Results on cyclic signal processing systems

We present a state space description for cyclic LTI systems which find applications in cyclic filter banks and wavelets. We also revisit the notions of reachability and observability in the cyclic context, and show a number of important differences from traditional noncyclic case. A number of related problems such as the paraunitary interpolation problem and the cyclic paraunitary factorizability problem can be understood in a unified way by using the realization matrix defined by the state space description.