The tuning and damping of the resonator impulse response are governed by the relation
where
To obtain a specific decay time-constant
, we must have
Therefore, given a desired decay time-constant
(and the
sampling interval
), we may compute the damping parameter
for
the digital waveguide resonator as
Note that this conclusion follows directly from the determinant analysis of Eq.(C.161), provided it is known that the poles form a complex-conjugate pair.
To obtain a desired frequency of oscillation, we must solve
for
, which yields
Note that this reduces to