Bell Models

The bell of a woodwind instrument is generally modeled as a ``cross-over filter'' in which the reflectance (back down the bore) is a lowpass filter (rolling off above 1500 Hz for a clarinet [16]), and the transmittance (into the surrounding air) is a complementary high-pass filter. Typically, the reflection filter must be designed based on an empirical impulse response measured using, e.g., pulse reflectometry [148], but one can use theoretical approximations as well [101,142]. See §8 below for discussion of a method for reducing the computational complexity of bell filters.