What is the Nyquist rule, and what is aliasing?

The Nyquist limit and aliasing

To track a vibration component correctly, the sampling frequency fs must be more than twice that component's frequency. If the highest component is f_max, the condition is fs > 2 × f_max. This is the core idea of the Nyquist–Shannon sampling theorem.

When the condition fails, a component above fs/2 is not recorded as it is. It shows up at a lower frequency, which is called aliasing. A component f sampled at fs appears at |f − k × fs|, where k is the integer that makes the result smallest.

Aliasing cannot be undone after recording. Prevention therefore happens before sampling, with an analog low-pass filter. A digital filter cannot correct data that has already been folded to a wrong frequency.

Two worked examples and a choice of fs

Two hypothetical examples first:

• A 60 Hz vibration sampled at 50 Hz appears at |60 − 50| = 10 Hz. Since fs/2 = 25 Hz, this component aliases.
• A 0.9 Hz oscillation read once per second by a PLC value appears at |0.9 − 1| = 0.1 Hz.

To inspect a spectrum up to 2,000 Hz, FFT analyzers commonly use 2.56 times that frequency: fs = 2.56 × 2,000 = 5,120 Hz. This leaves a 560 Hz guard band between 2,000 Hz and fs/2 = 2,560 Hz, room for the anti-alias filter's transition.

Common mistakes

Three mistakes come up often:

• Assuming a digital filter can remove aliasing. Aliasing happens during sampling and cannot be separated afterwards.
• Downsampling without a low-pass filter first. Without it, high-frequency content folds into the new, lower sampling band.
• Reading PLC or historian values as if they were a waveform. Scan timing, poll rate and deadband compression in a historian all distort the shape, and can produce false oscillations that look like aliasing.

Follow-up questions