Implementation of high order recursive filters as sub-filters

A new technique for partitioning high-order recursive digital filters is described, and some examples are presented of its application to all-pole systems, which, although not of very high order, exhibit the basic problems of high-order systems, i.e., many poles in close proximity. The key element is the incomplete partial fraction expansion (IPFE) which enables a rational polynomial to be split into the sum of two or more rational polynomials. It is shown that for tame problems when conventional parallel and cascade spectra could be found, the IPFE implementation behaves similarly to them. When the problem becomes less tame, it is difficult to demonstrate inconvertably that the PIFE method works.< >