The PLSI method of stabilizing two-dimensional nonsymmetric half-plane recursive digital filters (Q1773659)

Summary: Two-dimensional (2D) recursive digital filters find applications in image processing as in medical X-ray processing. Nonsymmetric half-plane (NSHP) filters have definitely positive magnitude characteristics as opposed to quarter-plane (QP) filters. In this paper, we provide methods for stabilizing the given 2D NSHP polynomial by the planar least squares inverse (PLSI) method. We prove in this paper that if the given 2D unstable NSHP polynomial and its PLSI are of the same degree, the PLSI polynomial is always stable, irrespective of the relationship among its coefficients. Examples are given for 2D first-order and second-order cases to prove our results. The generalization is done for the \(N\)th order polynomial.