NUMERICAL EVALUATION OF THE FAR-FIELD DIRECTIVITY PATTERN USING THE FAST FOURIER-TRANSFORM

The far-field directivity pattern can be computed using the fast Fouri er transform (FFT) algorithm, Numerical implementation of the angular spectrum approach (ASA) is generally used to compute the pressure fiel d. The aim of this paper is to demonstrate that the discrete far-field pressure can be only computed by the calculation of the DFT of the no rmal velocity. In fact, using the asymptotic expression of the Rayleig h's integral, which is also the solution of Helmholtz equation, it wil l be shown that the analytical far-field pressure is given by the Four ier transform of the normal velocity. Guidelines for the selection of sampling interval and the size of the baffle in which the source is mo unted will be given. Then this paper shows that the size of baffle inf luences the angular resolution at which the far field is computed and when the source is oversampled the computed discrete pressure becomes better. Numerical results concerning a transducer that exhibits harmon ic oscillations will be considered and discussed. (C) 1998 Acoustical Society of America. [S0001-4966(98)00106-4].