Joint Modeling of Bridge Admittance and Body Radiativity for Efficient Synthesis of String Instrument Sound by Digital Waveguides

In the context of efficient sound synthesis by digital waveguides, we present a novel methodology for joint modeling of string instrument body radiativity and driving-point bridge admittance functions, as obtained from experimental data. From our modeling framework, aimed at simulation of guitar and bowed string sound, here we focus on the body of the instrument and leave aside the strings. First, a modal decomposition of the measured bridge admittance is obtained by means of a novel frequency-domain algorithm for optimization of recursive digital filters in parallel form. Then, from extracted modal parameters, the radiativity, and admittance functions are modeled by projecting measurements over a common modal basis, enforcing passivity of the two-dimensional admittance model by means of semidefinite programming. We propose a formulation that enables the joint realization of bridge reflectance and sound radiativity as a lumped delay line termination in which a single bank of resonant filters is shared among all string reflection and body radiation outputs. Our approach provides efficient means to model two-dimensional (2-D) bridge reflectance, 2-D string–string coupling, sound radiation with an arbitrary number of outputs, and (implicitly) vibrational energy loss from the bridge transmittance to nonradiating modes and dissipation.