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FDNs as Digital Waveguide Networks

As discussed in §C.15, the FDN using a Householder-reflection feedback matrix $ \mathbf{A}_N = \mathbf{I}_N -
(2/N)\underline{u}\underline{u}^T$ is equivalent to a network of $ N$ digital waveguides intersecting at a single scattering junction [465,466,388]. The wave impedance in the $ i$ th waveguide is simply $ \underline{u}[i]$ , the $ i$ th element of the axis-of-reflection vector $ \underline{u}$ . The choice $ \underline{u}^T=[1,1,\dots,1]$ corresponds to all of the waveguides having the same impedance (the ``isotropic junction'' case).


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``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
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