Phase-space analysis of acoustics fields and its application to waveguide

A description of two-dimensional acoustic fields by means of a joint “space-wave number” representation is discussed. A function defined in the phase-space domain (x,y,kx,ky) is associated with a signal which is a function of spatial coordinates (x,y). This paper presents two methods to realize it. The first is to associate with each point (x,y) of the wave field a two-dimensional wave number spectrum (kx,ky), called local spectrum. The second is to process by other coordinates the wave field along an arbitrary direction, introduced in quantum mechanics for the study of classical billiards, and provided by the Birkhoff variables (s,cos φ). Phase-space diagrams are given by quadratic phase-space distributions. Simulations are presented for wave fields in a 2D planar waveguide for a pedagogical point of view with Gaussian beam or point-source excitation, and nonuniform waveguides as a sudden area expansion chamber and an open billiard with a single incoming mode at the entrance of each of them. In these pro...