The first-order case is very simple while enabling separate control of
low-frequency and high-frequency reverberation times. For simplicity,
let's specify
and
, denoting the desired
decay-time at dc (
) and half the sampling rate
(
). Then we have determined the coefficients of a
one-pole filter:
The dc gain of this filter is
where
denotes the
th delay-line length in
seconds. These two equations are readily solved to yield
The truncated series approximation
has been found to work well in practical FDN reverberators.