The discretization of continuous-time systems is considered, and an extension of the bilinear transform to the case of time-varying systems is introduced. Termed the “time-varying bilinear transform,” the transform generates a sequence of digital filter coefficients in response to continuous-time system changes that keeps the digital filter state compatible with the changing digital filter coefficients. Accordingly, transients in the digital filter output that don’t appear in the continuous system output are avoided. For an Nth-order continuous-time system, a step change in the system produces a sequence of N intermediate sets of digital filter coefficients, bracketed by what would be generated by the bilinear transform applied to the initial and final systems. Sequences are tabulated for direct and transpose canonical forms and first-order and second-order systems, and examples of first-order and second-order analog filters with time-varying components are presented.

Authors: Abel, Jonathan S.; Berners, Dave
Affiliations: Universal Audio; CCRMA, Stanford University, Stanford, CA, USA(See document for exact affiliation information.)
AES Convention: 141 (September 2016) Paper Number: 9686
Publication Date: September 20, 2016
Subject: Signal Processing

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