An Approach to Savitzky–Golay Differentiators

  • Natanael S. Figueiredo
  • Luís H. C. FerreiraEmail author
  • Odilon O. Dutra
Short Paper


This short paper presents a new approach to the calculation of Savitzky–Golay differentiators based on symmetric differentiation. Some comparisons with the regular polynomial derivative are made in order to find differences and similarities between the two methods. The evaluation shows that the new symmetric differentiation approach presents lower noise power gain, which is an interesting characteristic for digital signal processing purposes.


Savitzky–Golay differentiators Digital differentiation Low-performance microcontrollers Noise power gain 



This work was supported in part by National Council for Scientific and Technological Development under Grant 303041/2015-3. The authors would like to thank the reviewers for their useful suggestions.


  1. 1.
    Ç. Candan, H. Inan, A unified framework for derivation and implementation of Savitzky–Golay filters. Signal Process. 104, 203–211 (2014)CrossRefGoogle Scholar
  2. 2.
    D. Chen, Y. Chen, D. Xue, Digital fractional order Savitzky–Golay differentiator. IEEE Trans. Circuits Syst. II Express Briefs 58(11), 758–762 (2011)CrossRefGoogle Scholar
  3. 3.
    S.J. Johnston, M. Scott, S.J. Cox, Recommendations for securing internet of things devices using commodity hardware. In 2016 IEEE 3rd World Forum on Internet of Things (WF-IoT), pp. 307–310 (2016)Google Scholar
  4. 4.
    R.J. LeVeque, Finite difference approximations, Finite Difference Methods for Differential Equations (University of Washington, Washington, 2005)Google Scholar
  5. 5.
    J. Luo, K. Ying, P. He, J. Bai, Properties of Savitzky–Golay digital differentiators. Digit. Signal Process. J. 15, 122–136 (2005)CrossRefGoogle Scholar
  6. 6.
    E.N. Nishida, O.O. Dutra, L.H.C. Ferreira, G.D. Colletta, Application of Savitzky–Golay digital differentiator for QRS complex detection in an electrocardiographic monitoring system. In 2017 IEEE International Symposium on Medical Measurements and Applications (MeMeA), pp. 233–238 (2017)Google Scholar
  7. 7.
    S.J. Orfanidis, Signal processing applications, Introduction to Signal Processing, chapter 8 (Prentice Hall, Inc., Upper Saddle River, 1996), pp. 427–452Google Scholar
  8. 8.
    A. Savitzky, M.J.E. Golay, Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36(8), 1627–1639 (1964)CrossRefGoogle Scholar
  9. 9.
    R.W. Schafer, What is a Savitzky–Golay filter? [lecture notes]. IEEE Signal Process. Mag. 28(4), 111–117 (2011)CrossRefGoogle Scholar
  10. 10.
    Y.S. Shmaliy, O. Ibarra-Manzano, Noise power gain for discrete-time FIR estimators. IEEE Signal Process. Lett. 18(4), 207–210 (2011)CrossRefGoogle Scholar
  11. 11.
    K.K. Singh, M.K. Bajpai, R.K. Pandey, Reconstruction of original signal from contaminated signal using fractional order differentiator. In 2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), pp. 274–278 (2015)Google Scholar
  12. 12.
    J. Steiner, Y. Termonia, J. Deltour, Comments on smoothing and differentiation of data by simplified least square procedure. Anal. Chem. 44(11), 1906–1909 (1972)CrossRefGoogle Scholar
  13. 13.
    B.S. Thomson, The symmetric derivative, Symmetric Properties of Real Functions, chapter 7 (Marcel Dekker, Inc., New York, 1994), pp. 249–292Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Systems Engineering and Information Technology InstituteFederal University of ItajubáItajubáBrazil

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