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.