Planar least squares inverse polynomials and practical-BIBO stabilization on n- dimensional linear shift-invariant filters

Development of simple procedures for the design of stable recursive n-dimensional (n -D) filters continues to be an important field of study. Because of the involved computations required to incorporate the stability constraints in the design stage, the search for a technique by which the stability problem could be separated from the approximation problem is of great importance. Continuing in this direction, some results concerning properties of PLSI (Planar Least Squares Inverse) polynomials vis-ai-vis Agathoklis and Bruton concept of practical-BIBO (Bounded-Input Bounded-Output) stability [1] are reported in this paper. It is shown that PLSI technique always leads to a BIBO stable n - D digital filter, with input signals whose region of support is unbounded at most in one dimension.