Necessity of Oversampling Theorem for Affine Frames ()
Qiquan Fang,
Xianliang Shi,
Weicai Li
College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha, China.
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, China.
DOI: 10.4236/jamp.2014.22003
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Abstract
In this paper we prove
that n is relatively prime to a which is also necessary.
Share and Cite:
Fang, Q. , Shi, X. and Li, W. (2014) Necessity of Oversampling Theorem for Affine Frames.
Journal of Applied Mathematics and Physics,
2, 18-23. doi:
10.4236/jamp.2014.22003.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
C. Lee, P. Linneman and C. K. Chui, “An Introduction to Wavelets,” Academic Press, Boston, 1992.
|
|
[2]
|
I. Daubechies, “Ten Lectures on Wavelets,” Society for Industrial and Applied Mathematics, Philadelphia, 1992.
http://dx.doi.org/10.1137/1.9781611970104
|
|
[3]
|
C. K. Chui and X. L. Shi, “Bessel Sequences and Affine Frames,” Applied and Computational Harmonic Analysis, Vol. 1, No. 1, 1993, pp. 29-49. http://dx.doi.org/10.1006/acha.1993.1003
|
|
[4]
|
C. K. Chui and X. L. Shi, n× Oversampling preserves any tight affine frame for odd n, Proceedings of the American Mathematical Society, Vol. 121, No, 2, 1994, pp. 511-517.
|