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2017 A Guide on Spectral Methods Applied to Discrete Data in One Dimension
Martin Seilmayer, Matthias Ratajczak
J. Appl. Math. 2017: 1-27 (2017). DOI: 10.1155/2017/5108946

Abstract

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 $\texttt{spectral}$ package, which has been published for the statistical environment R prior to this article.

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Martin Seilmayer. Matthias Ratajczak. "A Guide on Spectral Methods Applied to Discrete Data in One Dimension." J. Appl. Math. 2017 1 - 27, 2017. https://doi.org/10.1155/2017/5108946

Information

Received: 2 January 2017; Accepted: 10 April 2017; Published: 2017
First available in Project Euclid: 15 August 2017

zbMATH: 07037480
MathSciNet: MR3683278
Digital Object Identifier: 10.1155/2017/5108946

Rights: Copyright © 2017 Hindawi

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