Three-dimensional cone filter banks

Three dimensional (3-D) narrow cone-shaped filter passbands are ideally required for the selective filtering of sampled broad-band 3-D plane waves on the basis of their directions of arrival. A method is proposed for approximating narrow 3-D cone-shaped passbands using a 3-D cone-filter-bank structure in which the subbands consist of band limited 3-D narrow-band infinite impulse response (IIR) beam filters having 3-D uniform bandwidths that are approximately proportional to their distance from the origin in the 3-D frequency space. The 3-D beam filters may be realized from a cascade of 3-D IIR frequency-planar filters. It is shown that the proposed 3-D cone filter bank achieves low distortion of broad-band passband 3-D plane waves, and significant attenuation of broad stopband plane waves.