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Journal of Applied Mathematics
Volume 2017 (2017), Article ID 5108946, 27 pages
Review Article

A Guide on Spectral Methods Applied to Discrete Data in One Dimension

Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany

Correspondence should be addressed to Martin Seilmayer

Received 2 January 2017; Accepted 10 April 2017; Published 24 July 2017

Academic Editor: Zhichun Yang

Copyright © 2017 Martin Seilmayer and Matthias Ratajczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment prior to this article.