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Abstract
Computational modelling of audio systems commonly involves discretising lumped models. The properties of common discretisation schemes are typically derived through analysis of how the imaginary axis on the Laplacetransform splane maps onto the Ztransform zplane and the implied stability regions. This analysis ignores some important considerations regarding the mapping of individual poles, in particular the case of highlydamped poles. In this paper, we analyse the properties of an extended class of discretisations based on Möbius transforms, both as mappings and discretisation schemes. We analyse and extend the concept of frequency warping, wellknown in the context of the bilinear transform, and we characterise the relationship between the damping and frequencies of poles in the s and zplanes. We present and analyse several design criteria (damping monotonicity, stability) corresponding to desirable properties of the discretised system. Satisfying these criteria involves selecting appropriate transforms based on the pole structure of the system on the splane. These theoretical developments are finally illustrated on a diode clipper nonlinear model.
Original language  English 

Title of host publication  Proceedings of the 18th International Conference on Digital Audio Effects 
Editors  Peter Svensson, Ulf Kristiansen 
Place of Publication  Trondheim, Norway 
Pages  371–378 
Number of pages  8 
Publication status  Published  30 Nov 2015 
Externally published  Yes 
Event  18th International Conference on Digital Audio Effects (DAFx15)  Norwegian University of Science and Technology, Trondheim, Norway Duration: 30 Nov 2015 → 03 Dec 2015 
Publication series
Name  DAFx Proceedings 

Publisher  DAFx 
ISSN (Print)  24136700 
ISSN (Electronic)  24136689 
Conference
Conference  18th International Conference on Digital Audio Effects (DAFx15) 

Country/Territory  Norway 
City  Trondheim 
Period  30/11/2015 → 03/12/2015 
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Dive into the research topics of 'Design Principles for Lumped Model Discretisation Using Möbius Transforms'. Together they form a unique fingerprint.Activities
 1 Participation in conference

18th International Conference on Digital Audio Effects (DAFx15)
Kurt Werner (Participant)
30 Nov 2015 → 03 Dec 2015Activity: Participating in or organising an event types › Participation in conference