String vibration forms the basis for a wide variety of physical modelling sound synthesis environments. Direct simulation in the space-time domain (through techniques such as, for example, the finite difference time domain method) allows for great generality and flexibility, particularly if one is concerned with essential nonlinear features such as, e.g., nonlinear excitation or collisions. Both theoretical and experimental investigations have shown that decay times of linear string transverse modes are frequency-dependent in a nontrivial way. This profile plays an important role in the perceived realism of the synthetic sound, but is nontrivial to reproduce in a pure space-time domain framework. Recent work has demonstrated different approaches to tackle similar problems, sharing a common principle: the impedance of the lossy part of the system is approximated by the input impedance of a network of passive circuit elements, with a readily available time-domain realisation. This paper outlines a procedure for optimising the parameters of such a model against a reference loss profile, which may come from a theoretical model or from experimental measurements of string decay times. Passivity is ensured by enforcing positive-realness of the approximated impedance. The corresponding time domain system is then translated to the discrete time setting; a finite difference scheme is chosen such that the passivity property is preserved, leading to guarantees of numerical stability. The decay times of the transverse modes of simulated plucked strings are measured and compared to the original data, in order to assess the fidelity of the reproduced loss profile, at different orders of approximation.
