typed op• Data kinds: signal → signal
• Call: fullseye.apply(img, "tb_apply_weighting", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_apply_weighting: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_apply_weighting: other inputs (docs site)
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.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_signal 0.50 0.50 tb_apply_weighting 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op apply_weighting. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
signal as input)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 operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.