Physical Wave Propagation Modeling for Real-Time Synthesis of Natural Sounds (Thesis)

Abstract:

This thesis proposes banded waveguide synthesis as an approach to
real-time sound synthesis based on the underlying physics. So far
three main approaches have been widely used: digital waveguide
synthesis, modal synthesis and finite element methods. Digital
waveguide synthesis is efficient and realistic and captures the
complete dynamics of the underlying physics but is restricted to
instruments that are well-described by the one-dimensional string
equation. Modal synthesis is efficient and realistic yet abandons
complete dynamical description and hence cannot used for certain
types of performance interactions like bowing. Finite element methods
are realistic and capture the behavior of the constituent physical
equations but on current commodity hardware does not perform in
real-time.

Banded waveguides offer efficient simulations for cases for which
modal synthesis is appropriate but traditional digital waveguide
synthesis is not applicable. The key realization is that the dynamic
behavior of traveling waves, which is being used in waveguide synthesis,
can be applied to individual modes and that the efficient
computational structure can be utilized to achieve an approximate
dynamical description in the neighborhood of modes. Secondly this
realization is connected to related work on the theory of asymptotics
and periodic orbits and hence shown to apply to higher dimensions
also.

This theoretical approach is studied in applications to
bowed bar percussion instruments, complex stroke patterns on Indian
Tabla drums as well as rubbed wine glasses and Tibetan singing
bowls. None of these instruments and performance types has been
synthesized efficiently before. The simulations are compared to
experiments.