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Introduction

Filters, whose parameters can be varied in time provide an important new resource in musical timbres. High Q filters are also desirable since most musical instruments involve high Q mechanical filters. Unfortunately, tuning a high Q filter can introduce artifacts which change the energy in the filter and produce unpleasant transients in the sound. A mechanical filter consisting of an object on a spring provides a simple example of the problem. The resonant frequency of the object-spring system can be changed by either changing the stiffness of the spring or the mass of the object. But if the mass of the object is changed while the object is moving, the kinetic energy in the object will be changed. Likewise, if the stiffness of the spring is changed while the spring is stretched, the potential energy stored in the spring will be changed. Any change of energy will cause a change in the amplitude of the oscillation.


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Download smac03maxjos.pdf

``Methods for Synthesizing Very High Q Parametrically Well Behaved Two Pole Filters'', by Max Mathews and Julius Smith, Proceedings of the Stockholm Musical Acoustics Conference (SMAC-03), pp. 405-408, August 6-9, 2003.
Copyright © 2008-03-12 by Max Mathews and Julius Smith
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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