Discrete-time modeling of woodwind instrument bores using wave variables

Area of Science:

• Acoustics
• Computational Musicology
• Physical Modeling

Background:

• Accurate simulation of acoustical bores is crucial for physical modeling sound synthesis of woodwind instruments.
• Existing methods like Digital Waveguide Modeling (DWM) and Multi Convolution Algorithm (MCA) have limitations in modeling wave propagation.
• These methods explicitly compute traveling pressure waves, which can be restrictive.

Purpose of the Study:

• To present a novel Wave Digital Modeling (WDM) method for simulating acoustical bores.
• To overcome limitations of existing DWM and MCA methods by employing a more generalized wave variable definition.
• To construct an efficient and modular discrete-time model for sound synthesis.

Main Methods:

• The Wave Digital Modeling (WDM) method is based on a one-dimensional model of wave propagation.
• It utilizes a generalized definition of wave variables, avoiding explicit computation of traveling pressure waves.
• Elemental bore units (cylindrical/conical sections, toneholes) are digitally represented, and frequency-dependent losses are approximated with digital filters.

Main Results:

• An efficient and spatially modular discrete-time model was constructed.
• The stability of simulating a complete acoustic bore was empirically investigated.
• Simulations of a full clarinet demonstrated strong agreement with established transmission-line theory.

Conclusions:

• The Wave Digital Modeling (WDM) method provides an effective approach for simulating acoustical bores.
• This method offers an improvement over existing techniques by using a more general wave variable definition.
• The WDM method facilitates accurate sound synthesis for woodwind instruments through physical modeling.