Frequency-Dependent Air-Absorption
Filtering
More generally, frequency-dependent air
absorption can be modeled using the substitution
where

denotes the
filtering per sample in the
propagation medium. Since air absorption cannot amplify a wave at any
frequency, we have

. A lossy
delay line for
plane-wave simulation is thus described by
in the
frequency domain, and
in the time domain, where `

' denotes
convolution, and

is
the
impulse response of the per-sample loss filter

. The effect
of

on the
poles of the system is discussed in §
3.7.4.
For spherical waves, the loss due to spherical spreading is of the form
where

is the distance from

to

. We see that the spherical
spreading loss factor is ``hyperbolic'' in the propagation distance

, while air absorption is
exponential in

.
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