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

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 arbitrary magnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability with the expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage of approximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from the approximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need for stabilization 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 least squares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be used to 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.