Integrated Savitzky-Golay Filter from Inverse Taylor Series Approach

The purpose of this paper is to use the Inverse Taylor series approach on the Savitzky-Golay (S-G) filter to derive an Integrated S-G filter which acts as a low-pass filter for noise while simultaneously directly estimating values of signal x(t) and its first k ---1 derivatives. It is similar in structure to a Finite Impulse Response (FIR) filter, and its coefficients are calcuated using the method of least squares. Initial tests indicate that this filter has significantly greater attenuation of frequencies above the cutoff frequency than the S-G filter does.