SMOOTHING AND DIFFERENTIATION BY AN ADAPTIVE-DEGREE POLYNOMIAL FILTER

The Savitzky-Golay method for data smoothing and differentiation calcu lates convolution weights using Gram polynomials that exactly reproduc e the results of least-squares polynomial regression. Use of the Savit zky-Golay method requires specification of both filter length and poly nomial degree to calculate convolution weights. For maximum smoothing of statistical noise in data, polynomials with low degrees are desirab le, while high polynomial degree is necessary for accurate reproductio n of peaks in the data. Extension of the least-squares regression form alism with statistical testing of additional terms of polynomial degre e to a heuristically chosen minimum for each data window leads to an a daptive-degree polynomial filter(ADPF). Based on noise reduction for d ata that consist of pure noise and on signal reproduction for data tha t is purely signal, ADPF performed nearly as well as the optimally cho sen fixed-degree Savitzky-Golay filter and outperformed suboptimally c hosen Savitzky-Golay filters. For synthetic data consisting of noise a nd signal, ADPF outperformed both optimally chosen and suboptimally ch osen fixed-degree Savitzky-Golay filters.