typed op• Datenarten: beatcube → signal
• Aufruf: fullseye.apply(img, "tb_beamform_delay_sum", a=0.5, b=0.5) (das 2-D-Modell ist ein Bild plus zwei skalare Regler a,b∈[0,1])
Delay-and-Sum-(Bartlett-)Winkelspektrum für eine Range-Doppler-Zelle.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
Takes the per-antenna complex value at a single range-Doppler cell — by
default the strongest one — and for each steering angle removes the expected
inter-element phase and sums:
`P(theta) = |sum_k conj(exp(1j*2*pi*d*k*sin(theta)/lambda)) * x_k|^2`
which peaks at the true arrival angle with value `(N_a * |a|)^2`: the
aperture gives `N_a in amplitude, N_a^2` in power. That is the exact
ground truth the tests pin. Measured with 8 elements: the peak power is
bit-exactly `(N_a*N_c*N_s)^2 = 268435456` (relative error 0.0), and
sweeping the true angle from -80 to +80 degrees in 5-degree steps (33 cases)
the reported angle matches the truth with a maximum error of 0.0 degrees.
The steering grid defaults to `arange(-90, 90.5, 1.0). normalize=True`
divides by `N_a^2 * N_c^2 * N_s^2` so that a unit-amplitude bin-centred
target peaks at 1.0.
Returns a 1-D float64 array of powers, one per grid angle — a plain signal,
so :mod:dsp's `find_peaks and :mod:funct1d`'s smoothing apply to it.
Use :func:beamform_doa if you want the angles themselves.
*range_bin* is a plain `0..N_s-1` index; *doppler_bin* is the signed
velocity bin, the same convention :func:range_doppler_peaks reports, so a
detection can be handed straight back in. Both or neither — half a cell
address raises rather than quietly beamforming the strongest cell instead.
Raises `ValueError`: no aperture — either a single element, or many
elements packed into under ~0.28 wavelengths. In both cases the spectrum is
flat to within float noise and `argmax` returns the first grid angle, i.e.
a confident report of -90 degrees that is pure tie-breaking (measured: 8
elements at 1e-12 m spacing gave a peak-to-trough spread of exactly 0.0 and
reported -90.0). Also: an all-zero cube or an all-zero selected cell; only
one of *range_bin* / *doppler_bin*; an out-of-bounds bin index; an angle grid
outside `[-90, 90]`; an FFT that overflows to NaN; plus the usual cube and
scalar refusals.
Typed bridge of the rangedoppler op `beamform_delay_sum into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives wavelength_m (default 0.0038934); b` is unused.
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• (noch keine)
signal als Eingabe)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 Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.