Beamforming

A uniform linear microphone array sees one or more far-field sound sources. Three direction-of-arrival estimators — Bartlett, MVDR, and MUSIC — share the same data and disagree about where the sources are. Drag sources, change the geometry, and watch them argue.

Scene · drag the sources

Array geometry

Wavefront · what each element sees

Time × element

Each row is one element. The wave from an off-broadside source hits the elements at staggered times — that tilt across rows is what the algorithms read. When d > λ/2 the tilt aliases, which is the same fact as a grating lobe.

Spatial spectrum

Power vs. angle
Bartlett (delay-and-sum) MVDR (Capon) MUSIC True DOA

Array geometry

Elements8
Element spacing4.3 cm
Source frequency4.0 kHz
Wavelength λ8.6 cm
d / λ0.50
Aperture30.1 cm
Rayleigh limit16.4°
Grating lobesnone

Signals & noise

SNR per source10 dB
Snapshots200

Sources drag in scene, or use sliders

Teaching presets

All three estimators receive the same snapshots from the same noisy array — the only differences below are in the math each one applies.