A 3-D Sparse FIR Frustum Filter for Enhancing Broadband Plane Waves

A 3-D finite-extent impulse response (FIR) frustum filter having sparse coefficients is proposed for enhancing broadband plane waves (PWs) received by uniform aperture arrays. Motivated by the design technique of 1-D interpolated FIR filters, the proposed filter is realized by cascading a spatially-upsampled 3-D FIR prototype filter having a frustum-shaped passband and a 3-D FIR masking filter having a parallelepiped passband. Sparsity of the filter coefficients is achieved through the spatial upsampling of the coefficients of the prototype filter and by hard-thresholding the coefficients of both prototype and masking filters. The proposed 3-D FIR frustum filter saves 39.5% multiplications and 66.6% additions compared to the state-of-the-art 3-D FIR frustum filters without degrading the performance in enhancing broadband PWs.