| Popis: |
Viscothermal losses for models of one-dimensional wave propagation in ducts are usually expressed, in the frequency domain, in terms of a series impedance/shunt admittance pair. A wellknown model is that of Zwikker and Kosten, for which the immittances are not expressed in terms of rational functions of the frequency variable—and thus a difficult match to time domain simulation methods. One approach to finite order rational approximation is based on a high-frequency approximation, leading to a representation in terms of fractional powers of the frequency variable, which can then be further approximated in terms of a rational function using standard techniques. Another is to approximate the Zwikker-Kosten model directly, and a major design consideration is to ensure positive realness under a finite order approximation, leading to a passive or dissipative representation. Though closed-form solutions based on continued fraction expansion are available, another approach is to make use of optimisation over a parameterised finite order rational function for which the positive realness property is inbuilt. This paper focuses on the optimisation problem, using standard iterative techniques such as gradient descent and its extensions, particularly with regard to model order, and extensions to the case of optimisation in a discrete time setting are also discussed. Optimisation results, for a variety of model orders and frequency optimisation ranges, are presented. |
