level op• 資料種類:無 → table(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫:import acoustics; acoustics.octave_bands(fraction=3, f_min=22.0, f_max=22050.0, base=10)(或 opsacoustics.get("octave_bands"))
由定義的構造給出 1/N 倍頻程的中心頻率與帶邊。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The band system is a geometric progression through 1 kHz:
`f_c = 1000 * G**(x/b) for odd b and 1000 * G**((2x+1)/(2b))` for
even `b, with edges at f_c * G**(-+1/(2b)). base=10` uses
`G = 10**(3/10)` (the base-ten system, in which ten third-octaves span
almost exactly a decade); `base=2 uses G = 2` exactly. No published
table of centre frequencies is transcribed — the *exact* centres are
computed, which is why `centers` reads 1000.0, 1258.925, 1584.893 rather
than the 1000, 1250, 1600 a published series would give.
**The parity of `fraction` changes where 1 kHz sits, and this surprises
people.** With an odd `b` (1/1, 1/3) there is a band *centred* on exactly
1000.0 Hz. With an even `b` (1/2, 1/6, 1/12, 1/24) the offset in the
exponent means there is no 1 kHz band at all — instead 1000.0 Hz is
exactly a band *edge*, shared by two bands. Measured across
`fraction` = 1, 2, 3, 6, 12, 24: a centre lands on 1000.0 for 1 and 3, and
a lower edge lands on it for 2, 6, 12 and 24, in every case to within
`rtol=1e-12`. That is the defining construction, not an artefact, and it
matters when a level is quoted "at 1 kHz": in an even system that number
comes from one of two adjacent half-bands, not from a band on the tone.
`nominal` is the exact centre rounded to three significant figures, for
labelling only. It is a rounding, not the published nominal series, and
it differs from it: measured, the 1/1-octave centres round to 31.6, 63.1,
126.0, 251.0, 501.0, 1000.0, 2000.0, 3980.0, 7940.0, 15800.0, where the
published series has 125 and 250 where this has 126 and 251. Do arithmetic
with `centers` and supply your own labels if they have to match a report.
Returns a dict: `centers, lower, upper, nominal, fraction`,
`base, ratio (G**(1/b)), bandwidth (upper - lower`),
`index (the integer x`).
Exact identities, asserted in the tests: `upper/lower = G**(1/b)` for every
band, `center = sqrt(lower*upper)` (the centre is the geometric mean of its
edges, by construction), and successive centres are in the ratio `G**(1/b)`.
Measured for `fraction=3, base=10` over 22 Hz - 22.05 kHz (30 bands): the
band containing 1000 Hz has `lower = 891.250938, center = 1000.000000`,
`upper = 1122.018454; upper/lower - G**(1/3) = 2.2e-16`;
`|center - sqrt(lower*upper)| <= 1.8e-12` over all bands; and successive
centre ratios deviate from `G**(1/3) by at most 6.7e-16. With base=2`
the octave centres come out exactly 31.25, 62.5, 125, 250, 500, 1000, 2000,
4000, 8000, 16000 Hz.
Raises `ValueError: fraction not an int in [1, 24], base`
not 2 or 10, non-positive or non-finite `f_min / f_max`,
`f_min >= f_max, and a request for more than :data:MAX_BANDS` bands.
• acoustic_condition_monitoring 族使用指南
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者・年份)與用途見上面的族使用指南。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
table 作為輸入)level)octave_spectrum · weighting_response · apply_weighting · equivalent_level · percentile_level
*Provenance: acoustics.py — ACOUSTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.