Glossary of the main terms

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].