Structural acoustics often utilizes Fourier transformation to either reveal a phenomenon 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.