UC San Diego

The two dimensional waveguide mesh is one possible discrete representation

of the wave equation based on the theoretical framework of the one dimensional

waveguide model. The digital waveguide model provides intuitive parametric control

of physical properties, making it conducive to musical synthesis. However,

interesting inharmonic and percussive timbre from the modeling of membranes

and surfaces has often been off limits to real-time synthesis due to the computational

expense of larger two dimensional mesh models.

This thesis covers the results of investigating methods to convert the two dimensional

waveguide mesh into transfer function representations that can be computed

faster in real-time, without compromising the parameters of control that

the physical model provides. Two methods for analyzing the mesh and extracting a transfer function are explored, one conducive to deriving an analytical representation of the mesh, the other a numerical representation. Issues concerning

implementation of analysis and the using the transfer functions as filters are investigated.

Finally, methods for approximating the parametric control of the physical

model in the filter representations are introduced.