beamform opbeatcube → signalimport fullseye as fs; fs.ledger.beamform_delay_sum(cube, wavelength_m=0.0038934, element_spacing_m=None, angles_deg=None, range_bin=None, doppler_bin=None, normalize=False) (実装を直接呼ぶなら import rangedoppler; rangedoppler.beamform_delay_sum(cube, wavelength_m=0.0038934, element_spacing_m=None, angles_deg=None, range_bin=None, doppler_bin=None, normalize=False)、台帳から引くなら opsrangedoppler.get("beamform_delay_sum"))Delay-and-sum (Bartlett) angle spectrum for one range-Doppler cell.
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.
py -3.11 examples/fmcw_range_doppler.pypy -3.11 examples/poc_multibeam_bathymetry.pysignal を入力に取れる)—
beamform)Provenance: rangedoppler.py — RANGEDOPPLER 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.