beamform op• データ種: beatcube → signal
• 呼び出し: 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) (または 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.
• 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
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.