The Character of Multiple Affine Pseudoframes with Filter Banks Based on a Pyramid Decomposition Scheme

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In recent years, frames have been the focus of active research, both in theory and applications. In this paper, the notion of multiple affine pseudoframes for subspaces of space is introduced. The concept of a generalized multiresolution structure(GMRS) is proposed. The sufficient condition for the existence of a class of multiple pseudoframes with filter banks is obtained by virtue of a generalized multiresolution structure. An approach for constructing one GMRS of Paley-Wiener subspaces of is presented based on the pyramid decomposition scheme The characteristics of affine pseudoframes for subspaces of space is provided.

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Periodical:

Key Engineering Materials (Volumes 439-440)

Edited by:

Yanwen Wu

Pages:

1111-1116

DOI:

10.4028/www.scientific.net/KEM.439-440.1111

Citation:

T. Q. Zhang "The Character of Multiple Affine Pseudoframes with Filter Banks Based on a Pyramid Decomposition Scheme", Key Engineering Materials, Vols. 439-440, pp. 1111-1116, 2010

Online since:

June 2010

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$38.00

[1] D. Gabor, Theory of communication: J. Inst. Elec. Engrg., Vol. 93, pp.429-457, (1946).

[2] R. J. Duffin, A. C. Schaeffer: A class of nonharmonic Fourier series , Trans. Amer. Math. Soc., Vol. 72, pp.341-366. (1952).

DOI: 10.1090/s0002-9947-1952-0047179-6

[3] I. Daubechies, A. Grossmann, A. Meyer: Painless nonorthogonal expansions. J. Math. Phys. Vol 27, pp.1271-1283. ( 1986).

[4] A. Ron, Z. Shen: Affine systems in L^2(R^d). (II) Dual systems. J. Fourier Anal. Appl. Vol 4, pp.617-637. ( 1997).

[5] I. Daubechies: Ten Lectures on Wavelets. SIAM: Philadelphia. (1992).

[6] S. Li, M. Ogawa: Pseudoframes for Subspaces with Applications. J. FourierAnal. Appl. Vol 10, pp.409-431. (2004).

[7] S. Li: A Theory of Geeneralized Multiresolution Structure and Pseudoframes of Translates. J. Fourier Anal. Appl. Vol 6(1), pp.23-40. (2001).

[8] J. J. Benedetto, S. Li: The theory of multiresolution analysis frames and applications to filter banks. Appl. comput. Harmon. Anal. vol5, pp.389-427. ( 1998).

[9] P. G. Casazza: The art of frame theory, Taiwanese Journal , of mathe-matics, Vol. 4, No. 2, pp.129-201. (2000).

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