Two-dimensional non-symmetric half-plane recursive doubly complementary digital filters

This paper deals with the problem of two-dimensional (2-D) recursive doubly complementary (DC) digital filter design. We present a structure of 2-D recursive DC filters by using 2-D non-symmetric half-plane (NSHP) digital all-pass filters (DAFs). The novelty of using 2-D NSHP recursive DAFs to construct a 2-D recursive DC filter is that the resulting 2-D NSHP recursive DC filter shows better performance than conventional 2-D recursive DC filter based on 2-D quarter-plane (QP) DAFs. Moreover, the proposed structure possesses a favorable 2-D doubly complementary half-band (DC-HB) property that allows about half of the 2-D NSHP recursive DAF's coefficients to be zero. This leads to considerable savings in computational burden. To deal with the stability of the 2-D NSHP recursive DC filter during the design process, we can either impose some necessary constraints on the phases of the 2-D NSHP recursive DAFs or utilize a penalty function involving a stability error computed by using a spectral factorization-based algorithm to ensure the stability of a designed 2-D NSHP recursive DC filter pair. Design of a diamond-shape decimation/interpolation filter is presented for illustration and comparison.