Algorithms and Structures for Synthesis Using Physical Models

Abstract

Sound synthesis by means of simulated physical models has gained popularity in the last few years. One of the principal reasons for this interest is that this technique, based on modeling the mechanism of production of sound, seems to offer the musician simpler tools for controlling and producing both new and traditional sonorities. In general the aim of any model is to describe the fundamental aspects of the phenomenon in question by means of mathematical relationships. Most often models are used for purposes of analysis. In science and engineering, models are commonly used for the purpose of understanding physical phenomena. This is especially true in musical acoustics, where it is common practice to study a traditional instrument through its physical model in order to understand how it works (Keefe 1992; Woodhouse 1992). In the pioneering work of Hiller and Ruiz (1971), physical models were used with the goal of producing musical sounds. Since that time, physical models have been used for synthesis purposes. In this article we examine how models can be constructed for musical applications and discuss the principles that inspire the most widely used synthesis algorithms. We will also try to compare physicalmodel-based and traditional synthesis methods by discussing their structural properties. For all structures and models discussed below there are some important general truths. First, a common way of approaching the problem of modeling physical systems is to describe their observed behavior in the frequency domain. Frequency models are particularly effective for the description of linear systems, but such systems rarely apply for musical instruments. When nonlinearities must be taken into account, modeling in the frequency domain often becomes unfeasible, especially when strong nonlinearities are involved. In this case, models in the time domain are preferable. Moreover, we know that any simulation requires the continuous-time model to be made discrete. This, of course, must be done in such a way as to reproduce with good approximation the behavior of the continuous-time model to which it refers.