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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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Applied Mathematics and Computing, volume 54, in 2017 following peer review. The final publication is available at Springer via DOI: 10.1007/s12190-016-1015-x

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