signal op• 資料種類:signal → signal
• 呼叫: import fullseye as fs; fs.ledger.companding_mu_law(x, mu=255.0, bits=8)(要直接呼叫實作,import dsp; dsp.companding_mu_law(x, mu=255.0, bits=8);從台帳取用則 ops1d.get("companding_mu_law"))
μ 律壓擴 —— 把 G.711 的曲線用於任意一維訊號。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Compress with `F(v) = sign(v) * ln(1 + mu|v|) / ln(1 + mu)` on the signal
scaled to `[-1, 1]`, quantise uniformly, expand back. The steps end up fine
near zero and coarse near full scale, which is the right allocation when the
interesting part of the signal is small compared with its peaks — speech,
vibration, anything with a large crest factor.
This is where mu-law comes from: the image operator
`companding_mu_law` is the same curve applied to intensity. Reporting both
keeps the family honest about which dimension the technique was designed for.
Applicability — it is the crest factor that decides. Measured on a sine
of amplitude *A* with one sample pinned at full scale, so the crest factor is
exactly `1/A` (mean square error relative to a uniform quantiser):
crest 50 4 bit 0.011 6 bit 0.014 (about 90x better)
crest 20 4 bit 0.122 6 bit 0.101
crest 6.7 4 bit 0.613 6 bit 0.616
crest 2.0 4 bit 4.22 6 bit 6.03 (several times WORSE)
So the rule is crest factor above roughly 7 — speech, vibration, impact.
Below that, a plain uniform quantiser wins and mu-law actively hurts.
★Note the peak is a single sample: on random signals of the same family
the advantage swung between 0.55 and 0.87 purely with the seed, because the
largest excursion sets the scale. Measure the crest factor of *your* signal,
do not assume it from the distribution.
Other limits: `mu` near 0 degenerates to uniform quantisation (that is how
you check the curve is doing anything), and the curve is fixed — unlike a
Lloyd-Max codebook fitted to the signal — which is the point when values must
stay comparable across recordings.
• 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。
• gallery2d_gray_arith — py -3.11 examples/gallery2d_gray_arith.py
signal 作為輸入)create_funct_1d_array · create_funct_1d_pairs · smooth_funct_1d_gauss · smooth_funct_1d_mean · derivate_funct_1d · integrate_funct_1d · zero_crossings_funct_1d · local_min_max_funct_1d
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · resample
*Provenance: dsp.py — ONED 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.