SMOOTHING AND DIFFERENTIATION BY AN ADAPTIVE-DEGREE POLYNOMIAL FILTER

The Savitzky-Golay method for data smoothing and differentiation calculates convolution weights using Gram polynomials that exactly reproduce the results of least-squares polynomial regression. Use of the Savitzky-Golay method requires specification of both filter length and polynomial degree to calculate convolution weights. For maximum smoothing of statistical noise in data, polynomials with low degrees are desirable, while high polynomial degree is necessary for accurate reproduction of peaks in the data. Extension of the least-squares regression formalism with statistical testing of additional terms of polynomial degree to a heuristically chosen minimum for each data window leads to an adaptive-degree polynomial filter(ADPF). Based on noise reduction for data that consist of pure noise and on signal reproduction for data that is purely signal, ADPF performed nearly as well as the optimally chosen fixed-degree Savitzky-Golay filter and outperformed suboptimally chosen Savitzky-Golay filters. For synthetic data consisting of noise and signal, ADPF outperformed both optimally chosen and suboptimally chosen fixed-degree Savitzky-Golay filters.