Automatic Selection of Optimal Savitzky−Golay Smoothing

Abstract

A method to select the optimal window size of the Savitzky-Golay (SG) algorithm is presented. The approach is based on a comparison of the fitting residuals (i.e., the differences between the input signal and the smoothed signal) with the noise of the instrument. The window size that yields an autocorrelation of the residuals closest to the autocorrelation of the noise of the instrument is considered optimal. The method is applied in two steps. In a first step, the lag-one autocorrelation value of the noise of the instrument is computed through the study of a blank signal. In a second step, the SG algorithm is applied to "smooth" the signal using different window sizes. The method was applied to data from NMR, chromatography, and mass spectrometry and was shown to be robust. It finds the optimal window size for different signal features. This allows the method to be used in an unsupervised way, embedded in a more complex algorithm in which smoothing and/or differentiation of signals is required, provided that the lag-one autocorrelation value of the instrument noise does not change.

Error propagation in open respirometric assays

“…In most cases, this problem may be overcome by using digital filters or larger time windows (Savitzky and Golay, 1964;Bromba and Zlegler, 1981). Although there are several methods to select the optimal window size of digital filters (Vivo-Truyols and Schoenmakers, 2006), the selection of very large values of t w may produce a flattened effect on R ex curves, masking the actual behavior of the respiration rate as a function of time. Moreover, large t w values in combination with a high sampling rate (e.g., a very low Δt value) produce very large data files, which are difficult to process due to computer limitations.…”

Savitzky-Golay Method for the Evaluation of Deceleration of the Firction Lift

“…a moving average which can be described as a special example of a simple Savitzky-Golay filter) 12. Savitzky-Golay method is also used by the authors in other fields of operation such as chemical industry 1,13.…”

Inertia Estimation Using EKF-SGF Combination

“…7) The approach is performed by finding the minimum value of the difference between residuals of the fitting (measurement-smoothing solution) and the noise of the instrument (measurement-estimated solution). Using this approach, a proper window-size of 19 has been determined with the noise level ¼ 10 À4 rad/s.…”