fmcw_beat_simulate — RANGEDOPPLER `simulate` op

• Datenarten: keine → beatcube (ein Operator, der allein durch seine Argumente bestimmt ist — er nimmt kein Bild und keine Daten entgegen)

• Aufruf: import rangedoppler; rangedoppler.fmcw_beat_simulate(ranges_m=(10.0,), velocities_ms=(0.0,), angles_deg=None, amplitudes=None, n_samples=64, n_chirps=32, n_antennas=1, sample_rate_hz=10000000.0, slope_hz_per_s=20000000000000.0, chirp_period_s=5e-05, wavelength_m=0.0038934, element_spacing_m=None, phase_deg=0.0, noise_sigma=0.0, seed=0) (oder opsrangedoppler.get("fmcw_beat_simulate"))

Verwendung

Synthetisiert den komplexen `(A, C, S)`-Beat-Würfel für bekannte Ziele.

> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.

The forward model. Every target `t` contributes

`a_t * exp(1j*(2*pi*f_b_t*n/f_s + 2*pi*f_d_t*m*T_c + 2*pi*d*k*sin(th_t)/lam + phi))`

over fast-time sample `n, chirp m and antenna k`, with

`f_b = 2*S*R/c and f_d = 2*v/lambda`. Contributions add linearly, which

is what makes a multi-target cube a valid ground truth: each target's peak

stands at its own bin regardless of the others.

Sign conventions (see the module docstring): `velocities_ms` is

`dR/dt`, so positive is receding and lands in a positive Doppler bin;

`angles_deg` is measured from array boresight and a positive angle advances

the phase of the higher-index elements.

*amplitudes* defaults to 1.0 for every target — there is no radar equation

here, no `1/R^4`, no propagation loss (module docstring, honest limits).

*noise_sigma* adds circular complex Gaussian noise with that per-component

standard deviation, drawn from `numpy.random.default_rng(seed)`; the

default 0.0 returns the exact noiseless cube, which is what the closed-form

tests compare against.

Ground truth: a target placed at an exact bin centre — `R = j*dR` and

`v = i*dv from :func:fmcw_design` — puts the whole of its energy in bin

`(i, j) of :func:range_doppler_map`, whose peak magnitude is then exactly

`a * N_s * N_c`. Measured on the default configuration: the peak magnitude

is bit-exactly 2048.0 (`N_s*N_c`, relative error 0.0), the largest other

cell in the map is 2.6e-16 of it, and with three targets at different bins

and different amplitudes the recovered ranges and velocities are exact to

0.0 metres and 0.0 m/s with amplitudes within 5.6e-17. See

`tests/test_rangedoppler.py`.

Raises `ValueError: a range at or beyond c*f_s/(2S)`, a speed at or

beyond `lambda/(4*T_c), an angle at or beyond asin(lambda/(2d))` — the

three aliasing limits, refused rather than folded silently; a non-positive

range; mismatched target-list lengths; a cube over

:data:MAX_CUBE_ELEMENTS (checked *before* allocation); a negative

amplitude or noise sigma; a non-integer seed; and the usual

string/bool/complex/NaN scalar refusals.

Ausführlicher Anwendungsleitfaden

• Leitfaden zur Familie fmcw_range_doppler

Referenzen (Beispieldaten, Literatur)

• 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.

• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.

Ausführbare Beispiele (verifizierte Samples, die diesen Operator wirklich aufrufen)

• fmcw_range_doppler — py -3.11 examples/fmcw_range_doppler.py

Typkompatible Folge-Operatoren (nehmen `beatcube` als Eingabe)

fmcw_window_apply · range_doppler_map · fmcw_range_profile · beamform_delay_sum · beamform_doa

Gleiche Kategorie (`simulate`)

—

*Provenance: rangedoppler.py — RANGEDOPPLER Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*

fmcw_beat_simulate — RANGEDOPPLER simulate op