On the use of Fourier transform with acoustical fields

Abstract

The Fourier Transform is a powerful tool to deal with the radiated far field pattern of source distributions [l], PI. In this paper it is made a theoretical introduction to the possibility of using the Fourier Transform to study the fields produced by distributions, either continuous or discrete, of acoustical source distributions. With this new approach we can have a deep insight in the field and it is possible to develop and simplify methods of analysis and synthesis of fields produced by acoustical sources. All the procedure is based on the Theorem of the Small Complex Translation presented. In this case, and with a convenient choice of variables, the far field pattern is related with an window on the Fourier Transform of source distribution. The analysis and synthesis are made using the Fourier Transform firoprieties and the tools provided by the signal processing theory using the Fourier Transform