Length
FIR Loop Filter Controlled by ``Brightness'' and ``Sustain''
Another convenient parametrization of the second-order symmetric FIR
case is when the dc normalization is relaxed so that two degrees of
freedom are retained. It is then convenient to control them
as brightness
and sustain
according to the
formulas
where

is the
period in seconds (total loop delay),

is the
desired sustain time in seconds, and

is the brightness parameter
in the interval
![$ [0,1]$](http://www.dsprelated.com/josimages_new/pasp/img1241.png)
. The sustain parameter

is defined here as
the time to decay by
dB (or
time-constants) when
brightness

is maximum (

) in which case the loop gain is

at all frequencies, or

. As the brightness is
lowered, the dc gain remains fixed at

while higher frequencies
decay faster. At the minimum brightness, the gain at half the
sampling rate reaches zero, and the loop-filter
amplitude-response
assumes the form
A
Faust function implementing this
FIR filter as the damping filter in
the
Extended Karplus Strong (
EKS) algorithm is described
in [
454].
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