A recursive construction of a class of finite normalized tight frames

Document Type: Research Paper

Authors

Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Islamic Republic of Iran

Abstract

Finite normalized tight frames are interesting because they provide decompositions in applications and some physical interpretations. In this article, we give a recursive method for constructing them.

Keywords


[1] J. J. Benedetto and M. Fickus, Finite normalized tight frames, Adv. Comput. Math., 18(2003), 357-385.
[2] O. Christensen, Frames and bases, An introductory course. Birkhauser, Boston, 2008. ¨
[3] N. Cotfas and J. P. Cazeau, Finite tight frames and some applications, J. Phys. A: Math. Theor. 43 (2010)
193001. doi:10.1088/1751-8113/43/19/193001.
[4] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series , Trans. Amer. Math. Soc., 71,(1952)
341-366.
[5] D. Feng, L. Wang and Y. Wang, Generation of finite tight frames by Householder transformations, Adv. Comput.
Math., 24(2006), 294-309.
[6] J. Kovacevic and A. Chebira, ˇ Life beyond bases:The advent of frames (Parts I and II), IEEE Signal Proces. Mag.,
24(4),(2007), 86-104, 115-125.
[7] D. F. Li and W. C. Sun, Expansion of frames to tight frames, Acta Math. Sinica, English Series, 25, (2)(2009),
287-292.
[8] V. N. Malozemov and A. B. Pevnyi, Equiangular tight frames, J. Math. Sci., 157(6)(2009), 3-25.
[9] A. Safapour and M. Shafiee, Constructing Finite Frames via Platonic Solids, Iran. J. Math. Sci. Info., 7(1)(2012),
35-41.
[10] E. Soljanin, ˇ Tight frames in quantum information theory, DIMACS Workshop on Source Coding and Harmonic
Analysis, Rurgers, New Jersey, May 2002.
[11] T. Strohmer and R. Heat, Grassmannian frames withnapplications to codingamd commucations, Appl. Comp.
Harm. Anal. 14(3)(2003), 257-275.
[12] J. C. Tremain, Algorithmic constructions of unitary matrices and tight frames, arXiv:1104.4539v1 [math.FA] 23
APR 2011.
[13] G. Zimmermann, Normalized tight frames in finite dimensions, Inter. Seri. Numer. Math., 137(2001), 249 - 252.