Formation of the block Toeplitz matrix for two-dimensional PLSI polynomials (Q1092865)

The planar least-squares inverse (PLSI) polynomials are used to stabilize two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.