fullseye

quantize — ONED signal op

• データ種: signal → signal
• 呼び出し: import fullseye as fs; fs.ledger.quantize(x, bits=8, mode='round', dither=None, seed=0) (実装を直接呼ぶなら import dsp; dsp.quantize(x, bits=8, mode='round', dither=None, seed=0)、台帳から引くなら ops1d.get("quantize"))

使い方

Scalar quantiser with the error model stated, plus optional dither.

bits sets the number of levels L = 2**bits over the signal’s own min..max range. mode is "round" (mid-tread, unbiased) or "truncate" (floor, the convention PIL’s posterize and most fixed-point casts use).

The two differ by more than a rounding convention. With step Delta = range/(L-1) both have error variance Delta**2/12, but truncation also carries a mean of -Delta/2, so its mean square error is

truncate:  Delta**2/12 + (Delta/2)**2 = Delta**2/3
round:     Delta**2/12

— a factor of 4. Anything that measures a level (not just displays it) must round.

dither adds noise before quantising so the error stops being a function of the signal: "tpdf" (triangular, the audio standard — two uniform draws summed, so the error’s variance no longer depends on the sample value) or "rpdf" (one uniform draw). Dither raises the total error power but removes the correlation that makes quantisation audible as distortion rather than as hiss. seed fixes the draw so the op stays deterministic.

Applicability. (1) The range is taken from this signal, so two signals quantised separately do not share a scale. (2) bits=1 with no dither is a comparator, not a quantiser — the error model does not apply. (3) The error model assumes the signal moves by more than a step between samples; on a flat stretch the error is a constant offset, not noise.

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)

• poc_cold_chain_excursion — py -3.11 examples/poc_cold_chain_excursion.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 · companding_mu_law · 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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