Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b
Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wave...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/270492 |
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| _version_ | 1832566838349791232 |
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| author | R. S. Pathak Ashish Pathak |
| author_facet | R. S. Pathak Ashish Pathak |
| author_sort | R. S. Pathak |
| collection | DOAJ |
| description | Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values of b when asymptotic expansions of the function and the wavelet near origin are given. |
| format | Article |
| id | doaj-art-8cd6a978a863406c8057af04a931f35b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8cd6a978a863406c8057af04a931f35b2025-02-03T01:03:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/270492270492Asymptotic Expansions of the Wavelet Transform for Large and Small Values of bR. S. Pathak0Ashish Pathak1Department of Mathematics, Banaras Hindu University, Varanasi 221 005, IndiaDepartment of Mathematics, Banaras Hindu University, Varanasi 221 005, IndiaAsymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values of b when asymptotic expansions of the function and the wavelet near origin are given.http://dx.doi.org/10.1155/2009/270492 |
| spellingShingle | R. S. Pathak Ashish Pathak Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b |
| title_full | Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b |
| title_fullStr | Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b |
| title_full_unstemmed | Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b |
| title_short | Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b |
| title_sort | asymptotic expansions of the wavelet transform for large and small values of b |
| url | http://dx.doi.org/10.1155/2009/270492 |
| work_keys_str_mv | AT rspathak asymptoticexpansionsofthewavelettransformforlargeandsmallvaluesofb AT ashishpathak asymptoticexpansionsofthewavelettransformforlargeandsmallvaluesofb |