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

被引:45
|
作者
Candan, Cagatay [1 ]
Inan, Hakan [2 ]
机构
[1] Middle E Tech Univ, Dept Elect & Elect Engn, TR-06531 Ankara, Turkey
[2] Stanford Univ, Dept Elect Engn, Stanford, CA 94305 USA
关键词
Savitzky-Golay filters; Polynomial interpolation; Smoothing; Differentiation; Fractional delay; DIFFERENTIATION; SELECTION;
D O I
10.1016/j.sigpro.2014.04.016
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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 2N+1 samples is fitted, can be implemented with N-L/2 multiplications per output sample instead of N+1 multiplications with the suggested structure. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码:203 / 211
页数:9
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