Abstract
A method is presented for fitting a piecewise cubic polynomial to a sequence of data which contains oscillating components superposed on rapid background changes. The first step of smoothing is performed by a one-pass method proposed by Ichida et al.[2] where the polynomail pieces are calculated as the data is scanned only once from left to right. The knots of the approximating piecewise cubic polynomail are determined successively using a modified Powell criterion which has a free parameter μ determing the degree of smoothing(μ = 1 corresponds to the original Powell criterion). As μ grows large, the fitting curve becomes smoother and the oscillating components with longer periods can be separated. If a rapid background change needs to be preserved in the smoothed data, the sum of squares of residuals is locally minimized in the neighborhood of the rapid change as the second step. The proposed method which involves two steps is capable of separating the oscillating components from the rapid background changes. Some examples of good separation are displayed.
