Closed-Form Green’s Function of a 2-D Rectangular Room

Closed-form enough-accurate Green's function for wave-propagation modeling in a rectangular 2-D room is presented using the characteristic Green's function technique. This Green's function is first developed in an integral form. Then, its spatial-domain closed form is obtained using three fast methods. In the first method, the integral is computed by the stationary phase method. In the second one, the integral is computed analytically by expanding the integrand into a complex exponential series. In the third method, the integrand is approximated by a series of rational functions and the integral is computed using Cauchy's residue theorem. The results of these three methods are studied and compared in an example. The results show that the methods are fast while preserving accuracy.