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Schur Functions

A Schur function $ S(z)$ is any stable discrete-time rational transfer function having a modulus not exceeding $ 1$ on the unit circle,

$\displaystyle \left\vert S(e^{j\omega T})\right\vert\leq 1
$

The corresponding continuous-time transfer function $ S_c(s)$ satisfies the same condition on the $ j\omega$ axis, i.e.,

$\displaystyle \left\vert S_c(j\omega)\right\vert\leq 1
$

The reflection transfer function (``reflectance'') corresponding to any positive-real immittance is a Schur function


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``Lumped Elements, One-Ports, and Passive Impedances'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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