Modeling Wind Instrument Sound Radiation using Digital Waveguides

This paper develops the theory and digital waveguide implementation for modeling threedimensional (3D) sound emission from wind instrument air columns. It is shown that the current acoustic theory regarding sound radiation from ducts and holes can be implemented in the digital waveguide context using properly designed digital filters. Each radiating sound source or hole requires a first- or second-order digital filter to account for angular- and frequency-dependent pressure distribution characteristics. Sound propagation delay from the source to the pickup is modeled with a delay line and possibly a fractional-delay interpolation filter. An additional digital filter to model attenuation in free space can also be used. The results of this model compare well with frequency-domain polar radiation calculations. A simplified system appropriate for real-time synthesis is developed that allows continuous pickup movement within an anechoic 3D space.