Savitzky-Golay Smoothing and Differentiation Filter
        Copyright (c) 2011, Diederick
        The Savitzky-Golay smoothing/differentiation filter (i.e., the
        polynomial smoothing/differentiation filter, or  the least-squares
        smoothing/differentiation filters) optimally fit a set of data
        points to polynomials of different degrees. 
        See for details in Matlab Documents (help sgolay). The sgolay
        function in Matlab can deal with only uniformly
        spaced data of even number.
        This function presented here is a general implement of the sgolay
        function in Matlab. The Savitzky-Golay filter coefficients for even
        number, and nonuniformly spaced data can be
        obtained. And the filter coefficients for the initial point or the
        end point can be obtained too. In addition, either numerical
        results or symbolical results can be obtained. Lastly, this
        function is faster than MATLAB's sgolay.
 
  Usage:
        [fc,df] = savitzkyGolay(x,n,dn,x0,flag)
    input:
        x    = the original data point, e.g., -5:5 
        n    = polynomial order
        dn   = differentation order (0=smoothing),  default=0
        x0   = estimation point, can be a vector    default=0
        W    = weight vector, can be empty          
               must have same length as x0          default=identity
        flag = numerical(0) or symbolical(1),       default=0
 
    output:
        fc   = filter coefficients obtained (B output of sgolay).
        df   = differentiation filters (G output of sgolay).
  Notes:
  1.    x can be arbitrary, e.g., odd number or even number, symmetrical or
        nonsymmetrical, uniformly spaced or nonuniformly spaced, etc.       
  2.    x0 can be arbitrary, e.g., the initial point, the end point, etc.
  3.    Either numerical results or symbolical results can be obtained.
  Example:
        sgsdf([-3:3],2,0,0,[],0)
        sgsdf([-3:3],2,0,0,[],1)
        sgsdf([-3:3],2,0,-3,[],1)
        sgsdf([-3:3],2,1,2,[],1)
        sgsdf([-2:3],2,1,1/2,[],1)
        sgsdf([-5:2:5],2,1,0,[],1)     
        sgsdf([-1:1 2:2:8],2,0,0,[],1)
  Author:
        Diederick C. Niehorster <dcniehorster@hku.hk> 2011-02-05
        Department of Psychology, The University of Hong Kong