Using Discrete Fourier Transforms to Compute Acoustic Impedance in Digitized Media

Abstract This article presents a new approach to numerical acoustics. By discretizing a spatial continuum within a square grid of points, the surface acoustic impedance of a radiator is computed directly using plane waves as basis functions in a Discrete Fourier Transform (DFT) formulation. The novelty of this study is rewriting the expression for plane wave propagation in this format. This is possible since both the plane wave pressure and its derivative (velocity) contain the same cosine and sine terms, i.e., orthogonal functions identical to those of the DFT. A distinct advantage of the resulting orthogonal matrix is that the use of its Hermitian (conjugate transpose) avoids matrix division. This relationship avoids the usual problems with singularities often encountered when inverting matrices. The inherent simplicity of this numerical method is the essence of the article. This feature will facilitate easy dissemination and use among students, engineers, and scientists in relevant disciplines.