Aperture and operating frequency of a beamformer are generally proportional to its resolution, and inversely proportional to its beamwidth. This paper addresses the design and implementation of a beamformer with a frequency-dependent limitation of its aperture such that the frequency-dependence of its resolution is eliminated. Operating across a number of octaves, firstly an octave-invariance design is achieved by means of a nested array structure. Secondly, within each octave, a frequency-dependent aperture control then removes the remaining frequency-dependency. By exploiting Fourier properties and correspondences between coefficient and beamspace, we show that this design is exact, and can accommodate the inclusion of arbitrary shading and different look directions.
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