A STABLE ACOUSTIC IMPEDANCE MODEL OF THE CLARINET USING DIGITAL WAVEGUIDES
Gary P. Scavone, Julius O. Smith · 2006
Digital waveguide (DW) modeling techniques are typically associated with a traveling-wave decomposition of wave variables and a “reflection function ” approach to simulating acoustic systems. As well, it is often assumed that inputs and outputs to/from these systems must be formulated in terms of traveling-wave variables. In this paper, we provide a tutorial review of DW modeling of acoustic structures to show that they can easily accommodate physical input and output variables. Under certain constraints, these formulations reduce to simple “Schroeder reverb-like ” computational structures. We also present a stable single-reed filter model that allows an explicit solution at the reed / air column junction. A clarinet-like system is created by combining the reed filter with a DW impedance model of a cylindrical air column. 1. REFLECTION FUNCTION CALCULATIONS The use of digital waveguides (DW) to model wave propagation within cylindrical air columns has been well documented [1, 2]. A DW structure like that diagrammed in Fig. 1 can be used to compute the time-domain pressure reflection function, rp(t), of a uniform pipe. The reflection function is defined as the pressure response at the input of an air column caused by the introduction there of a pressure impulse, assuming no reflections at the input end (an anechoic input termination). The digital filter RL models the frequency-dependent reflectance of the load impedance connected to the far end of the pipe. It can be expressed as