Asymptotic Expansion of Wavelet Transform

Ashish Pathak¹, Prabhat Yadav², Madan Mohan Dixit^2*

¹Department of Mathematics & Statistics, Dr. Harisingh Gour Central University, Sagar, India.
²Department of Mathematics, North Eastern Regional Institute of Science and Technology (NERIST), Nirjuli, India.

DOI: 10.4236/apm.2015.51002                

Abstract

In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican Hat wavelet transform are obtained as special cases.

Keywords

Asymptotic Expansion, Wavelet Transform, Mellin Convolution, Integral Transform

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Pathak, R.S. (2009) The Wavelet Transform. Atlantis Press/World Scientific, Amsterdam.
[2]	López, J.L. (2007) Asymptotic Expansions of Mellin Convolutions by Means of Analytic Continuation. Journal of Computational and Applied Mathematics, 200, 628-636. http://dx.doi.org/10.1016/j.cam.2006.01.019
[3]	Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansion of Wavelet Transform for Small Value a. In: Pathak, R.S. and Chui, C.K., Eds., The Wavelet Transform, World Scientific, Amsterdam, 164-169.
[4]	Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansion of Wavelet Transform with Error Term. In: Pathak, R.S. and Chui, C.K., Eds., The Wavelet Transform, World Scientific, Amsterdam, 154-164.
[5]	Pathak, R.S. and Pathak, A. (2009) Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b. The International Journal of Mathematics and Mathematical Sciences, 2009, Article ID: 270492, 13 p.
[6]	Erde’lyi, A., Magnus, W., Oberhettinger F. and Tricomi, F.G. (1954) Tables of Integral Transform. McGraw-Hill, New York.