Fold Finder
Feed it a sampled series. It looks for a rate the signal repeats at, then folds the whole signal onto one period so you can see the hidden waveform. Two detectors: waveform (the raw series) and energy / envelope (the squared series, the squared-envelope spectrum used in vibration monitoring), which catches repetition in the signal's strength and is far more sensitive to impulse-like repetition. No training data, no model. Every rate is gated by a permutation test: 200 order-shuffled copies of your own signal, and the rate has to beat them.
1. Signal
Bearing-like impulse train
Weak bearing fault (energy mode only)
Weak buried tone
Real recording: window AC fan
Pure noise (trap)
No signal loaded.
3. Result
Spectrum of the window. A real repeating rate shows as a comb of peaks at the rate and its multiples.
Match score vs candidate rate. Each candidate is checked against the whole comb, not just one peak. Dashed line = the scramble control.
| Rate (Hz) | Period | Scramble p | Floor | Fold |
|---|
Tap a row to fold the signal at that rate. Scramble p is the main gate: the share of 200 order-shuffled copies that scored as high as the real signal at this rate. p ≤ 0.01 = the rate survives. Floor is the family fold threshold, reported as a second label next to each hit, not a wall.
Folded waveform at the selected rate: one period, averaged over every repeat in the window.
What this is / is not
Is: a repetition-rate finder for a uniformly sampled series. It builds a spectrum, tests each candidate rate against a whole harmonic comb, then folds the signal at the winner so you can see the underlying waveform. No training data. The folded shape is what tells a periodic machine fault from a one-off event.
Two detectors. Waveform folds the raw series. Energy / envelope folds the squared series (the squared-envelope spectrum long used in vibration monitoring). It reads repetition in the signal's strength, and it is much more sensitive to impulse-like repetition: on a weak bearing-fault impulse train the raw waveform finds nothing while the energy detector pulls the true rate out of the noise. It is a lag-0 cyclic slice, not the full cyclic autocorrelation or spectral correlation, so cyclostationary structure that lives off the carrier (e.g. a BPSK symbol rate) is still out of scope. And a rate is a repetition rate, not a physical origin. Confirm against the control and, if it matters, on a second recording.
Read the scramble column. A rate near 1x is noise. The number that matters is the scramble p: how often a copy of the same signal with its order destroyed still scored as high. p ≤ 0.01 means the rate is real. The floor is a second label, kept because if you watch it over time you learn whether it lines up with the real signals or cuts some out.