Abstract
Similarly to periodic polynomial splines, existence of the set of embedded discrete periodic splines spaces \(\varPi [N]= \fancyscript{S}_{[0]}\supset {}^{2r} \fancyscript{S}_{[1]}\supset \cdots \supset {}^{2r} \fancyscript{S}_{[m]}\cdots \), combined with the DSHA provides flexible tools for design and implementation of wavelet and wavelet packet transforms. As in the polynomial case, all the calculations consist of fast direct and inverse Fourier transforms (FFT and IFFT, respectively) and simple arithmetic operations. Raising the splines order does not increase the computation complexity.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R.R. Coifman, V.M. Wickerhauser, Entropy-based algorithms for best basis selection. IEEE Trans. Inform. Theor. 38(2), 713–718 (1992)
N. Saito, R.R. Coifman, Local discriminant bases and their applications. J. Math. Imaging Vis 5(4), 337–358 (1995)
N. Saito, R.R. Coifman, in Improved Discriminant Bases Using Empirical Probability Density Estimation. Proceedings of the Statistical Computing Section, American Statistical Association, pp. 312–321, Washington 1997
M.V. Wickerhauser, in Adapted Wavelet Analysis: From Theory to Software (AK Peters, Wellesley, 1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Averbuch, A.Z., Neittaanmaki, P., Zheludev, V.A. (2014). Discrete Periodic Spline Wavelets and Wavelet Packets. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8926-4_14
Download citation
DOI: https://doi.org/10.1007/978-94-017-8926-4_14
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-8925-7
Online ISBN: 978-94-017-8926-4
eBook Packages: EngineeringEngineering (R0)