Commonly, the degree of the fitting polynomial for the Savitzky-Golay filter is fixed. However, the polynomial degree can vary according to the sum of squares of fitting residuals and the statistical testing to obtain the adaptive-degree polynomial filter.
This function obtains the polynomial degree (output: polynomial_degree) selected in the adaptive-degree polynomial filter (Savitzky-Golay filter)for the data subset of length 2M+1 (intput: data_frame).
The difference between this function and our previvous one (http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=6121&objectType=file) lies in that this one is for data differentiation (first derivative) and that is for data smoothing.
Run Pkmi_Calculate first to obtain the numerical table of gram polynomials so as to accelerate the calculation. And See the demo of above-mentionded function of data smoothing for reference.
Jianwen Luo <firstname.lastname@example.org, email@example.com> 2005-02-27
Department of Biomedical Engineering
Tsinghua University, Beijing 100084, P. R. China
 P. Barak,
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 M. Jakubowska and W. W. Kubiak,
"Adaptive-degree polynomial filter for voltammetric signals," Analytica Chimica Acta, vol. 512, pp. 241-250, 2004.
 A. Savitzky and M. J. E. Golay,
"Smoothing and Differentiation of Data by Simplified Least Squares Procedures," Analytical Chemistry, vol. 36, pp. 1627-1639, 1964.
P. A. Gorry,
"General Least-Squares Smoothing and Differentiation by the Convolution (Savitzky-Golay) Method," Analytical Chemistry, vol. 62, pp. 570-573, 1990.
 J. W. Luo, K. Ying, P. He and J. Bai,
¡°Properties of Savitzky-Golay digital differentiators,¡±
Digital Signal Processing, vol. 15, pp. 122-136, 2005.
Jianwen Luo (2022). Adaptive-degree polynomial (Savitzky-Golay) filter for data differentiation (https://www.mathworks.com/matlabcentral/fileexchange/7003-adaptive-degree-polynomial-savitzky-golay-filter-for-data-differentiation), MATLAB Central File Exchange. Retrieved .
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