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Bridge Reflectance

The bridge reflectance is needed as part of the loop filter in a digital waveguide model (Chapter 6).

As derived in §C.11.1, the force-wave reflectance of $ R_b(s)$ seen on the string is

$\displaystyle \hat{\rho}_b(s) \eqsp \frac{R_b(s)-R_0}{R_b(s)+R_0} \eqsp \frac{s^2+\frac{1}{m}(\mu-R_0)s + \omega_0^2}{s^2+\frac{1}{m}(\mu+R_0)s + \omega_0^2} \protect$ (10.7)

where $ R_0$ denotes the wave impedance of the ideal string, and $ \omega_0\isdeftext \sqrt{k/m}$ denotes the resonance frequency in radians per second. The velocity reflectance is simply minus the force reflectance (§C.11.1).


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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