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

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 lim...

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Main Authors: Martin Seilmayer, Matthias Ratajczak
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2017/5108946
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author Martin Seilmayer
Matthias Ratajczak
author_facet Martin Seilmayer
Matthias Ratajczak
author_sort Martin Seilmayer
collection DOAJ
description 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 R prior to this article.
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spelling doaj-art-08864044e3e945339263dfc42bfca61c2025-08-20T02:01:34ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/51089465108946A Guide on Spectral Methods Applied to Discrete Data in One DimensionMartin Seilmayer0Matthias Ratajczak1Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, GermanyHelmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, GermanyThis 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 R prior to this article.http://dx.doi.org/10.1155/2017/5108946
spellingShingle Martin Seilmayer
Matthias Ratajczak
A Guide on Spectral Methods Applied to Discrete Data in One Dimension
Journal of Applied Mathematics
title A Guide on Spectral Methods Applied to Discrete Data in One Dimension
title_full A Guide on Spectral Methods Applied to Discrete Data in One Dimension
title_fullStr A Guide on Spectral Methods Applied to Discrete Data in One Dimension
title_full_unstemmed A Guide on Spectral Methods Applied to Discrete Data in One Dimension
title_short A Guide on Spectral Methods Applied to Discrete Data in One Dimension
title_sort guide on spectral methods applied to discrete data in one dimension
url http://dx.doi.org/10.1155/2017/5108946
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