Our basic model [Rodet, 1995] is displayed in figure 1. We consider the oscillation of the upper lip only. The lip is modelled as a single mass oscillator m whose stiffness and damping coefficients are k and r. The resonator is simplified into a straight tube of cross section A.
We suppose an air jet under the lip. The mouth pressure 
is considered
to be steady, whereas the air flow in the mouth is neglected.
The lip displacement, the pressure and the air flow under the lip,
are respectively designated by x, p and u.
Let's call g(t) the impulse response of the bore, defined as the inverse Fourier transform of the input impedance of the instrument.
Figure 1: Our basic model of trumpet-like instruments
This physical model is described by the following system of equations (1) for positive x:
Let us write the impulse response of a straight lossless tube as:
where 
is the characteristic impedance of the tube
and reflect a negative coefficient greater than -1.