Characterizations of families of rectangular, finite impulse response, para-unitary systems

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 played by Hankel matrices.

Original languageEnglish
Pages (from-to)395-423
Number of pages29
JournalJournal of Applied Mathematics and Computing
Issue number1-2
StatePublished - 1 Jun 2017


  • Blaschke–Potapov
  • Co-isometry
  • Finite impulse response
  • Hankel operator
  • Isometry
  • Laurent polynomials
  • Realization


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