Technology / Technical guide
Wind Waveform Sampling: Nyquist Conditions & Aliasing
A sampled waveform contains values at selected instants rather than the complete continuous signal. Different continuous waves can produce the same sampled sequence. This ambiguity, called aliasing, matters whenever a frequency or rapidly changing quantity is inferred from wind equipment data.
The sample sequence does not identify every possible original wave.
Understand the signal bandwidth and sampling model before interpreting a low-frequency trace as a real physical variation.
01 / Sampling grid
A regular time grid creates a frequency boundary.
With ideal uniform sampling, successive observations are separated by Ts seconds and the sample rate is fs = 1/Ts samples per second.
With ideal uniform sampling, successive observations are separated by Ts seconds and the sample rate is fs = 1/Ts samples per second. A higher rate places observations closer together. It does not increase the analogue sensor’s bandwidth or undo distortion that occurred before conversion.
Samples per second describes the sampling process; cycles per second describes signal frequency. An averaged file’s row interval can differ from its internal sampling interval.
02 / Spectral overlap
Aliasing is an ambiguity between frequency components.
Sampling repeats the continuous spectrum at intervals of the sample rate.
Sampling repeats the continuous spectrum at intervals of the sample rate. When the repeated spectra overlap in the represented baseband, contributions cannot generally be separated from the sequence alone. A high-frequency component can then appear as a lower-frequency variation.
NI explains this frequency folding. Unlike random noise, an aliased component can be repeatable. Repeating or averaging observations cannot automatically identify the original continuous frequency.
03 / Ideal condition
Nyquist reconstruction needs more than a named rate.
For an ideal baseband signal with no content at or above bandwidth B, uniform sampling at fs greater than 2B permits ideal reconstruction with the appropriate interpolation model.
For an ideal baseband signal with no content at or above bandwidth B, uniform sampling at fs greater than 2B permits ideal reconstruction with the appropriate interpolation model. This statement assumes the signal is band-limited and the sampling model is valid.
It is not enough that the frequency of interest lies below fs/2 while other significant input components lie above it. Real filtering has transition regions, and real devices have additional limitations. The ideal theorem is a representation result, not a promised measurement accuracy.
04 / Alias illustration
Two cosine waves can share the same samples.
Hypothetical ideal example: sampling a 60 Hz cosine at 80 samples per second gives the same values as a 20 Hz cosine with the same amplitude and origin.
Hypothetical ideal example: sampling a 60 Hz cosine at 80 samples per second gives the same values as a 20 Hz cosine with the same amplitude and origin. At sample index n, the cosine phase differs by an integer number of complete turns and a sign reversal that leaves cosine unchanged.
The apparent 20 Hz trace does not prove a physical 20 Hz input. Denser interpolation of these invented samples cannot identify which continuous wave was present.
05 / Filtering role
Restricting content and smoothing samples are different.
An anti-aliasing boundary concerns the content reaching the sampler.
An anti-aliasing boundary concerns the content reaching the sampler. A later digital filter acts on the sequence already produced; where different inputs have become indistinguishable, it cannot generally separate them. Filtering after a new reduction in sample rate introduces another representation question.
A smooth curve can conceal lost information. Conversely, a correctly represented band-limited waveform can be reconstructed between observations under the stated model. Smoothness and identifiability are separate properties.
06 / Interpretation scope
Relate the principle to the actual data boundary.
Distinguish sensor response, analogue conditioning, sampling, aggregation and display interpolation.
Distinguish sensor response, analogue conditioning, sampling, aggregation and display interpolation. Each stage can change the information retained. The filtering guide explains timing effects that are separate from frequency folding.
No actual MARSTON sample rate, anti-alias filter or waveform-recording function is established here. These principles explain existing data without instructing changes to measurement hardware, logging settings or live electrical tests.
Continue the review with Wind Measurement Filtering: Bandwidth, Delay & Latency.
Continue the review with Wind Electrical Waveforms: RMS, Peak & Crest Factor.
Continue the review with Redundant Sensors: Voting, Agreement & Common Causes.
Extend the sampled-record review with FFT windows and spectral leakage, record length and frequency resolution, and sampling-clock jitter.
General background: NI: Nyquist sampling and frequency-aliasing principles. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Sample interval | Ts in seconds; fs = 1/Ts | Ideal uniform timing is assumed. |
| Signal bandwidth | B in Hz and the full relevant spectrum | Interest frequency alone is insufficient. |
| Nyquist boundary | fs/2 for baseband representation | Input content must satisfy the model. |
| Alias ambiguity | Different continuous components, identical sample sequence | Interpolation adds no independent observations. |
| Chain distinction | Analogue content, stored samples and displayed curve | Each stage has a different information boundary. |
Engineering questions.
Does faster sampling restore sensor information already lost?
No. Sampling cannot undo an earlier bandwidth or distortion limitation.
Is an alias ordinary random noise?
Not necessarily. It can be a stable, repeatable but misleading component.
Is fs greater than twice the desired frequency always enough?
No. Other input components and the band-limiting assumptions also matter.
Can extra plotted points identify the original 60 Hz wave?
No. Interpolation alone cannot resolve the hypothetical ambiguity.
Does later smoothing eliminate prior aliasing?
It cannot generally separate inputs that already produced identical samples.
Are the example rates MARSTON settings?
No. They are invented values in an ideal mathematical illustration.
Technical enquiry
Discuss the technical question.
A sampled waveform contains values at selected instants rather than the complete continuous signal. Share the model and applicable operating or design information for an engineering discussion.