The wave digital filter brass mouthpiece model

Abstract

Wave digital filter (WDF) techniques are applied to develop an efficient discrete-time two-port mouthpiece model that can be used in traveling-wave based modeling of brass instruments. WDF’s were principally developed for simulation of analog networks, and are used here to discretize the classical first-order lumped element mouthpiece model [J. Backus, J. Acoust. Soc. Am. 60, 470–480 (1976)]. The model is segmented into two-port units that are individually mapped to the digital domain using the two-port WDF approach [S. Lawson and A. Mirzai, Wave Digital Filters (Ellis Horwood, London, 1990)]. The realizability of the filter structure is ensured by choosing the port resistances in between the units such that delay-free loops are avoided. The two-port mouthpiece can be directly coupled to models of the lips and leadpipe, although special care must be taken concerning the local characteristic impedance. The WDF mouthpiece model is easy to plug in, its parameters are very intuitive, and it has low computational costs, which makes it particularly suitable for physical modeling with musical sound synthesis purposes. The functioning of the WDF brass mouthpiece model will be further illustrated in a digital wave guide modeling application of a trumpet, wherein all model parameters are derived from measured data.