Stabilization of 2D NSHP Recursive Digital Filters withGuaranteed Stability Using PLSI Polynomials

摘要

Two-dimensional digital filters have gained wide acceptance in recent years. For recursive filters, nonsymmetric half-plane versions(also known as semicausal) are more general than quarter-plane versions (also known as causal) in approximating arbitrarymagnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability withthe expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage ofapproximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from theapproximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need forstabilization procedures that produce a stable filter with similar magnitude response as that of the unstable filter. This paper,demonstrates a stabilization procedure for a two-dimensional nonsymmetric half-plane recursive filters based on planar leastsquares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be usedto obtain stable PLSI polynomials. Therefore obtaining PLSI polynomial is computationally less involved with the proposed form-preserving transformation as compared to existing methods, and the stability of the resulting filters is guaranteed.