Numerical Considerations

Since the difference equations (12-13) are based simply on the multiplication of two complex numbers, their extrapolation is guaranteed to be stable for any value of $f$ provided the computer arithmetic is perfect. Round-off errors in computer arithmetic will limit the maximum value of $\tau$, the accuracy of the resonant frequency, and the stability of the extrapolation in ways we have not studied in detail. Using 64 bit floating point arithmetic seems to be entirely adequate for musical purposes. For lower precision implementations, the alternate forms described in the following two subsections may be considered.