Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

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).


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA