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

CANDAN Ç., Inan H.

SIGNAL PROCESSING, cilt.104, ss.203-211, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 104
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.sigpro.2014.04.016
  • Dergi Adı: SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.203-211
  • Anahtar Kelimeler: Savitzky-Golay filters, Polynomial interpolation, Smoothing, Differentiation, Fractional delay, DIFFERENTIATION, SELECTION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.