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Physical Audio Signal Processing
Digital Waveguide Theory
The Lossy 1D Wave Equation
Loss Consolidation
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Loss Consolidation
In many applications, it is possible to realize vast computational savings
in digital waveguide models by commuting losses out of unobserved and
undriven sections of the medium and consolidating them at a minimum number
of points. Because the digital simulation is linear and time invariant
(given constant medium parameters
), and because linear,
time-invariant elements commute, the diagram in Fig.H.6 is
exactly equivalent (to within numerical precision) to the previous diagram
in Fig.H.5.
![\includegraphics[scale=0.9]{eps/flloss}](http://www.dsprelated.com/josimages/pasp/img2006.png) |
may be ``pushed through'' delay
elements and combined with other loss factors until an input or output
is encountered which inhibits further migration. If further
consolidation is possible on the other side of a branching
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Previous: The Lossy 1D Wave EquationNext: Frequency-Dependent Losses
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.
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