beamform op• データ種: beatcube → signal
• 呼び出し: import 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 dsp's find_peaks and funct1d's smoothing apply to it.
Use 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 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.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• fmcw_range_doppler — py -3.11 examples/fmcw_range_doppler.py
• poc_multibeam_bathymetry — py -3.11 examples/poc_multibeam_bathymetry.py
signal 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.