A data logger's minimum sample rate equals twice the highest frequency content of the input signal: f_s,min = 2 x f_max, per the Nyquist-Shannon sampling theorem as defined on engineering reference pages [S2][S3].
For a 50 Hz process signal, that floor is 100 Hz; the recommended rate is 500 Hz (10x), and the conservative rate is 1000 Hz (20x), because below the 10x margin a join-the-dots display will visibly distort the waveform even when the strict Nyquist criterion is met [S3][S4].
Why 2 x f_max Is a Floor, Not a Target
Sampling exactly at 2 x f_max is mathematically sufficient to preserve the information in the analog signal, but a straight line drawn between sample points does not reproduce the original shape: reconstruction requires ideal low-pass filtering of the impulse train, which most logging front-ends do not implement [S4]. A 40 Hz sine sampled at 100 Hz (Nyquist-compliant) looks like a triangle wave on a simple chart, while the same sine sampled at 1000 Hz (25 x oversampled) renders cleanly, demonstrating that headroom above 2 x is what the operator actually sees [S4].
Aliasing is the failure mode below the floor: a frequency component above f_s/2 folds back into the passband as a false low-frequency signal, and the artifact cannot be removed by post-processing because the original high-frequency content is no longer separable from the data [S1][S3]. For industrial data loggers, this means a once-lost vibration spike from a failing bearing becomes indistinguishable from a slow temperature drift in the recorded file.
Reading the Signal Bandwidth Before You Press Record
f_max must include noise, harmonics, and any mechanical resonance, not just the fundamental of interest, because any spectral content above f_s/2 will alias into the recorded band [S3]. A 50 Hz mains-borne measurement therefore needs f_max covering at least the 3rd harmonic (150 Hz) and ideally the 5th (250 Hz) if waveform fidelity matters, pushing the minimum rate from 100 Hz to 500 Hz before any safety margin is applied [S3].
Two practical shortcuts: (1) start from the transducer's specified bandwidth, since a sensor with a 200 Hz, -3 dB point cannot deliver content above that no matter how fast the logger runs; and (2) when in doubt, run a fast capture first (for example 10 kS/s) and inspect the FFT, then dial the rate back to the lowest value that keeps the highest meaningful tone below f_s/2 with the oversampling ratio you need. This is the same logic that applies to variable frequency drives setting PWM carrier ratios against motor electrical frequency, and to line-frequency furnace electrode current logging where 50/60 Hz mains plus arc flicker extends f_max well past the fundamental.
A 2 x / 10 x / 20 x Selection Matrix for Common Channels
For a band-limited process signal the engineering consensus is three tiers [S3]: minimum (2 x f_max) is acceptable only when the recorded data will be FFT-processed offline, never viewed as a time trace; recommended (10 x f_max) suits most control-loop monitoring where the trace must be human-readable; conservative (20 x f_max) is for shock, vibration, and transient capture where peak amplitude accuracy matters more than storage budget [S3][S4].
Comparison on four decision criteria:
Criterion / 2 x (Nyquist floor) / 10 x (recommended) / 20 x (conservative)
Time-trace readability on a chart: poor, requires ideal LPF reconstruction; good, looks like the original; excellent, near-analog fidelity [S4].
Storage per hour at 16-bit, 1 channel: 1 x baseline; 5 x baseline; 10 x baseline [S3].
Aliasing risk if f_max estimate is wrong: high (any overshoot aliases); low (small overshoot still inside passband); very low [S1].
Typical use case: offline spectral analysis only; general process trending and alarms; vibration, shock, power-quality transients [S3].
For a vibration channel where f_max is 500 Hz, these tiers become 1 kS/s, 5 kS/s, and 10 kS/s, with the 5 kS/s figure being the most common plant default, mirroring how construction machinery and equipment telematics log hydraulic pressure and engine RPM at similar oversampling ratios.
Anti-Aliasing Hardware vs Oversampling
An analog anti-aliasing low-pass filter with a cutoff at or just below f_s/2 must precede the ADC, otherwise out-of-band noise and harmonics will fold into the passband before digitisation and no amount of digital oversampling can recover them [S1][S4]. This is why most industrial data loggers ship with a fixed-order Butterworth or Bessel filter matched to the selected range rather than relying on the ADC's raw bandwidth.
Oversampling in the digital domain (sampling well above 2 x f_max, then digitally filtering and decimating) achieves the same noise-folding and dynamic-range benefits as a steeper analog filter, at the cost of ADC throughput and memory write bandwidth, and is the standard method inside modern sigma-delta front-ends [S1]. The Nyquist formula for the noiseless channel also shows that doubling the data rate doubles the occupied bandwidth, so storage scaling is roughly linear with the chosen sample rate once compression is ignored [S5].
Failure Modes and Common Sizing Errors
Three errors dominate field reports. First, using the fundamental frequency as f_max when harmonics, switching ripple, or mechanical resonance extend the band by 3 x to 10 x, which causes high-tone aliasing into the logged trend [S3]. Second, ignoring the transducer's own bandwidth ceiling, which caps usable content regardless of logger speed, a mistake often seen when a fast industrial lamps and light fittings photometric sensor is paired with a slow thermocouple logger front-end. Third, treating 2 x f_max as a safe operating point rather than a mathematical floor: the resulting time trace looks wrong even though the spectral content is technically recoverable [S4].
For applications that mix slow and fast channels, decimation of a high-rate master stream down to per-channel rates is preferred over running the slow channel at the fast rate, because decimation after a clean digital low-pass filter is mathematically lossless in the band of interest [S4]. A 10 kS/s master decimationally reduced to 100 Hz for a temperature channel, for example, contains the same information as a dedicated 100 Hz capture, while freeing storage for the high-bandwidth channels on the same lighting equipment and electric lamps production-line test rig.
Sourcing, Standards, and Where to Verify
The 2 x f_max rule traces to the Nyquist-Shannon sampling theorem, summarised on the National Instruments data acquisition fundamentals page (updated 2026-09-03) and on the ScienceDirect engineering topic page, which defines Nyquist as the principle that the highest representable frequency is half the sampling rate [S1][S2]. The 10 x and 20 x engineering rules of thumb are documented in the Firgelli sampling-rate calculator (published 2026-02-23) and demonstrated in the University of St Andrews DataView tutorial, which shows that a 40 Hz signal sampled at 100 Hz meets Nyquist but looks triangular on a join-the-dots plot [S3][S4].
For noise-free channel capacity the classic Nyquist formula C = 2 B log2(M) bits per second, where B is bandwidth and M is the number of signal levels, gives the upper bound on noiseless data rate, a relation distinct from the sampling-rate theorem but often confused with it in datasheets [S5]. The general-form Nyquist frequency definition is catalogued on Wikipedia as the folding frequency of a sampler, equal to half its sample rate [S6].
Trackable next signals for an engineer sizing a logger channel: (1) re-measure the channel with a 10x higher rate than planned and confirm via FFT that no spectral content sits above the intended f_s/2, and (2) verify that the analog input filter cutoff is matched to the chosen f_s/2, not to the transducer's rated bandwidth. Both checks are runnable in a single afternoon and turn a guess into a documented data logger configuration. For related industrial I/O trade-offs at the protocol level, the Ethernet vs PROFINET remote I/O comparison covers the same oversampling-vs-throughput tension from a different angle.