Browse > Article

FRAMES AND SAMPLING THEOREMS IN MULTIWAVELET SUBSPACES  

Liu, Zhanwei (School of Information Engineering, Zhengzhou University)
Wu, Guochang (College of Information, Henan University of Finance and Economics)
Yang, Xiaohui (Institute of Applied Mathematics, School of Mathematics and Information Sciences, Henan University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 723-737 More about this Journal
Abstract
In this paper, we investigate the sampling theorem for frame in multiwavelet subspaces. By the frame satisfying some special conditions, we obtain its dual frame with explicit expression. Then, we give an equivalent condition for the sampling theorem to hold in multiwavelet subspaces. Finally, a sufficient condition under which the sampling theorem holds is established. Some typical examples illustrate our results.
Keywords
Frame; regular sampling; multiwavelet; sampling theorem; shift-invariant subspace;
Citations & Related Records
연도 인용수 순위
  • Reference
1 I. W. Selesnick, Interpolating multiwavelet bases and the sampling theorem, IEEE Trans. Signal Processing, 47(6)(1999), pp. 1615-1621.   DOI   ScienceOn
2 C. K. Chui and J. Lian, A study of orthonormal multi-wavelets, Appl, Numer. Math., 20(3)1996, pp. 273-298.   DOI   ScienceOn
3 X. G. Xia and Z. Zhang, On sampling theorem, wavelet and wavelet transforms, IEEE Trans. Signal Processing, 41(12)1993, pp. 3524-3535.   DOI   ScienceOn
4 A. J. E. M. Janssen, The Zak transform and sampling theorems for wavelet subspaces , IEEE Trans. Signal Processing, 41(12)1993, pp. 3360-3364.   DOI   ScienceOn
5 Y. Liu, Irregular sampling for spline wavelet subspaces, IEEE Trans. Inform. Theory, 42(2)(1996), pp. 623-627.   DOI   ScienceOn
6 W. Chen, S. Itoh, J. Shiki. A sampling theorem for shift-invariant spaces, IEEE Trans Signal Processing, 46(3)(1998), pp. 2802-2810.
7 J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory, 78(3)(1994), pp. 373-401.   DOI   ScienceOn
8 W. C. Sun and X. W. Zhou, Sampling theorem for multiwavelet subspaces, Chin. Sci. Bull., 44(14)(1999), pp. 1283-1286.   DOI
9 C. Zhao, P. Zhao Sampling Theorem and Irregular Sampling Theorem for Multiwavelet subspaces, IEEE Trans Signal Processing, 53(3)(2005), pp. 705-713.
10 D. Zhou, Interpolatory orthogonal multiwavelets and refinable functions, IEEE Trans. Signal Processing, 50(3)(2002), 520-527, 2002.   DOI   ScienceOn
11 X. W. Zhou, W. C. Sun, On the Sampling Theorem for Wavelet Subspaces, J. Fourier. Anal. Appl, 5(4)(1999), pp. 347-354.   DOI
12 X. W. Zhou, W. C. Sun, Sampling Theorem for Wavelet Subspaces: Error Estimate and Irregular Sampling, IEEE Trans Signal Processing, 48(1)(2000), pp. 223-226.   DOI   ScienceOn
13 O. Christensen, An Introduction to Frames and Riesz bases, Birkhauser, Boston, MA, 2003.
14 C. Blanco, C. Cabrelli and S. Heineken, Functions in Sampling Spaces, Sampling Theory In Signal and Image Processing, 5(3)2006, pp. 275-295.
15 G. G. Walter, A sampling theorem for wavelet subspaces, IEEE Trans. Inform. Theory, 38(2)(1992), pp. 881-884.   DOI   ScienceOn