Asymptotic Expansion of Wavelet Transform

DOI: 10.4236/apm.2015.51002   PDF   HTML   XML   3,310 Downloads   3,797 Views   Citations

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.

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Pathak, A. , Yadav, P. and Dixit, M. (2015) Asymptotic Expansion of Wavelet Transform. Advances in Pure Mathematics, 5, 21-26. doi: 10.4236/apm.2015.51002.

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.

  
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