Passive admittance synthesis for sound synthesis applications

Abstract

In physics‐based sound synthesis, it is in general possible to incorporate a mechanical or acoustical admittance/impedance in the form of a digital filter. Examples include modeling of the termination of a string or a tube. However, when digital filters are fitted to measured admittance or impedance data, care has to be taken that the resulting filter corresponds to a passive mechanical or acoustical system, otherwise the stability of the instrument model is at risk. This paper presents a simple method for designing inherently passive admittance or impedance filters. The admittance/impedance is composed as a linear combination of positive real (PR) functions, and the weights are determined by a constrained least squares optimization. The resulting filter is a parallel set of second‐order sections. For wave‐based modeling, such as digital waveguides (DWGs) or wave digital filters (WDFs), the admittance/impedance is converted to a reflectance filter. The parallel filter structure is retained during conversi...