Fast modal synthesis by digital waveguide extraction

From a modal synthesis point of view, digital waveguides allow the efficient synthesis of harmonically spaced components for a fixed number of arithmetic operations. They are thus well suited to audio synthesis based on one-dimensional physical models (such as strings or tubes) that possess nearly harmonic spectra. In higher dimensions, however, modal frequencies do not fall in harmonic series. In this letter, we show how digital waveguide structures may be extracted from higher dimensional problems, yielding algorithms more efficient than modal synthesis, with reference to the solution of the two-dimensional wave equation defined over a square region. Numerical results are presented.