Decay properties of the discrete wavelet transform in n dimensions with independent dilation parameters
Abstract The purpose of this paper is to study the decay properties of the discrete wavelet transform with n independent dilation parameters for functions f in L 2 ( R n ) $L^{2}({ {\mathbb {R}}}^{n})$ and a relationship with its continuity. The method we used to study the discrete wavelet transform...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-0961-z |
| Summary: | Abstract The purpose of this paper is to study the decay properties of the discrete wavelet transform with n independent dilation parameters for functions f in L 2 ( R n ) $L^{2}({ {\mathbb {R}}}^{n})$ and a relationship with its continuity. The method we used to study the discrete wavelet transform of f with respect to a radially symmetric admissible function was through the fact of considering two parameters in Z n ${ {\mathbb {Z}}}^{n}$ . We conclude that the continuity of f at x = 0 $x=0$ is determined by the existence of the limit of the discrete wavelet transform when each one of the independent dilation parameters tends to zero. |
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| ISSN: | 1029-242X |