typed op• 데이터 종류: signal → signal
• 호출: fullseye.apply(img, "tb_apply_weighting", a=0.5, b=0.5)(2-D 는 이미지 1 장 + 스칼라 노브 2 개 a,b∈[0,1] 모델)
*그림은 128×128 합성 입력에서 실제로 실행한 출력. 왼쪽이 입력, 오른쪽이 출력. 점군은 위에서 본 산점도(밝기 = z), 1-D 열은 꺾은선, 볼륨은 z 방향 최대값 투영, 동영상은 가운데 프레임, 복소 영상은 진폭이며, 그림이 되지 않는 반환값은 값 자체를 표시한다.*
*노브 a 는 출력을 바꾸지 않는다(실측: 0.1 / 0.5 / 0.9에서 동일).*
*노브 b 는 출력을 바꾸지 않는다(실측: 0.1 / 0.5 / 0.9에서 동일).*
단계(앞에 오는 op → 이 op, 왼쪽에서 오른쪽으로):
▸ tb_apply_weighting: 단계 (문서 사이트)
다른 영상에서도(합성 장면 / 사진 / 동전. 윗줄이 입력, 아랫줄이 그 출력. 노브는 기본값):
▸ tb_apply_weighting: 다른 입력 이미지 (문서 사이트)
신호에 A / C / Z 주파수 가중을 제로 위상(zero-phase)으로 적용.
> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.
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 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 _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.
• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.
• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.
아래 프로그램은 실제로 실행됨을 확인했습니다(그림과 같은 입력). Studio 도움말에서는 이 블록이 버튼이 되어 즉시 불러와 실행할 수 있습니다.
img_to_signal 0.50 0.50 tb_apply_weighting 0.50 0.50
아래 예제는 원래의 대장 op apply_weighting를 호출한다. 이 브리지 op는 같은 구현을 fn(v, a, b) 규약에 맞춘 것뿐이므로 동작은 그대로 적용된다(호출 형식만 다름).
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
signal 를 입력으로 받는 것)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
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.