Glossary of the main terms

Abstract

Because the DFT has a very wide range of applications in many different fields of science and technology (see end of Sec. 1.2), it is not surprising that the terminology used in the vast DFT literature is far from being consistent and uniform. In many cases different authors use different terms for the same entities, and what is even worse, the same terms are often used in different meanings by different authors. As a few examples among many others, let us mention here the various Fourier theorems (or “rules”; see Sec. 2.4), whose names greatly vary between different sources. For instance, the inversion rule [Kammler07 p. 199] is called symmetry rule in [Brigham88 p. 107], while in [Bracewell86 pp. 364–365] it is called reciprocity and the term symmetry is reserved to properties related to oddness and evenness [Bracewell86 p. 366]. Similarly, the reflection rule [Kammler07 p. 199] is called in [Bracewell86 p. 366] reversal while in [Nussbaumer82 p. 82] the term being used is symmetry (again!). Even the aliasing artifact is often called foldover, and the leakage artifact is sometimes called ringing [Brigham88 pp. 94, 106].