Alternative Representations of the Two Dimensional Waveguide Mesh
Ryan Michael Done · eScholarship (California Digital Library) · 2017
The two dimensional waveguide mesh is one possible discrete representationof the wave equation based on the theoretical framework of the one dimensionalwaveguide model. The digital waveguide model provides intuitive parametric controlof physical properties, making it conducive to musical synthesis. However,interesting inharmonic and percussive timbre from the modeling of membranesand surfaces has often been off limits to real-time synthesis due to the computationalexpense of larger two dimensional mesh models.This thesis covers the results of investigating methods to convert the two dimensionalwaveguide mesh into transfer function representations that can be computedfaster in real-time, without compromising the parameters of control thatthe 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 concerningimplementation of analysis and the using the transfer functions as filters are investigated.Finally, methods for approximating the parametric control of the physicalmodel in the filter representations are introduced.