typed op• 数据种类:signal → signal
• 调用:fullseye.apply(img, "tb_apply_weighting", a=0.5, b=0.5)(2-D 的模型是一张图 + 两个标量旋钮 a,b∈[0,1])
对信号施加 A / C / Z 频率计权，零相位。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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.
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• (暂无)
signal 作为输入)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_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal
*Provenance: ops.py — 2D 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.