07. Conjectured Properties

GUIDE: Elementary Digital Filter Theory - Julius O. Smith III. Conjectured Properties

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Introduction to Digital Filters with Audio Applications", by Julius O. Smith III, Copyright © 2017-11-26 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Conjectured Properties

The following conjectures are true for analog positive-real functions, but no rigorous attempt was made to establish them in the discrete-time case.

  • If all poles and zeros of a PR function are on the unit circle, then they alternate along the circle.
  • If $B(z)/A(Z)$ is PR, then so is $B^\, where the prime denotes differentiation in $z$.

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