FDNs as Digital Waveguide Networks

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Physical Audio Signal Processing

FDN Reverberation

Tonal Correction Filter

FDN Reverberators in Faust

The wave impedance in a propagation medium is the force variable (such as pressure for acoustic waves) divided by the velocity variable. In ideal plane waves and traveling waves, the wave impedance is a real, positive number. For spherical waves in air, the wave impedance is different at each frequency. — Click for https://ccrma.stanford.edu/~jos/OnePorts/Impedance.html

A waveguide restricts wave propagation to a particular subspace, which is usually a line. Vibrating strings, woodwinds, and transmission lines are examples of one-dimensional waveguides. — Click for http://en.wikipedia.org/wiki/Waveguide

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Tonal Correction Filter

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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 digital waveguides intersecting at a single scattering junction [465,466,388]. The wave impedance in the th waveguide is simply $\underline{u}[i]$ , the 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

FDNs as Digital Waveguide Networks

``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

``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