Perturbation of regular sampling in shift-invariant spaces for frames

IEEE Transactions on Information Theory

Volumn 52, Issue 10, 2006, Pages 4643-4648

  Zhao, Ping ^a,b   Zhao, Chun ^c   Casazza, Peter G ^d  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c TIANJIN NORMAL UNIVERSITY   (China)

^d UNIVERSITY OF MISSOURI   (United States)

Author keywords

Frame; Irregular sampling; Perturbation; Riesz basis; Sampling; Wavelets

Indexed keywords

MATHEMATICAL MODELS; SAMPLING; THEOREM PROVING;

IRREGULAR SAMPLING; RIESZ BASIS;

PERTURBATION TECHNIQUES;

EID: 33947398341     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.881704     Document Type: Article

References (17)

1. G.G. Walter, "A sampling theorem for wavelet subspace," IEEE Trans. Inf. Theory, vol. 38, pp. 881-884, Apr. 1992.
2. W. Sun and X. Zhou, "Frames and sampling theorem," Sci.China, vol. 41, no. 2, pp. 606-612, 1998.
3. A. J. E. M. Janssen, "The Zak transform and sampling theorem for wavelet subspaces," IEEE Trans.Signal Process., vol. 41, pp. 3360-3364, 1993.
4. W. Chen and S. Itoh, "A sampling theorem for shift-invariant sub-space," IEEE Trans.Signal Processing, vol. 46, pp. 2822-2824, 1998.
5. W. Sun and X. Zhou, "Sampling theorem for wavelet subspaces: Error estimate and irregular sampling," IEEE Trans.Signal Process., vol. 48, pp. 223-226, 2000.
6. Y. Liu and G. Walter, "Irregular sampling in wavelet subspaces," J. Fourier Anal. Appl., vol. 2, no. 2, pp. 181-189, 1995.
7. W. Chen, S. Itoh, and J. Shiki, "Irregular sampling theorems for wavelet subspaces," IEEE Trans. Inf. Theory, vol. 44, pp. 1131-1142, 1998.
8. _, "On sampling in shift invariant spaces," IEEE Trans. Inf. Theory, vol. 48, pp. 2802-2810, 2002.
9. O. Christensen, "A Paley-Wiener theorem for frames," Proc. Amer. Math. Soc., vol. 123, no. 7, pp. 2199-2202, 1995.
10. _, "Frame perturbations," Proc. Amer. Math.Soc., vol. 123, no. 4, pp. 1217-1220, 1995.
11. P. G. Casazza and O. Christensen, "Perturbation of operators and applications to frame theory," J. Fourier Anal. Appl., vol. 3, no. 5, pp. 543-558, 1997.
12. C. K. Chui, "An introduction to wavelets," in Wavelet Analysis and Its Applications. New York: Academic, 1992, vol. 1.
13. J. J. Benedetto and S. Li, "Multiresolution analysis frames with applications," in ICASSP'93, Minneapolis, Apr. 26-30, 1993, vol. III, pp. 304-307.
14. O. Christensen, "Frames, Riesz bases, and discrete Gabor wavelet expansions," Bull. Amer. Math. Soc., vol. 38, no. 3, pp. 273-291, 2001.
15. P. Zhao, G. Liu, and C. Zhao, "Frames and sampling theorems for translation-invariant subspaces," IEEE Signal Process. Lett., vol. 11, pp. 8-11, 2004.
16. C. Zhao and P. Zhao, "Sampling theorem and irregular sampling theorem for multiwavelet subspaces," IEEE Trans. Signal Process., vol. 53, pp. 705-713, 2005.
17. R. Young, An Introduction to Non-Harmonic Fourier Series. New York: Academic, 1980.