I am working on a signal-smoothing algorithm for personal interest. I understand the basic concept of the Savitzky-Golay algorithm but I would like to understand how the coefficients were discovered. Can someone please explain the the mathematics behind it, so I could calculate the coefficients on my own?
How would the matrix look? For example here states: "For n=5 and p=3, the filtering coefficients are b= [-0.0857 0.3429 0.4857 0.3429 -0.0857]." However, it does not show the steps to achieve this. If n equal the number of points to sample and p equals the power of the polynomial.