Other Mathematics Commons^™

Characterizations Of Families Of Rectangular, Finite Impulse Response, Para-Unitary Systems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class U). First, we offer three characterizations of these systems. Then, introduce a description of all FIRs in U, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs.

Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in U, so is the whole family.

A key role is …