Elementary Integration Methods for Velocity Excitations in Displacement Digital Waveguides

Elementary integration methods for waveguides are compared. One using non-local loading rules based on Heaviside step functions, one using input side integration and one using integration of the output of traveling velocity waves. We show that most approaches can be made consistent with the wave equation in principle, under proper circumstances. Of all methods studied the Heaviside method is the only method shown to not suffer from undesirable numerical difficulties and amendable to standard waveguide loop filtering practices, yet it gives incorrect results for Neumann boundary conditions. We also discuss localized velocity excitations, time-limited input-side excitations and the relation of loop filters to wave variable type.