Problems of Smoothing and Differentiation of Data by Least-Squares Procedures and Possible Solutions

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Abstract

Smoothing and differentiation of experimental data sometimes necessitate least-squares polynomial fitting of a large number of data points at a time (17, 19, or 21 points) rather than 3, 5, or 7 points with repetition of the procedure for several Iterations. For a 5- or 7-polnt fit, one loses smoothing of only 2 or 3 points, respectively, at each end, and for a 19- or 21-polnt fit one loses 9 or 10 points, respectively, at each end. No other smoothing procedure is known today to handle the edge point smoothing and differentiation. In this paper a procedure is suggested for smoothing and differentiating essentially every data point. In addition, different orders of polynomial fits have been tried for the same data set. It is noticed that the parabolic fit gives the best smoothing of the noisy data set.

Original languageEnglish (US)
Pages (from-to)654-657
Number of pages4
JournalAnalytical Chemistry
Volume59
Issue number4
DOIs
StatePublished - Jan 1 1987

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Polynomials

All Science Journal Classification (ASJC) codes

  • Analytical Chemistry

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abstract = "Smoothing and differentiation of experimental data sometimes necessitate least-squares polynomial fitting of a large number of data points at a time (17, 19, or 21 points) rather than 3, 5, or 7 points with repetition of the procedure for several Iterations. For a 5- or 7-polnt fit, one loses smoothing of only 2 or 3 points, respectively, at each end, and for a 19- or 21-polnt fit one loses 9 or 10 points, respectively, at each end. No other smoothing procedure is known today to handle the edge point smoothing and differentiation. In this paper a procedure is suggested for smoothing and differentiating essentially every data point. In addition, different orders of polynomial fits have been tried for the same data set. It is noticed that the parabolic fit gives the best smoothing of the noisy data set.",
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Problems of Smoothing and Differentiation of Data by Least-Squares Procedures and Possible Solutions. / Khan, Arshad.

In: Analytical Chemistry, Vol. 59, No. 4, 01.01.1987, p. 654-657.

Research output: Contribution to journalArticle

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