The Journal of the Indian Mathematical Society

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An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter


Affiliations
1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India
2 Department of Mathematics, NERIST, Nirjuli - 791109, India
     

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In this paper, we derive asymptotic expansion of the wavelet transform for small values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Morlet wavelet, Mexican Hat wavelet and Haar wavelet transform are obtained as a special cases.


Keywords

Asymptotic expansion, Wavelet transform, Fourier transform, Mellin transform.
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  • An Asymptotic Expansion of Continuous Wavelet Transform for Small Dilation Parameter

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Authors

Ashish Pathak
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India
Prabhat Yadav
Department of Mathematics, NERIST, Nirjuli - 791109, India
M. M. Dixit
Department of Mathematics, NERIST, Nirjuli - 791109, India

Abstract


In this paper, we derive asymptotic expansion of the wavelet transform for small values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Morlet wavelet, Mexican Hat wavelet and Haar wavelet transform are obtained as a special cases.


Keywords


Asymptotic expansion, Wavelet transform, Fourier transform, Mellin transform.

References





DOI: https://doi.org/10.18311/jims%2F2022%2F29311