Properties of Positive Real Functions

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA

Abstract:

The purpose of this note is to develop facts about positive real transfer functions for discrete-time linear systems, i.e., in the $z$ plane. Positive real functions arise naturally as the impedance functions of passive continuous-time systems.

Detailed Contents (and Navigation)

• Introduction
• Relation to Stochastic Processes
• Relation to Schur Functions
• Relation to functions positive real in the right-half plane
• Special cases and examples
• Minimum Phase (MP) polynomials in $z$
• Conjectured Properties
• Bibliography
• About this document ...