fullseye

tb_apply_weighting — 2D typed op

tb_apply_weighting: input → output

図は合成の入力 128×128 で実際に走らせた出力。左が入力、右が出力。点群は上から見た散布(明るさ = z)、1-D 列は折れ線、体積は z 方向の最大値投影、動画は中央フレーム、複素画像は振幅、絵にならない返り値は値そのもの。

つまみ a は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。

つまみ b は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。

段階(前置きの op → この op。左から順):

tb_apply_weighting: stages

別の画像でも(合成シーン / 写真 / 硬貨。上段が入力、下段がその出力。つまみは既定):

tb_apply_weighting: other inputs

使い方

Apply an A / C / Z frequency weighting to a signal, zero-phase.

The weighting is applied as a real, even gain in the frequency domain, so it introduces no phase distortion and no group delay — the result is aligned sample-for-sample with the input, which a recursive filter implementation would not be.

Measured: a 1 kHz sine at 16 kHz (16000 samples, exactly 1000 periods) is returned unchanged by both A and C weighting — max absolute difference 1.078e-13 for A and 1.225e-13 for C — because both curves are exactly 0 dB at 1 kHz by construction. A 100 Hz sine of amplitude 1.0 comes back with amplitude 0.110373 under A weighting, against the closed form 10**(-19.1428/20) = 0.110373.

kind="Z" returns a copy, unchanged.

A tone that is not a whole number of periods in the record reads too loud, by up to 17 dB, and nothing raises. The multiplication is over the record’s own DFT, which treats it as periodic; a tone that does not close on itself leaks across every bin. That leakage would be harmless if the weighting were flat, but A weighting spans about 40 dB between 20 Hz and 1 kHz, so a sidelobe 40 dB below a 31.5 Hz tone arrives at 1 kHz weighted 40 dB higher and takes over the sum. Measured, 0.5 s at 48 kHz, error against the closed-form A(f) for a pure tone:

========== ============= ========== ============== f (Hz) periods error (dB) bin-centred? ========== ============= ========== ============== 22.0 11.0 +0.0000 yes 31.5 15.75 +7.7986 no 20.5 10.25 +17.2116 no (worst, 20-200 Hz) 63.0 31.5 +0.1121 no 100.0 50.0 +0.0000 yes 1000.0 500.0 -0.0000 yes ========== ============= ========== ==============

31.5 Hz is a nominal one-third-octave centre, so this is a path a real measurement walks into rather than a contrived one. The error is always positive — leakage only ever adds power at frequencies the curve favours.

Two things confirm the diagnosis is dynamic range and not arithmetic. The same 31.5 Hz tone under C weighting, whose tilt over the same span is a few dB rather than forty, is off by only +0.0493 dB. And lengthening the record to where the tone does close on itself removes it entirely: at 31.5 Hz the error is +7.7524 dB over 0.25 s, +7.7986 over 0.5 s, +0.4615 over 1 s, and -0.0000 over 2 s and 4 s (63 and 126 whole periods).

Two candidate cures were measured (error in dB against the closed form, 0.5 s at 48 kHz):

=================================== ======== ======== ======== treatment 31.5 Hz 20.5 Hz 22.0 Hz =================================== ======== ======== ======== as implemented (rectangular) +7.7986 +17.2116 +0.0000 zero-pad x4 (linear convolution) +5.5620 +14.3352 +0.7969 Hann window, corrected for its gain +0.0534 +0.1841 +0.1505 =================================== ======== ======== ========

Padding barely helps — zero-padding a tone puts an abrupt edge into the record and an edge is broadband. A Hann window does essentially cure it, turning +17 dB into +0.18 dB, at the cost of the bin-centred columns which go from exactly 0 to about 0.15 dB. So why is it not the default?

Because it would trade a loud error for a quiet one. L_eq is an energy average over the record, and a window is not energy-preserving for anything that is not stationary. Measured with Z weighting (so the window is the only thing acting) on a 50 ms 1 kHz burst inside a 0.5 s record, all three placements being -13.0103 dB unwindowed as they must be:

============== ============ =========== burst position Hann (dB) difference ============== ============ =========== start -36.0587 -23.05 centre -8.8218 +4.19 end -36.0587 -23.05 ============== ============ ===========

A window makes the answer depend on where in the record the sound happened, which is precisely the “plausible wrong number” this module refuses to ship by default. So the rectangular behaviour stays, and the Hann estimate is available by asking for it: equivalent_level(..., window="hann"). Use it when the record is stationary and tonal — which is exactly when the leakage bites — and never when the level of a transient is the point.

A cure with neither cost is a different implementation entirely: the standard cascade of A-weighting biquads in the time domain, which would give up the exact-0-dB-at-1-kHz-by-construction property this function is built on, and the zero group delay promised above.

Also worth doing: give the analysis enough record that the content is many periods long, prefer durations that are whole multiples of the period you care about, and read a low-frequency A-weighted level from :func:octave_spectrum (which reports per-band power, so leakage is visible as energy in bands where none belongs) rather than from a single number.

Raises ValueError: everything :func:_as_signal refuses, an unknown kind, rate <= 0.

Typed bridge of the acoustics op apply_weighting into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b are unused.

参考(サンプルデータ・文献)

Studio で試す

下のプログラムは実際に走ることを確かめてある(図と同じ入力)。Studio のヘルプではこのブロックがボタンになり、その場で読み込んで実行できる。

img_to_signal 0.50 0.50
tb_apply_weighting 0.50 0.50

実行できる例(この op を実際に呼ぶ検証済みサンプル)

次の例は元の台帳 op apply_weighting を呼ぶもの。この橋渡し op は同じ実装を fn(v, a, b) 規約に合わせただけなので、挙動はそのまま当てはまる(呼び出し形だけ違う)。

型が繋がる次の op(signal を入力に取れる)

identity · tb_create_funct_1d_array · tb_smooth_funct_1d_gauss · tb_smooth_funct_1d_mean · tb_derivate_funct_1d · tb_integrate_funct_1d · tb_zero_crossings_funct_1d · tb_abs_funct_1d

同カテゴリ(typed)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_points_render · tb_statistical_outlier_removal · tb_radius_outlier_removal

Provenance: ops.py — 2D 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.

This site is open source. Improve this page.