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 replacing the FIR filter length in determining the maximum
switching rate, where is the time for the *external* impulse
response of the model component to decay by dB. Note that the dc
response must also decay to insignificance by .

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