Choosing a Sampling Rate
Nyquist is about the highest frequency present, not the highest one you care about — and everything above half your rate folds back in permanently. What rate each job actually needs, and the six things to write down.
Most sampling rates are chosen the way a default is chosen: the device offered 1 Hz, the network tolerated it, and nobody wrote down why. That works until the day the data is asked a question it cannot answer, and by then the measurement campaign is over and the machine has been repaired.
Start with the theorem everyone half-remembers. Nyquist says you must sample at more than twice the highest frequency present in the signal. The trap is in that last word. Not the highest frequency of interest — the highest frequency present. Anything above half the sample rate does not disappear; it folds down into your band and appears as a lower frequency that is indistinguishable from a real one. A 130 Hz vibration component sampled at 100 Hz shows up at 30 Hz, sits in your spectrum looking entirely plausible, and no amount of post-processing will ever remove it, because the information needed to separate the two was destroyed at the converter.
The defence is an analogue low-pass filter ahead of the ADC, with its corner set below half the sample rate and enough roll-off to attenuate what lies beyond. This is a hardware property, not a software setting. Digital filtering after the fact cannot undo aliasing; it only smooths what has already been corrupted. Plenty of inexpensive data loggers and general-purpose analogue inputs ship without a proper anti-alias filter, and the specification sheet often does not say so — it is worth asking the vendor directly rather than assuming.
With that settled, the rate follows from the job, and the jobs differ by orders of magnitude.
Process trending is governed by the process time constant, not by the sensor. A tank level with a twenty-minute fill time is fully described by a reading every ten or thirty seconds; sampling it at 10 Hz produces a hundred times the data and no additional knowledge. Closed-loop control is different: the usual guidance is a scan rate several times faster than the loop's bandwidth — commonly cited as five to ten times — so the controller sees a disturbance while it can still act on it.
Vibration is where the numbers grow. Bearing and gear defect frequencies are multiples of shaft speed, and useful diagnosis typically wants an analysis bandwidth reaching ten to twenty-five times running speed. A machine at 3,000 rpm turns at 50 Hz; twenty-five times that is 1,250 Hz of analysis bandwidth, which implies sampling at 3 kHz or more once filter margin is included. Power quality is higher still: harmonics to the fiftieth order on a 50 Hz supply reach 2.5 kHz, so 6.4 kHz is a common converter choice. Motor current signature analysis, partial discharge and acoustic emission climb from there into the hundreds of kilohertz.
Those rates raise an obvious objection: nobody wants to ship 6 kHz of raw waveform from a hundred machines. They do not have to, and this is the pattern that resolves most of these arguments. Sample fast, store slow. Acquire at the rate the physics demands, compute the features on the device — RMS, peak, crest factor, band energies, a spectrum — and transmit those at a rate the network is happy with, perhaps once a minute. The raw window stays local and only leaves when something asks for it.
Which requires a trigger. Keep a rolling buffer in the device, freeze it when a threshold or a state change fires, and ship a window that includes data from before the trigger as well as after. Post-trigger-only capture is a common and expensive mistake: the interesting part of a transient is usually its onset, which happened before anything noticed.
Two smaller traps are worth naming. Averaging is not a free reduction — an averaged value hides exactly the excursion that mattered, so carry minimum and maximum alongside the mean whenever the data might be used for diagnosis rather than reporting. And decimation must be filtered: taking every tenth sample of a 10 kHz stream to make a 1 kHz stream aliases just as thoroughly as sampling at 1 kHz in the first place. Low-pass first, then discard.
Finally, the sample clock itself matters. Jitter in the timing of conversions smears energy across the spectrum and raises the noise floor, which is why serious vibration hardware disciplines its converter clock rather than relying on a software timer. A rate is only as good as the regularity of the intervals underneath it.
None of this needs a long document. Write down six things: the highest frequency the sensor can physically see, the anti-alias filter's corner and roll-off, the sample rate and why, what is computed on the device, what leaves it and how often, and what triggers a raw capture. A team that can answer those six has made a defensible engineering decision. A team that cannot has a default.