When , the eigenvalues reduce to

Assuming , the eigenvalues can be expressed as

where denotes the angular advance per sample of the oscillator. Since corresponds to the range , we see that in this range can produce oscillation at any digital frequency.

For , the eigenvalues are real, corresponding to exponential growth and/or decay. (The values were excluded above in deriving Eq.(C.165).)

In summary, the coefficient in the digital waveguide oscillator ( ) and the frequency of sinusoidal oscillation is simply

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University