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Lossy Acoustic Propagation

Attenuation of waves by spherical spreading, as described in §2.2.5 above, is not the only source of amplitude decay in a traveling wave. In air, there is always significant additional loss caused by air absorption. Air absorption varies with frequency, with high frequencies usually being more attenuated than low frequencies, as discussed in §B.7.15. Wave propagation in vibrating strings undergoes an analogous absorption loss, as does the propagation of nearly every other kind of wave in the physical world. To simulate such propagation losses, we can use a delay line in series with a nondispersive filter, as illustrated in §2.2.2 above. In practice, the desired attenuation at each frequency becomes the desired magnitude frequency-response of the filter in Fig.2.4, and filter-design software (typically matlab) is used to compute the filter coefficients to approximate the desired frequency response in some optimal way. The phase response may be linear, minimum, or left unconstrained when damping-filter dispersion is not considered harmful. There is typically a frequency-dependent weighting on the approximation error corresponding to audio perceptual importance (e.g., the weighting $ 1/f$ is a simple example that increases accuracy at low frequencies). Some filter-design methods are summarized in §8.6.

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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