Double-Sum Technique for Performing a Fourier Transformation on an IntegrandComposed of Aliased Factors

摘要

Structural acoustics often utilizes Fourier transformation to either reveal aphenomenon that is more directly recognized in one domain than in its Fourier conjugate domain or to employ complementarity in order to decipher a phenomenon. In this paper, a novel computational technique is introduced. This technique advantageously performs this transformation in situations in which specific spatial scales govern aliased factors in the integrand of a Fourier transformation. The technique can factorially save computational steps over corresponding computations that employ discrete Fourier transform procedures.