The basic concept of S-G is that it fits a polynomial to each central point in the data set and k side points on either side of that point. It then calculates the smoothed and derivative values from the polynomial. So, any attempt to calculate derivatives of the first or last k points in the data set need to use some other approximation. The estimate of the derivative will be worse at the edges simply because less data is used.
Because the values of the derivative at the beginning and end of the dataset would be less accurate, perhaps you could think about other options. Right now you are losing 480 out of 10000 points. If you acquire 10480 points you could get good derivative calculations on 10000 points. Or acquire data continuously and process it in overlapping segments so that the endpoints can be discarded.
I looked at the section in Numerical Recipes on derivatives. All the techniques discussed require processing of multiple points of the data.
Think about it this way: When you have a finite data set, it probably represents a segment of the data measured from some continuous or ongoing process. The act of extracting a segment of the continuous data is the same as multiplying the continuous signal by a square pulse. The derivative of the product of two functions includes information about both functions. The derivative of the square pulse is two impulses, one at each edge. You can see that the derivatives of a "chopped off" real data set will have some hard to define regions at the edges.
What will you be doing with the derivatives after you calculate them? Do you have a mathematical model of the process which generates the data?
Lynn
