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Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space
The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a nove...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2014
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3948392/ https://www.ncbi.nlm.nih.gov/pubmed/24603904 http://dx.doi.org/10.1371/journal.pone.0090500 |
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author | Bao, Guobin Schild, Detlev |
author_facet | Bao, Guobin Schild, Detlev |
author_sort | Bao, Guobin |
collection | PubMed |
description | The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. |
format | Online Article Text |
id | pubmed-3948392 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-39483922014-03-13 Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space Bao, Guobin Schild, Detlev PLoS One Research Article The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. Public Library of Science 2014-03-06 /pmc/articles/PMC3948392/ /pubmed/24603904 http://dx.doi.org/10.1371/journal.pone.0090500 Text en © 2014 Bao, Schild http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Bao, Guobin Schild, Detlev Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title | Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title_full | Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title_fullStr | Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title_full_unstemmed | Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title_short | Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space |
title_sort | fast and accurate fitting and filtering of noisy exponentials in legendre space |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3948392/ https://www.ncbi.nlm.nih.gov/pubmed/24603904 http://dx.doi.org/10.1371/journal.pone.0090500 |
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