The Scope and Limitations of Curve Fitting

Abstract

There is an increasing awareness that the separation of overlapping bands by the mathematical technique of curve fitting offers many pitfalls and should not be undertaken lightly. This review discusses critically the various factors involved, with particular reference to vibrational band systems; other types of overlapping band systems encountered in analytical work are considered in less detail. Five parameters are involved: the number of component bands, their positions, shapes and widths, and the form of the baseline. Curve fitting, by a least squares optimization method to a suitable goodness of fit criterion, is considerably facilitated if approximate values for some of the parameters are known at the outset. The methods available for peak finding are discussed and, although not free from problems, are reasonably effective. Similarly, band shapes can usually be defined semiquantitatively. However, it is seldom possible to obtain prior information on band widths; these should be determined during the curve fitting calculations. Although statistical goodness of fit criteria are available they should be used in conjunction with a visual plot, to locate any regions of poor fit. Furthermore, the overriding consideration must always be that the computer fit is plausible in terms of acceptable chemical species for the system being examined.