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...

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Bibliographic Details
Published in:PloS one 2014-03, Vol.9 (3), p.e90500-e90500
Main Authors: Bao, Guobin, Schild, Detlev
Format: Article
Language:English
Subjects:
Algorithms
Biology
Biophysics
Chemistry
Engineering
Fourier Analysis
Mathematical functions
Mathematics
Methods
Noise
Physics
Polynomials
Random variables
Statistics as Topic - methods
Time Factors
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0090500