On retiming of multirate DSP algorithms

The retiming of DSP algorithms exhibiting multirate behavior is treated. Using the non-ordinary marked graph model and the reachability theory, we provide a new condition for valid retiming of multirate graphs. We show that for a graph with n nodes the reachability condition can be split into the reachability condition for the topologically-equivalent unit-rate graph (all rates set to one), and (n/sup 2/-n)/2 rate-dependent conditions. Using this property a class of equivalent graphs of reduced complexity is introduced which are equivalent in terms of retiming. Additionally, the circuit-based necessary condition for valid retiming of multirate graphs is extended for the sufficient part.