The application of fourier integral transforms in a general theory of diffraction - WYRZYKOWSKI, Roman (Archives of Acoustics, 1983)
Integral transforms have frequently been used to solve different specific problems in diffraction. There has, however, been no application of this method to the fundamental equations of diffraction theory.The present author shows that a transition from the d'Alambert equation to the Helmholtz equation for transforms gives all pulse fields, i.e. the acoustic potential of this field as the inverse transform of the product of the transform of the time behaviour of the pulse and the potential for a harmonic wave. This method permits relatively easy calculations of the sound pulse fields, with the additional assumption that the pulse distribution on the source can be represented as the product of a position-dependent function and one which is time-dependent.