Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/non-translation-invariance-and-the-synchronization-problem-in-wavelet-XBJ4F8f8I6
References (16)
-
J.A. Hogan, J.D. Lakey (2005)
Advances in Analysis: Proceedings of the 4th International ISAAC Congress -
X. Xia, Zhen Zhang (1993)
On sampling theorem, wavelets, and wavelet transformsIEEE Trans. Signal Process., 41
-
A. Janssen (1988)
The Zak transform : a signal transform for sampled time-continuous signals.Philips Journal of Research, 43
-
J. Hogan, J. Lakey (2005)
Sampling and oversampling in Shift-Invariant and Multiresolution Spaces I: Validation of Sampling SchemesInt. J. Wavelets Multiresolution Inf. Process., 3
-
I. Djokovic, P. Vaidyanathan (1997)
Generalized sampling theorems in multiresolution subspacesIEEE Trans. Signal Process., 45
-
A. Janssen (1993)
The Zak transform and sampling theorems for wavelet subspacesIEEE Trans. Signal Process., 41
-
A. Aldroubi, K. Gröchenig (2001)
Nonuniform Sampling and Reconstruction in Shift-Invariant SpacesSIAM Rev., 43
-
A. Bastys (2000)
Translation Invariance of Orthogonal Multiresolution Analyses of L2(R)Applied and Computational Harmonic Analysis, 9
-
C. Berenstein, D. Struppa (1988)
Small Degree Solutions for the Polynomial Bezout EquationLinear Algebra and its Applications, 98
-
(2004)
Time‒Frequency and Time‒Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling -
C. Chui (1992)
Wavelets: A Tutorial in Theory and Applications -
J. Hogan, J. Lakey (2005)
Non-Translation-Invariance in Principal Shift-Invariant Spaces -
I. Daubechies (1992)
Ten Lectures on WaveletsComputers in Physics, 6
-
H. Dym, H. McKean (1972)
Fourier series and integrals -
A. Aldroubi, C. Cabrelli, C. Heil, K. Kornelson, U. Molter (2008)
Invariance of a Shift-Invariant SpaceJournal of Fourier Analysis and Applications, 16
-
C. Heil, D. Walnut (1989)
Continuous and Discrete Wavelet TransformsSIAM Rev., 31
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-009-9480-y
- Publisher site
- See Article on Publisher Site
Abstract
One of the major differences between Paley-Wiener spaces of bandlimited signals and the principal shift-invariant (PSI) spaces of wavelet theory is that the latter, although shift-invariant, are in general not translation-invariant. In this paper we study the extra difficulties non-translation-invariance creates for the sampling theory of PSI and multiresolution spaces. In particular it is shown that sampling in PSI spaces requires an extra initialization step to determine the times at which sampled data is acquired. An algorithm is developed to provide this initialization and its effectiveness shown theoretically and demonstrated on a synthetic data set.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Mar 5, 2009