State Variable Models For Sound Synthesis

Abstract

In this paper, we present an approach to sound synthesis which mes to unify the two current approaches, one that we call the signal approach and the other that we call the physical approach. These two approaches have their own advantages and drawbacks. 1. The signal approach inherits the whole set of signal processing techniques. It is based on the use of fairly general production models, the internal structure of which is not precisely defined. The input variables to the model are called parameters. The process of synthesizing a sound consists of finding the time varying values of the parameters. In general, there exist analysis techniques to determine parameter values from natural sounds (e.g. FFT ifor additive synthesis, LPC for source filter models). One of the drawbacks to this approach is the difficulty in determining the parameter values of a signal whose Characteristics vary rapidly. It is also difficult to control the model for certain sound effects since there is no internal description. 2. The physical approach consists of an explicit simulation of the physical system which produces the sound. In this case the internal description is precisely defined. Synthesis is accomplished by finding the numeric solution to the model equation. The control parameters directly correspond to the physical parameters of the system. The sound produced by such models are of great quality. The drawback to this synthesis method is that the modd equations are determined from a dePailed physical analysis of the insuument and that the parameters have to be obtained from physical measurements which are often long and complex to realise. To take advantage of the positive aspects of the preceding approaches, we explore a third approach. On the one hand it takes advantage of a precise description of the internal structure of a physical system. On the other hand, it determines certain parameter values by analyzing sounds produced by the system. Our new approach is based on the state variable description of physical systems. This formalism is largely used in process control theory. Kalmari filtering is one of the techniques that we use in order to obtain the parameter values that conool ihe model. We have applied this formalism to build a model of connected acoustic tubes. We have developped an algorithm for recursive consrmction of a state variable model given the structure of the system. Such a model can be excited by non linear systems to …