signal op• Data kinds: signal → signal
• Call: import fullseye as fs; fs.ledger.companding_mu_law(x, mu=255.0, bits=8) (implementation को सीधे call करना हो तो import dsp; dsp.companding_mu_law(x, mu=255.0, bits=8), registry से लेना हो तो ops1d.get("companding_mu_law"))
mu-law companding — G.711 curve, यहाँ किसी भी 1-D signal पर उपयोग।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
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.
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।
• gallery2d_gray_arith — py -3.11 examples/gallery2d_gray_arith.py
signal को input के रूप में लेते हैं)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 operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.