Stability tests for two-dimensional recursive filters

Abstract

The main objective of this work is to review the algebraic stability tests of two-dimensional recursive filters. Both frequency-domain methods and the data-domain method are presented. For the frequency-domain method, various existing algebraic methods are discussed. This include the Shanks, Huang, Maria-Fahmy, and Anderson-Jury methods. For the data-domain method, the extension of the Lyapunov theorem is presented including an approximate algebraic test. Both frequency-domain and data-domain proof are given for the approximate test. Some properties of a two-dimensional system which are different from a one-dimensional system are included. Several filters are evaluated by both methods and the agreement of the results is indicated.