Achieving Desired Reverberation Times

A lossless prototype reverberator, as in Fig.3.10 when , has all of its poles on the unit circle in the plane, and its reverberation time is infinity. To set the reverberation time to a desired value, we need to move the poles slightly inside the unit circle. Furthermore, due to air absorption (§2.3,§B.7.15), we want the high-frequency poles to be more damped than the low-frequency poles [317]. As discussed in §2.3, this type of transformation can be obtained using the substitution

where denotes the

Solving for , the propagation attenuation per-sample, gives

The last form comes from ln , where denotes the time constant of decay (time to decay by ) [454],

Series expanding and assuming samples ( seconds) provides the practically useful approximation

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