Stability analysis of 2-D digital filters having second kind singularities-analog approach

The authors show how stability analysis of a 2-D digital function can be carried out in the analog domain itself by testing the two-variable analog function from which the 2-D digital function is derived by the double bilinear transformation. This is particularly useful since one of the common methods of generating a 2-D digital function is by the application of double bilinear transformation on an appropriate two-variable analog function satisfying given frequency-response characteristics. By observing the conditions of the theorem, it may be stated that a necessary condition for stability or boundedness of a 2-D digital function is that the denominator of the corresponding 2-V analog function be scattering Hurwitz, as defined by A. Fetteweis (1984). Finally, these results have been used to study the existence of the double square integral in the analog domain.<>