Stability Testing and Quantisation Error Estimation for 2-D Recursive Filters by Complex Integrals Method

The stability testing of 2-Dimensional recursive digital filters had been a very hot problem in 1970´s and 80´s. The right solution is not yet available though some researchers have been working on this problem even now. We have proposed in this paper a test procedure to test the stability of 1-D recursive digital filters and quantization error estimation for the same filters. We also gave for a restricted order 2-D digital filters, a method to test the stability of the given transfer function which is devoid of nonessential singularities of the second kind. In both the 1-D and 2-D cases the available methods of evaluating the complex integrals for variance is used to conclude about the stability of the filter and also the estimation of quantization error.