Spline polynomial background

The applicability of the Kalman filter requires an accurate knowledge of the response of each component and an efficient procedure for background removal. Background subtraction has recently been treated with cubic splines polynomials(5,6] as smoothing interpolators between peak valleys and this has proved to be efficient for baseline resolution particularly for very low signal-to-noise ratios [7]. 

Background removal routines typically employ polynomial splines of some order (typically second or third order). These are defined over a series of intervals with the constraint that the function and a stipulated number of derivatives be continuous at the intersection between intervals. In addition, the observed EXAFS oscillations need to be normalized to a single-atom value and this is generally done by normalizing the data to the edge jump. 

If the background is changing or a pure spectrum of the background cannot be obtained, the use of broad approximations of the background across the entire spectrum can be used. Several points in the spectrum which are presumably only background are chosen and an appropriate function (linear, simple polynomials, splines, etc.) can be fit to these points. The function is then used to create an approximation of the background and it is subtracted from the given spectrum. 

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