A Note on Fourier Transform Conventions Used in Wave Analyses

Abstract

Temporal and spatial Fourier transforms are natural tools in the study of propagating waves in many applications. For example, the inverse spatial Fourier transform specifies how any wave can be built by summing plane waves. However, sign conventions necessary to describe waves are at odds with sign conventions used in spatio-temporal Fourier transforms. This note describes the problem and shows several ways that authors deal with it.