Generic resonator models for real-time synthesis of reed and brass instruments

From accurate measurements of bore profiles of various reed and brass instruments, a common and simplified geometrical model made of three parts totalizing seven geometrical parameters is proposed. From this geometry, it is shown that a good approximation of the input impedance can be obtained by a combination of two lumped elements gathered in series and parallel with a distributed element. Each element is approximated and discretized in order to end up with costless digital filters representing the impedance impulse response. These filters require the order of twenty multiplication/additions per sample and their coefficients are analytically expressed as functions of the geometrical parameters. The choice of the geometry and the time discretization schemes are validated both through comparison with continuous models and through the estimation of the geometrical parameters via a global optimization procedure, using measured input impedance curves.