fullseye

companding_mu_law — ONED signal op

• データ種: signal → signal
• 呼び出し: import fullseye as fs; fs.ledger.companding_mu_law(x, mu=255.0, bits=8) (実装を直接呼ぶなら import dsp; dsp.companding_mu_law(x, mu=255.0, bits=8)、台帳から引くなら ops1d.get("companding_mu_law"))

使い方

mu-law companding — the G.711 curve, used here on any 1-D signal.

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.

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)

• gallery2d_gray_arith — py -3.11 examples/gallery2d_gray_arith.py

型が繋がる次の op(signal を入力に取れる)

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

同カテゴリ(signal)

lowpass · highpass · bandpass · envelope · rms · local_std · quantize · resample

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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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