fullseye

spectrum — ONED signal op

• データ種: signal → pairs
• 呼び出し: import fullseye as fs; fs.ledger.spectrum(x, rate=1.0) (実装を直接呼ぶなら import dsp; dsp.spectrum(x, rate=1.0)、台帳から引くなら ops1d.get("spectrum"))
• 台帳経由の戻り値: fullseye.ledger.spectrum(...) は宣言 out 型 pairs の値だけを返す(本体は補助情報も返す)。捨てられた側が要るときは fullseye.ledger.spectrum.raw(...)、または dsp.spectrum を直接呼ぶ。

使い方

Raw one-sided magnitude spectrum -> (freqs, magnitude) (np.fft.rfft).

Scaling convention — read this before comparing any number. One-sided describes the frequency axis, not the amplitude axis. rfft keeps only the non-negative frequencies, so freqs runs from 0 to rate/2 in len(x)//2 + 1 bins — but magnitude is the unnormalised |rfft(x)|. It is not an amplitude and it grows with len(x): the same tone recorded twice as long comes back twice as tall. Nothing here divides by N; the caller does, and the exact factor depends on the bin::

freqs, mag = spectrum(x, rate)
amp = mag * (2.0 / len(x))       # one-sided amplitude, bins 1 .. N/2-1
amp[0] /= 2.0                    # DC has no mirror twin -> no factor 2
if len(x) % 2 == 0:
    amp[-1] /= 2.0               # nor does the Nyquist bin of an even N

The factor is 2/N and not 1/N because a real sinusoid of amplitude A splits its energy over a positive and a negative frequency; rfft discards the negative half, so the surviving bin holds A*N/2. DC and (for even N) Nyquist are their own mirror image and are not doubled — applying 2/N to them reports twice the true level.

Measured, so the convention can be checked rather than assumed. A unit sine at a bin centre (rate = 25600 Hz, N = 25600, 3000 Hz, amplitude exactly 1.0): the returned mag at 3000 Hz is 12799.999999999998 (= N/2), and mag * 2/N is 0.9999999999999999. A constant signal of value 1.0 with N = 1024: mag[0] = 1024.0, so mag[0] * 1/N is exactly 1.0 while mag[0] * 2/N would claim 2.0. Likewise cos(pi n) (amplitude 1.0 at Nyquist, N = 1024): mag[-1] = 1024.0, * 1/N = 1.0, * 2/N = 2.0.

Everything scale-invariant — where the peak is, the spectral centroid, the bandwidth, a ratio between two bins — is unaffected by the convention, which is why :func:signal_features can build on this directly. Everything absolute (an amplitude in the signal’s own units, a dB level) needs the division above. :func:acoustics.envelope_spectrum and :func:acoustics.order_spectrum already return calibrated one-sided amplitudes (they apply their own 2/N internally) — do not apply the factor twice when comparing their output with this one.

参考(サンプルデータ・文献)

• 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。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
• poc_bearing_diagnosis — py -3.11 examples/poc_bearing_diagnosis.py
• poc_gear_tooth_metrology — py -3.11 examples/poc_gear_tooth_metrology.py
• poc_machine_condition_fusion — py -3.11 examples/poc_machine_condition_fusion.py
• poc_pipe_wall_loss — py -3.11 examples/poc_pipe_wall_loss.py
• poc_recycling_sorting — py -3.11 examples/poc_recycling_sorting.py
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py

型が繋がる次の op(pairs を入力に取れる)

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同カテゴリ(signal)

lowpass · highpass · bandpass · envelope · rms · resample · spectrogram · zero_crossing_rate

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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.

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