The Coefficient Space Approach to the Stability of Multidimensional Digital Filters

This report is concerned with the development of a new approach to the problem of stability for multidimensional, causal, recursive, all pole, digital filters. The distinguishing feature of this approach is that general stability criteria can be derived directly in terms of the coefficients of the transfer function of the filter. Thus by use of this method it is sometimes possible to determine which coefficients of the transfer function are critical to the stability of the filter, information which is, of course, important in filter design. Also the emphasis of this approach is on the development of a conceptual method for considering the problem in complete generality.