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Physical Inputs

A digital waveguide input signal corresponds to a disturbance of the 1D propagation medium. For example, a vibrating string is plucked or bowed by such an external disturbance. The result of the disturbance is wave propagation to the left and right of the input point. By physical symmetry, the amplitude of the left- and right-going propagating disturbances will normally be equal.3.5 If the disturbance superimposes with the waves already passing through at that point (an idealized case), then it is purely an additive input, as shown in Fig.2.14.

Figure 2.14: Summing a signal into a digital waveguide corresponding to a superimposing disturbance at one point. The original state is unaffected, i.e., the input signal enters the waveguide in superposition with whatever is already going on.
\includegraphics{eps/BidirectionalDelayLineInput}

Note that the superimposing input of Fig.2.14 is the graph-theoretic transpose of the ideal output shown in Fig.2.13. In other words, the superimposing input injects by means of two transposed taps. Transposed taps are discussed further in §2.5.2 below.

In practical reality, physical driving inputs do not merely superimpose with the current state of the driven system. Instead, there is normally some amount of interaction with the current system state (when it is nonzero), as discussed further in the next section. Note that there are similarly no ideal outputs as depicted in Fig.2.13. Real physical ouputs must present some kind of load on the system (energy must be extracted). Superimposing inputs and non-loading outputs are ideals that are often approximated in real-world systems. Of course, in the virtual world, they are no problem at all--in fact, they are usually easier to implement, and more efficient.


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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
CCRMA