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A Simple Technique for Simultaneous Smoothing and Integration of Data

P. Nikitas and C. Malliakas

Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, Thessaloniki, Greece

J. Chem. Educ., 2002, 79 (1), p 135

DOI: 10.1021/ed079p135.2

Publication Date (Web): January 1, 2002

Abstract

The problem of the simultaneous smoothing and integration of data is examined using orthogonal polynomials and a simple approach for integration of the trial function is presented. This approach has the advantage that the procedure of integration does not introduce any error and that it can be used for integration of equally and non-equally spaced data. It is also shown that this technique of smoothing and integration can be easily performed on spreadsheets, such as those of Microsoft Excel 98 or 2000, within a moving data window or directly from a certain point to another one of the data set. For this purpose a new function has been written, named Integr(x, y, n, IDegree, xa, xb), which can be used for either smoothing or integration of data on spreadsheets of Microsoft Excel. From the arguments of this function x is a set of N x-values, y is the corresponding set of y-values, and n is the degree of the fitted polynomial. The function calculates the integral between the points x_m and x_m+1 when IDegree ≠ 0 and x_a, x_b are omitted. (In all cases, if N is the number of x points, m is equal to the integer part of the ratio N/2.) When values for x_a, x_b are included, then the function calculates the integral between these two points. If IDegree = 0, the function calculates the smoothed value at the point x_m+1.