Cylinder with Conical Cap

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Recent Developments in Musical Sound Synthesis Based on a Physical Model

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Sturm-Liouville Scattering

A zero is a point in the complex z plane at which the transfer function goes to zero. A pole is a point in the z-plane at which the transfer function goes to infinity. — Click for http://ccrma.stanford.edu/~jos/filters/Pole_Zero_Analysis_I.html

Click for http://ccrma.stanford.edu/~jos/filters/What_Filter.html

Search JOS Website, CCRMA Website, or Web

JOS Home Page

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Recent Developments in Musical Sound Synthesis Based on a Physical Model

Conical Digital Waveguide Bore Models

Conical Digital Waveguide Bore Models

Sturm-Liouville Scattering

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Cylinder with Conical Cap

$\epsfig{file=eps/cylconesp.eps,width=\textwidth}$

Cylinder open or closed on left side
Otherwise closed
Obviously passive physically
Reflection filters and transmission filters are unstable one-pole filters.
Instability is ``canceled'' by reflection from tip.
(More precisely, there is no instability.)

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Download SMAC03S.pdf
Download SMAC03S_2up.pdf

``Recent Developments in Musical Sound Synthesis Based on a Physical Model'', by Julius O. Smith III, (Stockholm Musical Acoustics Conference (SMAC-03), August 6--9, 2003).
Copyright © 2006-02-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
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