Modeling of a violin input admittance by direct positioning of second-order resonators

Abstract

When approaching violin sound synthesis, the theoretical advantage of body modeling by finite difference or finite element paradigms comes from parameterizing the model by geometry and material properties. However, difficulties in representing the complexity of physical phenomena taking place have kept such approaches from raising more success, due especially to limited modeling accuracy and high computational cost. Conversely, the design of digital filters from admittance measurements, although generally offering a less meaningful parameterization, represents a more affordable technique as it provides significant fidelity at lower computational cost. Within digital filter formulation applied to the violin, modal representations can be considered as among the most physically pertinent, since vibration modes defining the timbre signature are in general observable from admittance measurements. This work introduces a technique for designing violin passive admittances by direct, non-uniform positioning of second-order resonators. Starting from admittance measurements, second-order resonator parameters are designed so that desired modes are modeled from frequency-domain data. Positve real models providing significant accuracy at low order are obtained from second-order resonator parameter fits. As an example, a two-dimensional input admittance is designed from measurements, so that it can be used for a digital waveguide model to include a control for bowing angle.