signal op• Data kinds: positions → table
• Call: import fullseye as fs; fs.ledger.point_spectrum(positions, extent=None, n_freq=2048, f_max=None, method='direct', weights=None, bins_per_period=8) (to call the implementation directly, import dsp; dsp.point_spectrum(positions, extent=None, n_freq=2048, f_max=None, method='direct', weights=None, bins_per_period=8); from the registry, ops1d.get("point_spectrum"))
Periodogram of event positions — defects, impacts, counts, arrivals.
spectrum needs an evenly sampled signal, but a great deal of industrial data arrives as a *list of positions*: where each defect was on the web, when each particle was counted, at what angle each dent sits. The usual workaround is to histogram the positions and FFT the histogram, which works but hides two choices — bin width and record length — that decide the answer. This operator makes both explicit and returns them.
*method* picks the estimator:
"direct"
the point-process (Bartlett) periodogram
|sum_j w_j exp(-2 pi i f x_j) - rate * integral|^2 / sum_j w_j,
evaluated at each requested frequency. No binning at all, so no bin
width to choose and no aliasing from one. The subtracted term is the
contribution a *uniform* process of the same rate would make; without it
every spectrum peaks at f -> 0 simply because events exist.
"binned"
histogram the positions, then rfft, with the bin width set so the
finest frequency asked for still gets bins_per_period samples per
cycle. Cheaper for very many events, and the result is what a
histogram-and-FFT pipeline would have produced.
The frequency resolution is a property of the record, not of the method. Two periods closer than 1/extent apart cannot be told apart by either estimator, and the returned dict says so in resolution: read it before reading a peak, not after.
A periodic train of events is a comb, not a line. Its harmonics at k/period are as tall as the fundamental, so argmax of this spectrum routinely returns period/k rather than the period. Measured on 93 events (43 spaced 471.24 apart with 1.5 of jitter, plus 50 uniformly random) over a record of 20000: the global maximum lands on 58.90 with direct (the 8th harmonic) and 52.35 with binned (the 9th), while the fundamental is present and prominent in both — direct puts 0.947 of the maximum power at 1/471.24, binned 0.379. Take the lowest frequency whose first few harmonics *all* stand, rather than the tallest line — see examples/poc_web_roll_periodicity.py, which is what this operator was added for.
Returns a dict: freq (cycles per unit of *positions*), power, resolution (1/extent), extent, n_events, method, and bin_width (None for "direct").
Fail-closed: fewer than two events raises ValueError — a periodogram of one point is not a weak measurement, it is not a measurement.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py
table as input)—
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · companding_mu_law
*Provenance: dsp.py — ONED operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.