Abstract
In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmäki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.
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
References
A.Z. Averbuch, P. Neittaanmäki, V.A. Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Periodic Splines, vol I (Springer, Berlin, 2014)
P. Neittaanmäki, V. Rivkind, V. Zheludev, A wavelet transform based on periodic splines and finite element method, in Finite Element Methods (Jyväskylä, 1993), Lecture Notes in Pure and Appl. Math., ed. by M. Křížek, P. Neittaanmäki, R. Stenberg, vol 164 (Dekker, New York, 1994), pp. 325–334
P. Neittaanmäki, V. Rivkind, V. Zheludev, Periodic spline wavelets and representation of integral operators. Preprint 177, University of Jyväskylä, Department of Mathematics, (1995)
V. Zheludev, An operational calculus connected with periodic splines. Soviet. Math. Dokl. 42(1), 162–167 (1991)
V. Zheludev, Periodic splines and the fast Fourier transform. Comput. Math. Math. Phys. 32(2), 149–165 (1992)
V. Zheludev, Periodic splines, harmonic analysis, and wavelets, in Signal and Image Representation in Combined Spaces, Wavelet Anal. Appl., ed. by Y.Y. Zeevi, R. Coifman, vol 7 (Academic Press, San Diego, 1998), pp. 477–509
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Averbuch, A.Z., Neittaanmäki, P., Zheludev, V.A. (2019). Periodic Polynomial Splines. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-92123-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-92123-5_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92122-8
Online ISBN: 978-3-319-92123-5
eBook Packages: EngineeringEngineering (R0)