Characterizations of families of rectangular, finite impulse response, para-unitary systems Academic Article uri icon


  • 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 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.

publication date

  • January 1, 2017