Stability of general two-dimensional recursive digital filters

Two-dimensional recursive filters are defined from a different point of view. A general stability preserving mapping theorem is presented which allows most recursive filters of a particular type to be mapped into any other type of recursive filter. In particular, any type of filter can be mapped into a first-quadrant filter. This mapping is used to prove a number of general stability theorems. Among these is a theorem which relates the stability of any digital filter to its two-dimensional phase function. Furthermore, other stability theorems which are valid for any type of recursive filter are presented. Finally, a number of practical stability tests are developed including one which requires the testing of only several one-dimensional polynomial root distributions with respect to the unit circle.