fullseye
tb_beamform_delay_sum — 2D typed op
- データ種:
beatcube→signal - 呼び出し:
fullseye.apply(img, "tb_beamform_delay_sum", a=0.5, b=0.5)(2-D は 1 画像 + 2 スカラつまみa,b∈[0,1]のモデル)
図は合成の入力 128×128 で実際に走らせた出力。左が入力、右が出力。点群は上から見た散布(明るさ = z)、1-D 列は折れ線、体積は z 方向の最大値投影、動画は中央フレーム、複素画像は振幅、絵にならない返り値は値そのもの。
つまみ a を振る(0.1 / 0.5 / 0.9、もう一方は既定):
つまみ b は出力を変えない(実測: 0.1 / 0.5 / 0.9 で同一)。
段階(前置きの op → この op。左から順):
別の画像でも(合成シーン / 写真 / 硬貨。上段が入力、下段がその出力。つまみは既定):
使い方
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.
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.
参考(サンプルデータ・文献)
- 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。
Studio で試す
下のプログラムは実際に走ることを確かめてある(図と同じ入力)。Studio のヘルプではこのブロックがボタンになり、その場で読み込んで実行できる。
img_to_beatcube 0.50 0.50
tb_beamform_delay_sum 0.50 0.50
実行できる例(この op を実際に呼ぶ検証済みサンプル)
次の例は元の台帳 op beamform_delay_sum を呼ぶもの。この橋渡し op は同じ実装を fn(v, a, b) 規約に合わせただけなので、挙動はそのまま当てはまる(呼び出し形だけ違う)。
- fmcw_range_doppler —
py -3.11 examples/fmcw_range_doppler.py - poc_multibeam_bathymetry —
py -3.11 examples/poc_multibeam_bathymetry.py
型が繋がる次の op(signal を入力に取れる)
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
同カテゴリ(typed)
tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_points_render · tb_statistical_outlier_removal · tb_radius_outlier_removal
Provenance: ops.py — 2D 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.