Transient radiation field of annular-sectorial planar pistons: The Angular Spectrum method

A method for the calculation of the impulse response of annular-sectorial (also called annular-segmented) pistons embedded in an infinite rigid baffle is presented. Our calculations are grounded on the Angular Spectrum method following the main features of the theoretical development presented by Guyomar and Powers. Unlike in the original method, the mathematical formulation of the problem is expressed in polar coordinates, leading to the use of nth-order Hankel transform instead of the most frequently used 2D-FFT. The request of a new method arises from the fact that circular boundaries of a radiator must be approximated, when using rectangular grids. This approximation allows the occurrence of a significant error. In order to test the proposed method, numerical results of the impulse response of annular-sectorial pistons were compared with those obtained by means of the original algorithm, and also with the well known, currently used Stepanishen's method.