Real-Time Numerical Solution of Webster's Equation on A Nonuniform Grid

We present a numerical scheme for the real-time solution of the discretized one-dimensional linearized acoustics equation (Webster's equation) augmented with dissipative terms, in a tube with a spatially and temporally varying cross section. The resulting algorithm produces similar results as the Kelly–Lochbaum model but has several advantages over it: the tube length can change continuously, the area function can change in time and can be governed by a dynamical model itself, the scheme is of second-order accuracy, and the spatial and temporal discretization does not need to be uniform. We show how the model can be used to build a realistic real-time audio synthesis method for articulatory speech synthesis by coupling it to a lip radiation model, a dynamical wall model, and a glottal excitation model.