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A Simple Technique for Simultaneous Smoothing and Integration of Data
W
P. Nikitas and C. Malliakas, Laboratory of Physical Chemistry, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece
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 xm and xm+1 when IDegree ≠ 0 and xa, xb 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 xa, xb are included, then the function calculates the integral between these two points. If IDegree = 0, the function calculates the smoothed value at the point xm+1.
JChemEd.chem.wisc.edu • Vol. 79 No. 1 January 2002 • Journal of Chemical Education
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