signal op• データ種: positions → table
• 呼び出し: 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) (実装を直接呼ぶなら import dsp; dsp.point_spectrum(positions, extent=None, n_freq=2048, f_max=None, method='direct', weights=None, bins_per_period=8)、台帳から引くなら 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.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py
table を入力に取れる)—
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · companding_mu_law
*Provenance: dsp.py — ONED operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.