Piecewise Conical Bore Modeling

It is well known that a growing exponential appears when waves traveling within one conical taper angle reflect from a section with a smaller (or more negative) taper angle [4]. This phenomenon has precluded the use of a straightforward recursive filter model [5,8] since such a filter would have to be unstable. However, using TIIR principles, it is possible to use unstable digital filters in this way while resolving practical difficulties.

The main difference in the piecewise conical modeling case is that conical segments are not strictly FIR. However, in practical musical acoustics, they have quite short decay times. Therefore, we may apply TIIR principles with $t_{60}$ replacing the FIR filter length in determining the maximum switching rate, where $t_{60}$ is the time for the external impulse response of the model component to decay by $60$ dB. Note that the dc response must also decay to insignificance by $t_{60}$.