Numerical evaluation of the far-field directivity pattern using the fast Fourier transform

The far-field directivity pattern can be computed using the fast Fourier transform (FFT) algorithm. Numerical implementation of the angular spectrum approach (ASA) is generally used to compute the pressure field. 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 normal velocity. In fact, using the asymptotic expression of the Rayleigh’s integral, which is also the solution of Helmholtz equation, it will be shown that the analytical far-field pressure is given by the Fourier transform of the normal velocity. Guidelines for the selection of sampling interval and the size of the baffle in which the source is mounted will be given. Then this paper shows that the size of baffle influences 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 harmonic oscillations will be considered and discussed.