4 research outputs found
Characterizations of rectangular (para)-unitary rational Functions
We here present three characterizations of not necessarily causal, rational
functions which are (co)-isometric on the unit circle: (i) Through the
realization matrix of Schur stable systems. (ii) The Blaschke-Potapov product,
which is then employed to introduce an easy-to-use description of all these
functions with dimensions and McMillan degree as parameters. (iii) Through the
(not necessarily reducible) Matrix Fraction Description (MFD).
In cases (ii) and (iii) the poles of the rational functions involved may be
anywhere in the complex plane, but the unit circle (including both zero and
infinity).
A special attention is devoted to exploring the gap between the square and
rectangular cases.Comment: Improved versio
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 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