A Fast Method of Transforming Relaxation Functions Into the Frequency Domain

The limits to the error due to truncation of the numeric integration of the one-sided Laplace transform of a relaxation function in the time domain into its equivalent frequency domain are established. Separate results are given for large and small ω. These results show that, for a given ω, only a r...

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Detalles Bibliográficos
Autor principal: Mopsik, Frederick I.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: [Gaithersburg, MD] : U.S. Dept. of Commerce, National Institute of Standards and Technology 1999
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877121/
http://dx.doi.org/10.6028/jres.104.014
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author Mopsik, Frederick I.
author_facet Mopsik, Frederick I.
author_sort Mopsik, Frederick I.
collection PubMed
description The limits to the error due to truncation of the numeric integration of the one-sided Laplace transform of a relaxation function in the time domain into its equivalent frequency domain are established. Separate results are given for large and small ω. These results show that, for a given ω, only a restricted range of time samples is needed to perform the computation to a given accuracy. These results are then combined with a known error estimate for integration by cubic splines to give a good estimate for the number of points needed to perform the computation to a given accuracy. For a given data window between t(1) and t(2), the computation time is shown to be proportional to ln(t(1)/t(2)).
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spelling pubmed-48771212016-09-06 A Fast Method of Transforming Relaxation Functions Into the Frequency Domain Mopsik, Frederick I. J Res Natl Inst Stand Technol Article The limits to the error due to truncation of the numeric integration of the one-sided Laplace transform of a relaxation function in the time domain into its equivalent frequency domain are established. Separate results are given for large and small ω. These results show that, for a given ω, only a restricted range of time samples is needed to perform the computation to a given accuracy. These results are then combined with a known error estimate for integration by cubic splines to give a good estimate for the number of points needed to perform the computation to a given accuracy. For a given data window between t(1) and t(2), the computation time is shown to be proportional to ln(t(1)/t(2)). [Gaithersburg, MD] : U.S. Dept. of Commerce, National Institute of Standards and Technology 1999 1999-04-01 /pmc/articles/PMC4877121/ http://dx.doi.org/10.6028/jres.104.014 Text en https://creativecommons.org/publicdomain/zero/1.0/ The Journal of Research of the National Institute of Standards and Technology is a publication of the U.S. Government. The papers are in the public domain and are not subject to copyright in the United States. Articles from J Res may contain photographs or illustrations copyrighted by other commercial organizations or individuals that may not be used without obtaining prior approval from the holder of the copyright.
spellingShingle Article
Mopsik, Frederick I.
A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title_full A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title_fullStr A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title_full_unstemmed A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title_short A Fast Method of Transforming Relaxation Functions Into the Frequency Domain
title_sort fast method of transforming relaxation functions into the frequency domain
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877121/
http://dx.doi.org/10.6028/jres.104.014
work_keys_str_mv AT mopsikfredericki afastmethodoftransformingrelaxationfunctionsintothefrequencydomain
AT mopsikfredericki fastmethodoftransformingrelaxationfunctionsintothefrequencydomain

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