Design of 2-D Doubly Complementary Filters Based on Nonsymmetric Half-Plane Allpass Filters

A parallel-connected structure based on recursive nonsymmetric half-plane (NSHP) digital allpass filters is presented for designing two-dimensional (2-D) recursive doubly complementary (DC) filters. First, the theory of 2-D recursive digital allpass filters (DAFs) with NSHP support region for filter coefficients is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem that minimizes the phase error in the least-squares (L₂) sense with a closed-form solution. The novelty of the presented 2-D NSHP DAFs structure is that it possesses the advantage of better performance in designing DC filters over existing 2-D structures based on quarter plane (QP) DAFs and tremendously saves the computational complexity for designing sampling rate converters. Finally, a design example is provided for conducting illustration and comparison.