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.
:func: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.