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Feedforward Comb Filters

The feedforward comb filter is shown in Fig.2.23. The direct signal ``feeds forward'' around the delay line. The output is a linear combination of the direct and delayed signal.

Figure 2.23: The feedforward comb filter.

The ``difference equation'' [452] for the feedforward comb filter is

$\displaystyle y(n) = b_0 x(n) + b_M x(n-M). \protect$ (3.2)

We see that the feedforward comb filter is a particular type of FIR filter. It is also a special case of a TDL.

Note that the feedforward comb filter can implement the echo simulator of Fig.2.9 by setting $ b_0=1$ and $ b_M=g$ . Thus, it is is a computational physical model of a single discrete echo. This is one of the simplest examples of acoustic modeling using signal processing elements. The feedforward comb filter models the superposition of a ``direct signal'' $ b_0 x(n)$ plus an attenuated, delayed signal $ b_M x(n-M)$ , where the attenuation (by $ \vert b_M\vert<1$ ) is due to ``air absorption'' and/or spherical spreading losses, and the delay is due to acoustic propagation over the distance $ cMT$ meters, where $ T$ is the sampling period in seconds, and $ c$ is sound speed. In cases where the simulated propagation delay needs to be more accurate than the nearest integer number of samples $ M$ , some kind of delay-line interpolation needs to be used (the subject of §4.1). Similarly, when air absorption needs to be simulated more accurately, the constant attenuation factor $ b_M$ can be replaced by a linear, time-invariant filter $ G(z)$ giving a different attenuation at every frequency. Due to the physics of air absorption, $ G(z)$ is generally lowpass in character [352, p. 560], [47,321].

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University