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.
f_Nyquist = f_s / 2
48 kHz / 2
24 kHz
The highest frequency that can be represented unambiguously.
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.
Related tools
ADC Resolution & LSB Calculator
Step size, ENOB, quantisation noise and SNR for a given ADC bit depth and reference voltage.
Firmware
FFT Bin Resolution Calculator
Bin width, frequency resolution and capture time for a given FFT size and sample rate.
RF & Signals
RC / RL / LC Filter Calculator
Cutoff frequency and −3 dB response for low-pass, high-pass and band-pass filters, with a plotted Bode curve.
Circuits
Antenna Length Calculator
Quarter-wave, half-wave and dipole lengths for any frequency, with presets for 433, 868, 915 and 2400 MHz and the ham bands.
RF & Signals
Wavelength & Frequency Converter
Convert frequency to wavelength and back, including velocity factor for cable and PCB.
RF & Signals
Free Space Path Loss Calculator
Link budget and estimated range for LoRa, WiFi and BLE from TX power, gains and sensitivity.
RF & Signals