Development of a simple and accurate approximation method for the Gaussian beam expansion technique

Abstract

The calculation of the sound field can be greatly simplified by using the Gaussian beam expansion technique. The source distribution function is expressed as the superposition of a small number of Gaussian functions, and the expansion coefficients could be obtained by minimizing an object function in the spatial or k-space domain. In this paper, a fast algorithm is developed to determine the Gaussian function coefficients for a more accurate approximation. Two-stage procedures are employed in the proposed method. Firstly, two real coefficients are estimated by a simple search approach, and then the least mean square (LMS) algorithm is adopted for determining the optimal expansion coefficients. Finally, the presented method is evaluated in the case of calculation of sound fields radiated from a piston and a rectangular planar source. Simulation results show that, compared with the previous approaches, the developed scheme is simple to implement with high accuracy.