2-D Savitzky-Golay Differentiation Filter

2-D Savitzky-Golay Differentiation Filter.

Description

2-D Savitzky-Golay Differentiation Filter.
Here the filter coefficients for the central point and the first order derivative (differentiation) is taken into account.

Usage:
      h=sgdf_2d(x,y,nx,ny,flag_coupling)
      x = x data point, e.g., -3:3
      y = y data point, e.g., -2:2
      nx =x polynomial order default=1
      ny =y polynomial order default=1
      flag_coupling = with or without the consideration of the coupling terms, between x and y. default=0
Example:
      sgdf_2d(-3:3,-4:4,2,2)
      sgdf_2d(-3:3,-4:4,2,3,1)
Author:
      Jianwen Luo <[e-mail], [e-mail]> 2004-10-31
      Department of Biomedical Engineering
      Tsinghua University, Beijing 100084, P. R. China
Reference
[1]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.
[2]K. L. Ratzlaff and J. T. Johnson, "Computation of Two-Dimensional Polynomial Least-Squares Convolution Smoothing Integers,"
  Analytical Chemistry, vol. 61, pp. 1303-1305, 1989.
[3]J. E. Kuo, H. Wang, and S. Pickup, "Multidimensional Least-Squares Smoothing Using Orthogonal Polynomials,"
  Analytical Chemistry, vol. 63, pp. 630-635, 1991.
[4]http://research.microsoft.com/users/jckrumm/SavGol/SavGol.htm
[5] J. W. Luo, K. Ying, P. He and J. Bai,
¡°Properties of Savitzky-Golay digital differentiators,¡±
 Digital Signal Processing, in press.

• Acknowledgements: This submission has inspired the following:; z-transform of 1D & 2D Savitzky-Golay Smoothing and Differentiation Filter
• MATLAB release: MATLAB 6.5.1 (R13SP1)

[Jianwen Luo]

====Correction!====

h=inv(A'*A)*A';
if flag_coupling
    h=h(nx*(ny+1),:);% ?*x
else
    h=h(nx,:);% ?*x
end
h=reshape(h,ly,lx);

[habib kassem]

 

[Jianwen Luo]

x and/or y can be in even length, e.g., sgdf_2d(-2.5:2.5,-3.5:3.5,1,1) or sgdf_2d(-2.5:2.5,-3:3,1,1).