基于物理模型的琴弦数字仿真

Digital Simulation of Musical Instrument String Based on Physical Model

基于物理模型的乐器仿真是运用弹性力学理论,通过偏微分方程来精确描述乐器发声的一种方法,尽管它有着模型建立困难、计算开销大等缺点,但随着计算机计算能力的提高,该方法已逐渐成为该领域的研究热点。本文利用物理模型方法描述了琴弦的数学模型,并由此推导出了一种新的普通显式方程算法,该算法适于计算机实现。与L.R二阶递归系统算法相比,该算法不仅简单,而且还具有更高的仿真精度。这对乐器仿真、声音合成领域的科技人员有较好的参考价值。

Simulation of musical instrument based on physical model is a kind of method that is able to describe accurately sound of instrument by the theory of elasticity and PDE. Nowadays, the method is becoming an important research domain of instruments simulation with improvement of computers processing power. This paper depicts a simple numerical model of musical instrument string based on physical model, and then, derives a new kind of great facility algorithm with ordinary explicit expression to process on computer. Compared with L.R Second-order Recursive System, it has been proved that the arithmetic is not only simpler, but also more accurate. It is valuable to use as reference for researchers developing simulation of musical instrument and sound synthesis.