Modeling stiffness in virtual bowed-string instruments
Stefania Serafin, Julius O. Smith · The Journal of the Acoustical Society of America · 2000
Physical models of bowed-string instruments have achieved a degree of completeness that enables understanding and simulation of most of the phenomena that appear in real instruments. Moreover, improvements in hardware technology and the development of efficient signal processing algorithms enable the implementation of these models in real-time platforms, including also improvements and refinements which were not possible before. One of these elements is the stiffness of strings, whose main effect is to disperse the sharp corners that characterize the ideal Helmholtz motion. In this paper, a method is proposed for estimating numerical filters that model dispersion in strings. The phase dispersion of the string is modeled using allpass filters whose coefficients are obtained by minimizing the L-infinity norm of the error between the internal loop phase and its approximation by this filter cascade. This algorithm, which turns out to be a nonlinear version of the Remez exchange algorithm, can successfully design filters of low order which are suitable for real-time implementation, and also accurate enough to model strings of different materials.