Hz, kHz, MHz, or GHz; period units for T_s).
3. Set an oversampling factor (1 for strict limit, higher for robust designs).
4. Optionally add a guard band percentage to keep content away from Nyquist.
5. Click Calculate. Results will appear above the form.
6. Use Download CSV or Download PDF for reports.

Example recommendations use oversampling = 4 and guard band = 10%.

1) Why the Nyquist limit matters

The Nyquist limit is the highest frequency a sampled system can represent without ambiguity. For a sampling rate f_s, the limit is f_N = f_s/2. Any spectral content above f_N can fold into lower frequencies and corrupt measurements.

2) Connecting sampling rate and sampling period

Engineers often specify timing as a period T_s. The relationship is f_s = 1/T_s. For example, T_s = 20.833 us corresponds to 48 kHz. Converting between these forms helps when configuring timers, ADC clocks, and acquisition hardware.

3) What aliasing looks like in practice

Aliasing occurs when a component above f_N appears at a lower “mirror” frequency. A 30 kHz tone sampled at 48 kHz has f_N = 24 kHz, so it aliases to |30−48| = 18 kHz. The time signal looks plausible, but the spectrum is wrong.

4) Typical sampling rates with real data

Audio commonly uses 44.1 kHz (Nyquist 22.05 kHz) and 48 kHz (Nyquist 24 kHz), aligning with human hearing bandwidth. Vibration and machine monitoring often use 5–20 kHz sampling for low-frequency modes. Imaging and RF systems may use MHz to GHz rates depending on bandwidth.

5) Oversampling improves robustness

Sampling exactly at 2× f_max is a theoretical minimum. Oversampling at 2–8× pushes f_N higher, relaxes filter design, and improves estimation of frequency and phase. For f_max = 20 kHz, 4× oversampling suggests ~160 kHz before any guard band.

6) Guard band and filter transition planning

Anti-alias filters need a transition region between the passband and f_N. A 10% guard band means you target usable content below 0.9× f_N. This calculator applies the guard band to recommend a safer f_s so your filter can attenuate out-of-band energy before sampling.

7) Resolution tradeoffs in the time domain

Higher f_s gives finer time spacing and captures faster transients, but increases data volume. Doubling f_s doubles sample count for a fixed duration. Use this tool to balance fidelity and storage by computing the minimum and recommended rates, then picking a practical compromise.

8) A practical checklist for measurements

First, estimate true bandwidth after analog filtering and any modulation. Second, choose oversampling based on required margin and analysis method. Third, reserve guard band for filter roll-off and jitter sensitivity. Finally, validate with a spectrum check: unexpected peaks near f_N often indicate aliasing.

1) What is the Nyquist limit?

It is the highest frequency that can be represented without ambiguity for a given sampling rate. It equals f_N = f_s/2, assuming the signal is band-limited and properly filtered before sampling.

2) Is sampling at 2× f_max always enough?

It is the theoretical minimum, but often not sufficient in practice. Real signals have noise and harmonics, and real filters need transition width. Oversampling and a guard band reduce aliasing risk.

3) How does guard band change the recommendation?

A guard band reserves space between your highest useful frequency and Nyquist. For example, 10% guard band aims to keep content below 0.9× f_N, so the calculator recommends a higher sampling rate.

4) Why do 44.1 kHz and 48 kHz appear so often?

They place Nyquist around 22–24 kHz, covering the audible range with margin. These rates also integrate well with common production and broadcast workflows, making them practical standards for audio systems.

5) What if the signal is not band-limited?

Then aliasing is unavoidable without filtering, because high-frequency energy extends beyond Nyquist. Add an analog low-pass (anti-alias) filter, limit bandwidth, or sample much faster so out-of-band components are attenuated.

6) How does sampling period relate to sampling frequency?

They are reciprocals: f_s = 1/T_s. If T_s is in seconds, f_s is in hertz. This calculator converts ms/us/ns to seconds before computing rates.

7) Does clock jitter affect the Nyquist limit?

Jitter does not change the mathematical limit, but it reduces effective measurement quality at high frequencies. With significant jitter, high-frequency components become noisier, so higher oversampling and better clocking can improve results.