Array far-field patterns obey Fourier transform theorems, so directional elements spatially filter aliased lobes.

Evidence

One way of reducing the effect of spatial aliasing is to use directive loud­ speakers, instead of point sources, as the array elements. If one uses direc­ tive sources then their polar patterns will act as a form of spatial filter; that is, the off-axis side lobes will be reduced by the axis reduction in sound level that a directive source affords. … Because the far-field polar pattern of an array of point sources is related to the applied signals by a Fourier transform rela­ tionship, all the theorems that apply to the discrete Fourier transform apply to the array loudspeaker. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2892

Categorization

• XREF: Connects to signal-processing/DFT theory the reader likely knows from elsewhere — the array is literally a spatial sampler.
• DEEPTHINKING: The spatial/signal duality — beam pattern as Fourier transform of the aperture — is a lens worth sitting with.