#### Damping and Tuning Parameters

The tuning and damping of the resonator impulse response are governed by the relation

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

To obtain a desired frequency of oscillation, we must solve

for , which yields

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Eigenvalues in the Undamped Case

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Miscellaneous Properties