Adaptive-degree polynomial (Savitzky-Golay) filter for data differentiation

Adaptive-degree polynomial filter (Savitzky-Golay Filter) for data differentiation (1st derivative).

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.

Usage:
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.

Author:
Jianwen Luo <[e-mail], [e-mail]> 2005-02-27
Department of Biomedical Engineering
Tsinghua University, Beijing 100084, P. R. China

References:
[1] P. Barak,
"Smoothing and differentiation by an adaptive-degree polynomial filter," Analytical Chemistry, vol. 67, pp. 2758-2762, 1995.
[2] M. Jakubowska and W. W. Kubiak,
"Adaptive-degree polynomial filter for voltammetric signals," Analytica Chimica Acta, vol. 512, pp. 241-250, 2004.
[3] 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.
[4]P. A. Gorry,
"General Least-Squares Smoothing and Differentiation by the Convolution (Savitzky-Golay) Method," Analytical Chemistry, vol. 62, pp. 570-573, 1990.
[5] 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.
[6] http://www.mathworks.com/matlabcentral/fileexchange/loadFileList.do?objectType=search&criteria=savitzky&Search=Go
[7] http://uk.cambridge.org/chemistry/resources/delevie/