A unified framework for derivation and implementation of Savitzky-Golay filters

The Savitzky–Golay (SG) filter design problem is posed as the minimum norm solution of an underdetermined equation system. A unified SG filter design framework encompassing several important applications such as smoothing, differentiation, integration and fractional delay is developed. In addition to the generality and flexibility of the framework, an efficient SG filter implementation structure, naturally emerging from the framework, is proposed. The structure is shown to reduce the number of multipliers in the smoothing application. More specifically, the smoothing application, where an Lth degree polynomial to the frame of 2Nþ1 samples is fitted, can be implemented with N L=2 multiplications per output sample instead of Nþ1 multiplications with the suggested structure. & 2014 Elsevier B.V. All rights reserved.