ABSTRACT
This chapter identifies the stability properties of 2-D digital filters are examined and the necessary and sufficient conditions for stability. It provides some simple stability tests for low-order filters. Bounded-input, bounded-output stability can be studied in the frequency domain by examining the constraints imposed on the singularities of the transfer function by the requirement that the output of the filter be bounded when the input is bounded. Stability tests or criteria are efficient algorithms that can be used to determine whether a system is stable or not without actually finding the singularities of the transfer function. Another important approach to the study of stability is based on the classical results of Lyapunov. Frequently, the design of 2-D digital filters is carried out by using low-order filters in cascade or in parallel or an appropriate combination of cascade and parallel filters.
