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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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