Ircam - Centre Georges-Pompidou

State Space Sound Synthesis and a State Space Synthesiser Builder

Ph. Depalle, S. Tassart
ICMC 95, Banff (Canada),


This paper deals with sound synthesis using state space models. It focuses on two realizations we made of state space synthesiser builders applied to the case of wind instruments and more generally to transmission lines networks. The first realization, written in Maple is devoted to symbolic manipulation such as the derivation of different formalisms -- modal representation, ARMA filters or Kalman filtering equations. For efficiency purposes, a second version has been designed in C++ which directly reads the description of a physical instrument and computes its sound signal outputs.

We present recent developments of synthesis using State Space Models (SSM) and a state space synthesiser builder applied to the case of wind instruments. SSM are particularly interesting since they attempt to unify two main categories of sound synthesis techniques: signal modeling and physical modeling. This approach relies on the state space formalism which is widely used in control system theory. It allows to take into account all the physical parameters of the system under study and benefits from the methods developed for automatic tracking of parameters values, such as adaptive filtering or Kalman filtering.

Physical models usually require the complete construction of a model for each new instrument. On the other hand our SSMs provide a methodology for modular construction of instruments. This construction is done automatically in our formal calculus environment. It allows to obtain different theoretical representations (state space equation, external or modal representation) and a synthesiser which simulates the instrument.

This paper focuses on the production of state space representation of hierarchical networks. Thus, we only briefly present the physical systems involved in wind instruments. We give some basics concerning the state space representation and we describe in detail the methodology that we used to combine modules together into networks of arbitrary complexity. In the third section, we apply this methodology to transmission lines, and in the last section we describe two software realizations of synthesiser builders.

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Thu Feb 20 16:44:40 1997
Tassart Stéphan

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