Frames and its applications

P.Kalyani

doi:https://doi.org/10.14445/22315373/IJMTT-V49P527

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 49 | Number 3 | Year 2017 | Article Id. IJMTT-V49P527 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P527

Frames and its applications

P.Kalyani

Abstract

Different types of frames and operators are defined with examples and applications of each of the type of frames are explained.

Keywords

applications of each of the type of frames are explained.

References

[1] M.R.Abdollahpour ,M.H. Faroughi and A.Rahimi ,”PG-Frames in Banach spaces” Methods of Functional analysis and topology Vol.13 NO.3(2007),pp.201-210.
[2] R.BalanP.G.Casazza, D.Edidin and G.Kutynoik “ Decomopostion of frames and a new frame identity “ Wavelet XI (San Diego),CA(2005) pp.379-388 SPIE Proc 5914 ,SPIE Bellinginam WA.
[3] P.G.Casazza,The art of Frame theory Taiwanese Journal of Mathematics Vol.4,No.2(2000) pp 129-201.
[4] D.Han and D.R.Larson “Frames Bases and Group Representations” Memories Ams Nov 7 (2000) Providence RI.
[5] A.Najati and A.Rahimi “Generalized frames in Hilbert spaces” Bulletin of the Iranian Mathematical society Vol.35,No.1(2009) pp.97-109.
[6] A.Najati and M.H.Faroughi “P- frames of subspaces of separable Hilbert spaces South east AsainBulletion of Mathematics 31(2007)pp.713-726.
[7] G. Upender Reddy and N.Gopal Reddy ,Some results of Frame operator in Hilbert space, Journal of Mathematical education ,Volume XLV,No.3 September 2011.
[8]. Helmut Bolcskei ,Franz Hlawatsuh and Hans G.Feicgitinger ,” Frame –Theoretic analysis and design of oversampled filter banks “.In proc ,IEEE ISCAS 1996 .Atlanta ,GA,Vol 2 ,PP,409 -412 ,may 1996.
[9] . Helmut Bolcskei ,Franz Hlawatsuh and Hans G.Feicgitinger “Frame –Theoretic analysis of oversampled filter banks”,IEEE Trasactions and signal processing ,Vol 4,No 12,1998.
[10] . G.Upender Reddy and N. Gopal Reddy „A Note on Frame Potential in Finite Dimensional Hilbert Space‟, Journal of Indian Academy of Mathematics, Volume. 32, No.1, 2010.
[11]. G.Upender Reddy and N. Gopal Reddy ,A brief study of multi frames and super frames in Hilbert spaces”Journal of ultra scentist of physical sciences ,vol.20 (2)m,Aug 2008,501-510.
[12]. Zoran Cvetkoric and martin Votter li,”Over Sampled Filter banks ,IEEE Transaction on signal processing ,Vol 46 ,No 5,May 1998.
[13] I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory, vol. 36, pp. 961–1005, Sep. 1990.
[14] Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, 1992.
[15] C. E. Heil and D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev., vol. 31, pp. 628–666, Dec. 1989.
[16] R. M. Young, An Introduction to Nonharmonic Fourier Series. New York: Academic Press, 1980.
[17] D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613–627, Mar. 1995.
[18] D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika, vol. 81, no. 3, pp. 425–455, Aug. 1994.
[19] M. Rupf and J. L. Massey, “Optimum sequence multisets for synchronous code-division multipleaccess channels,” IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1261–1266, Jul. 1994.
[20] M. Sandell, “Design and analysis of estimators for multicarrier modulation and ultrasonic imaging,” Ph.D. dissertation, Lule˚a Univ. Technol., Lule˚a, Sweden, Sep. 1996.
[21] R. W. Heath, Jr. and A. J. Paulraj, “Linear dispersion codes for MIMO systems based on frame theory,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 2429–2441, Oct. 2002.
[22] M. Rudelson and R. Vershynin, “Geometric approach to error correcting codes and reconstruction.

Citation :

P.Kalyani, "Frames and its applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 3, pp. 188-194, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P527