Characterizations of families of rectangular finite impulse response,   para-unitary systems
  We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class $\mathcal{U}$). First, we offer three characterizations of these systems. Then, introduce a %easy-to-use description of all FIRs in $\mathcal{U}$, 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 $\mathcal{U}$, so is the whole family.   A key role is played by Hankel matrices. 
Daniel Alpay and Palle Jorgensen and Izchak Lewkowicz
math.CV