IJSTR

International Journal of Scientific & Technology Research

IJSTR@Facebook IJSTR@Twitter IJSTR@Linkedin
Home About Us Scope Editorial Board Blog/Latest News Contact Us
CALL FOR PAPERS
AUTHORS
DOWNLOADS
CONTACT
QR CODE
IJSTR-QR Code

IJSTR >> Volume 3- Issue 9, September 2014 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Discrete Wavelet Transforms Of Haar’s Wavelet

[Full Text]

 

AUTHOR(S)

Bahram Dastourian, Elias Dastourian, Shahram Dastourian, Omid Mahnaie

 

KEYWORDS

Keyword: approximation; detail; filter; Haar’s wavelet; MATLAB programming, multiresolution analysis.

 

ABSTRACT

Abstract: Wavelet play an important role not only in the theoretic but also in many kinds of applications, and have been widely applied in signal processing, sampling, coding and communications, filter bank theory, system modeling, and so on. This paper focus on the Haar’s wavelet. We discuss on some command of Haar’s wavelet with its signal by MATLAB programming. The base of this study followed from multiresolution analysis.

 

REFERENCES

G. Beylkin, R. Coifman and V. Rokhlin, “Fast wavelet tmnsforms and numerical algorithms,” Comm. Pure Appl. Math. , vol. 44, pp. 141-183, 1991.

I. Daubechies, “Ten Lectures on Wavelets.” CBMS-NFS regional series in applied mathematics. SIAM, 1992.

A. Grossmann and J. Morlet, “Decomposition of Hardy junctions into square integrable wavelets of constant shape,” SIAM J. Math. Anal., vol. 15, pp. 723-736, 1984.

R. Kronland-Martinet , J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet tronsforms,” Internat. J. Pattern Recognition and Artificial Intelligence, vol. 1, pp. 273-301, 1987.

Z. Liu, X. Mu and G. Wu, “MRA Pparseval frame multiwavelets in L^2 (R^d),” Bulletin of the Iranian Mathematical Society Vol. 38, No. 4, pp 1021-1045, 2012.

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. PAMI, vol. 11, pp. 674-693, 1989.

S. Mallat, “A Wavelet Tour of Signal Processing.” 2nd ed. Academic Press, 1999.

S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust . Signal Speech Process., vol. 37, pp. 2091-2110, 1989.

S. Mallat, “Multiresolution approximation and wavelets,” Trans. Amer. Math. Soc., vol. 315, pp. 69-88, 1989.

J. Morlet, “Sampling theory and wave propagation,” in NATO ASI Series, Vol. 1, Issues in Acoustic signal/Image processing and recognition, C. H. Chen, ed., Springer-Verlag, Berlin, pp. 233-261, 1983.

J. Morlet, G. Arens, I . Fourgeau, and D. Giard, “Wave propagation and sampling theory,” Geophysics, vol. 47, pp. 203-236, 1982.

J.A. Packer and M.A. Rieffel, “Projective multi-resolution analyses for L^2 (R^d),” J. Fourier Anal. Appl. 10, 439–464, 2004.

W. Rudin, “Real and Complex Analysis,” Mcgraw-Hill, New York, 1987.

P. Wojtaszczyk, ”A Mathematical Introduction to Wavelets,” London Mathematical Society Student Texts 37. Cambridge University Press, 1997.

P.J. Wood, “Wavelets and C*-algebras,” PhD thesis, Flinders University of South Australia, 2003.