Savitzky–Golay smoothing and differentiation filter for even number data

The Savitzky–Golay smoothing and differentiation filter optimally fits a set of data points to a polynomial in the least-squares sense. The Savitzky–Golay filter has been developed and generalized well in the literatures. However, the data subset is subject to an odd number (2m+1). In this communication, the Savitzky–Golay filter is extended for even number data. Simulations are performed to validate the feasibility of such an approach. And some corresponding properties are discussed.