Abstract
The paper describes the derivation of a recursive P-spline difference equation. It further demonstrates how a transformed spline can be used as a digital filter with an infinite impulse response and variable parameters. Frequency responses of a real-time spline filter correspond to frequency responses of low-frequency digital filters. The paper further examines the influence of some P-spline parameters on the efficiency of interpretation of real-time input measurement information.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Kochegurova, E.A., Kochegurov, A.I., Rozhkova, N.E.: Frequency analysis of recurrent variational P-splines. Optoelectron. Instrum. Data Process. 53(6), 591–598 (2017)
Oppenheim, A., Schafer, R.: Discrete-Time Signal Processing, 3rd edn. Prentice-Hall, Upper Saddle River (1989)
Ifeachor, E.C., Jervis, B.W.: Digital Signal Processing: A Practical Approach, 2nd edn. Prentice-Hall, Upper Saddle River (2002)
Rabiner, L.R., Gold, B.: Theory and Application of Digital Signal Processing. New Delhi, PHI, Learning, Verlag (2009)
Lyons, R.G.: Understanding Digital Signal Processing, 3rd edn. Prentice Hall, Upper Saddle River (2011)
Manolakis, D., Ingle, V.: Applied Digital Signal Processing: Theory and practice. Cambridge University Press, Cambridge (2011)
Bugrov, V.N.: Synthesis of integral recursive filters with arbitrarily given selective requirements. J. Dig. Signal Process. 2, 35–43 (2016)
De Boor, C.A.: Practical Guide to Splines. Springer, New York (2001)
Shumilov, B.M.: Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids. J. Comput. Math. Math. Phys. 56(7), 1236–1247 (2016)
Jauch, J., Bleimund, F., Rhode, S., Gauterin, F.: Recursive B-spline approximation using the Kalman filter. Int. J. Eng. Sci. Technol. 20(1), 28–34 (2017)
Chen, X.-D., Ma, W., Paul, J.-C.: Cubic B-spline curve approximation by curve unclamping. Comput. Aided Des. 42(6), 523–534 (2010)
Aguilera, A.M., Aguilera-Morillo, M.C.: Penalized PCA approaches for B-spline expansions of smooth functional data. Appl. Math. Comput. 219(14), 7805–7819 (2013)
Eilers, P.H.C., Marx, B.D.: Splines, knots, and penalties. Comput. Stat. 2(6), 637–653 (2010)
Iorio, C., Frasso, G., D’Ambrosio, A., Siciliano, R.: Parsimonious time series clustering using p-splines. Expert Syst. Appl. 52, 26–38 (2016)
Yang, L., Hong, Y.: Adaptive penalized splines for data smoothing. Comput. Stat. Data Anal. 108, 70–83 (2017)
Kochegurova, E., Gorokhova, E.: Current derivative estimation of non-stationary processes based on metrical information. In: Núñez, M., Nguyen, N.T., Camacho, D., Trawiński, B. (eds.) ICCCI 2015. LNCS (LNAI), vol. 9330, pp. 512–519. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24306-1_50
Simpkin, A., Newell, J.: An additive penalty P-Spline approach to derivative estimation. Comput. Stat. Data Anal. 68, 30–43 (2013)
Park, H.: Choosing nodes and knots in closed B-spline curve interpolation to point data. Comput. Aided Des. 33(13), 967–974 (2001)
Ülker, E., Arslan, A.: Automatic knot adjustment using an artificial immune system for B-spline curve approximation. Inf. Sci. 179(10), 1483–1494 (2009)
Park, H., Lee, J.H.: B-spline curve fitting based on adaptive curve refinement using dominant points. Comput. Aided Des. 39(6), 439–451 (2007)
Valenzuela, O., Delgado-Marquez, B., Pasadas, M.: Evolutionary computation for optimal knots allocation in smoothing splines. Appl. Math. Model. 37(8), 5851–5863 (2013)
Denisov, V.I., Faddeenkov, A.V.: Spline regression with variable penalty coefficients. Optoelectron. Instrum. Process. 51(3), 213–219 (2015)
Rozhenko, A.I.: A new method for finding the optimal smoothing parameter for the abstract smoothing spline. J. Approx. Theory 162(6), 1117–1127 (2010)
Aydin, D., Memmedli, M.: Optimum smoothing parameter selection for penalized least squares in form of linear mixed effect models. Optimization 61(4), 459–476 (2012)
Kochegurova, E.A., Gorokhova, E.S.: Current estimation of the derivative of a nonstationary process based on a recurrent smoothing spline. Optoelectron. Instrum. Data Process. 52(3), 280–285 (2016)
Iorio, C., Frasso, G., D’Ambrosio, A., Siciliano, R.: A P-spline based clustering approach for portfolio selection. Expert Syst. Appl. 95(1), 88–103 (2018)
Jhong, J.-H., Koo, J.-Y., Lee, S.-W.: Penalized B-spline estimator for regression functions using total variation penalty. J. Stat. Plan. Infer. 184, 77–93 (2017)
Acknowledgment
The reported study was funded by RFBR according to the research project № 18-07-01007
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Kochegurova, E., Khozhaev, I., Ezangina, T. (2018). Design of Recursive Digital Filters with Penalized Spline Method. In: Nguyen, N., Pimenidis, E., Khan, Z., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2018. Lecture Notes in Computer Science(), vol 11056. Springer, Cham. https://doi.org/10.1007/978-3-319-98446-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-98446-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98445-2
Online ISBN: 978-3-319-98446-9
eBook Packages: Computer ScienceComputer Science (R0)