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Damping Filters for Reverberation Delay Lines

In an FDN, such as the one shown in Fig.3.10, delays $ z^{-1}$ appear in long delay-line chains $ z^{-M_i}$ . Therefore, the filter needed at the output (or input) of the $ i$ th delay line is $ G^{M_i}(z)$ (replace $ g_i$ by $ G^{M_i}(z)$ in Fig.3.10).4.15 However, because $ G(e^{j\omega T})$ is so close to $ 1$ in magnitude, and because it varies so weakly across the frequency axis, we can design a much lower-order filter $ H_i(z)\approx G^{M_i}(z)$ that provides the desired attenuation versus frequency to within psychoacoustic resolution. In fact, perfectly nice reverberators can be designed in which $ H_i(z)$ is merely first order for each $ i$ [317,218].


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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
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