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In physics-based sound synthesis, it is generally possible to incorporate a mechanical or acoustical immittance (admittance or 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 immittance 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. In previous work, we have presented a simple method for designing and realizing inherently passive scalar admittances, by composing the admittance as a linear combination of positive real (PR) functions with nonnegative weights. In this paper the method is extended to multidimensional admittances (admittance matrices). The admittance matrix is synthesized as a sum of PR scalar transfer functions (second-order filters) multiplied by positive semidefinite matrices. For wave-based modeling, such as digital waveguides (DWGs) or wave digital filters (WDFs), the admittance matrix is converted to a reflectance filter. The filter structure is retained during conversion, resulting in a numerically robust implementation. As an example, a dual-polarization guitar string model based on the DWG approach is connected to the reflectance model parameterized from guitar bridge admittance measurements.

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Physical (or physics-based) modeling of musical instruments is one of the main research fields in computer music. A basic question, with increasing research interest recently, is to understand how different discrete-time modeling paradigms are interrelated and can be combined, whereby wave modeling with wave quantities (W-methods) and Kirchhoff quantities (K-methods) can be understood in the same theoretical framework. This paper presents recent results from the HUT Sound Source Modeling group, both in the form of theoretical discussions and by examples of Kvs. W-modeling in sound synthesis of musical instruments.

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