synthesis op• データ種: なし → signal(引数だけで決まる op —— 画像やデータの入力を取らない)
• 呼び出し: import acoustics; acoustics.synthesize_bearing_signal(rate=25600.0, duration=1.0, carrier_hz=3000.0, defect_hz=107.0, modulation=0.5, mode='am', damping=0.05, noise_sigma=0.0, seed=None) (または opsacoustics.get("synthesize_bearing_signal"))
既知の欠陥周期で振幅変調した共振 —— 答えの分かっている真値。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
This is the whole reason envelope analysis exists, built forwards so the
answer is known before the measurement. A spall on a bearing race does not
radiate at the defect rate; it strikes a structure that rings at a much
higher resonance, once per defect passage. What reaches the microphone is a
carrier at the resonance, modulated at the defect rate, and the defect
rate itself is not present in the signal as a frequency component at all.
`mode="am"` gives the exactly analysable case,
`x(t) = (1 + m cos(2 pi f_d t)) sin(2 pi f_c t)`. Its analytic envelope is
exactly `1 + m cos(2 pi f_d t) for m < 1`, so the single-sided envelope
spectrum has a line of amplitude exactly m at `f_d` and nothing else.
Measured with `m = 0.5: :func:envelope_spectrum` returns a peak at
107.000000 Hz of amplitude 0.499677 (the 0.06 % shortfall is the band-pass
filter rolling off across the two sidebands, not the demodulation).
`mode="impulse"` gives the physically shaped case: an impulse train at
`f_d, each impulse ringing down as `exp(-2 pi zeta f_c t) sin(2 pi f_c
t)`. The envelope spectrum then shows f_d` and its harmonics, which
is what a real record looks like. Measured with `f_d = 107` Hz: the
envelope-spectrum peak is at 107.000000 Hz and the harmonics at 214 and
321 Hz carry 0.6542 and 0.4748 of the fundamental's amplitude.
In am mode the raw spectrum has nothing at `f_d`: measured, the raw
single-sided amplitude at 107 Hz is 4.3e-16, while the carrier reads
1.000000 and each sideband at 2893 and 3107 Hz reads 0.250000 — exactly
`m/2`, as amplitude modulation requires. In impulse mode the raw amplitude
at 107 Hz is 0.01165, not zero (an impulse train is not a pure product), but
still 18x below what the envelope spectrum recovers from the same record.
Raises `ValueError`: any non-real / non-finite / string / bool scalar,
`rate <= 0, duration <= 0, modulation outside [0, 1)` in am
mode (at `m >= 1 the envelope is |1 + m cos|`, which folds and puts
energy at `2 f_d — a rectified envelope, not the modulation), damping`
outside `(0, 1), a total length over :data:MAX_SAMPLES`, and — the one
that matters — **any requested frequency at or above Nyquist, including the
upper modulation sideband** `f_c + f_d`. An aliased carrier would come
back as a plausible signal at the wrong frequency with no error.
• acoustic_condition_monitoring ファミリ ガイド
• 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。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
• poc_bearing_diagnosis — py -3.11 examples/poc_bearing_diagnosis.py
signal を入力に取れる)stft · envelope_spectrum · spectral_kurtosis · cepstrum · angular_resample · order_spectrum · octave_spectrum · weighting_response
synthesis)*Provenance: acoustics.py — ACOUSTICS 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.