Low-Complexity Maximally-Decimated Multirate 3-D Spatio-Temporal FIR Cone and Frustum Filters

A low-complexity multirate 3-D spatio-temporal FIR cone and frustum filter structure is proposed having potential applications as a spatio-temporal directional filter. The cone filter structure employs a 1-D modified discrete Fourier transform (DFT) filter bank and 2-D spatial filters. The frustum filter having a double-frustum-shaped passband oriented along the temporal frequency axis is approximated by employing an appropriate subset of subbands. Low computational complexity is achieved by maximal decimation in the temporal dimension, and by employing the DFT-polyphase realization to implement the 1-D modified DFT filter bank. The cone and frustum filters are almost alias free, and provide near-perfect reconstruction. The reduction in computational complexity, relative to undecimated and under-decimated realizations, is numerically confirmed by means of a potential application involving the attenuation of strong broadband plane wave interference.