Weighted Least-Squares Design of 2-D IIR Filters with Arbitrary Frequency Response using Iterative Second-Order Cone Programming

Two-dimensional (2-D) infinite-extent impulse response (IIR) filter design is a challenging problem due to the difficulty in verifying stability. Optimization methods proposed so far predominantly consider the design of 2-D IIR filters having quadrantally-symmetric frequency responses, where the transfer functions have separable denominators. In this paper, we propose a weighted least-squares (WLS) design method for 2-D IIR filters having arbitrary frequency response and stable in the practical bounded-input bounded-output (P-BIBO) sense. Our design considers transfer functions with nonseparable numerators and denominators having complex- and real-valued coefficients, respectively. We formulate the WLS design as an iterative second-order cone programming problem, which includes constraints to guarantee the P-BIBO stability. Design examples confirm that the proposed WLS method leads to P-BIBO stable 2-D IIR filters.