Nyquist Sampling Rate
Finds the lowest sample rate that can capture a signal’s highest frequency, and checks whether the rate you plan to use is fast enough. Test, controls and audio engineers use it when they set up a data-acquisition system or choose an analog-to-digital converter.
The sampling theorem
fs,min = 2·fmax fN = fs/2
fmax is the highest frequency present in the signal and fs,min the Nyquist rate, the least sample rate that can represent it [1]. fs is the sample rate you chose and fN its Nyquist frequency, the highest frequency that rate can represent. The rate passes when fs ≥ 2·fmax, that is, when fmax is no higher than fN.
Any content above fN doesn’t vanish when sampled. It folds back, or aliases, to a false lower frequency, and no processing afterward can tell it from a real signal [1].
Limits and common mistakes
- fmax is the highest frequency actually present, including noise and harmonics, not just the band you care about. Put an anti-aliasing low-pass filter ahead of the converter to remove the rest.
- Twice fmax is the theoretical floor. A real filter can’t cut off sharply, so in practice sample faster. Data loggers often use 2.5 to 10 times fmax. CD audio gets by with 2.2 times (44.1 kHz for a 20 kHz band) only because of a very steep filter.
- Capturing a waveform’s shape or peak value, rather than its frequency content, takes a higher rate still, often ten or more samples per cycle.
- The theorem applies to the sample rate of each channel. A multiplexed converter divides its total rate among its channels.
Worked example
A vibration probe on a pump bearing needs content up to 5 kHz. The data logger offers a 12.8 kHz sample rate. Check that it is fast enough.
- Enter Highest signal frequency (fmax) 5 kHz.
- Enter Chosen sample rate (fs) 12.8 kHz.
- Press Solve. The Solution shows:
Minimum required sample rate (Nyquist rate): 10,000 Hz
Nyquist frequency at chosen fs: 6,400 Hz
Satisfies sampling theorem?: Yes
Check: 2 × 5 kHz = 10 kHz, which 12.8 kHz clears, and 12.8/2 = 6.4 kHz. The 1.4 kHz between 5 and 6.4 kHz is the room left for the anti-aliasing filter to roll off. That is tight, so check that the logger’s filter is steep enough.
