Abstract: A tone synthesis system employs digital filtering methods to enable the practical usage of unstable filter elements in a real-time synthesis model. Truncated infinite impulse response (TIIR) filters are used to approximate portions of the reflection impulse response of an acoustic horn such as a trumpet bell. Methods for resetting filter state enable the use of internal unstable filter poles. Similar state resetting methods enable the use of unstable one-pole filters in the scattering junction formed between two conical acoustic bores. High quality tone synthesis can be achieved without the necessity of a complicated filter representing large sections of the bore of a woodwind instrument.