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https://scholarbank.nus.edu.sg/handle/10635/13470
DC Field | Value | |
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dc.title | Wavelet frames of dilation factor M | |
dc.contributor.author | LIM ZHI YUAN | |
dc.date.accessioned | 2010-04-08T10:33:17Z | |
dc.date.available | 2010-04-08T10:33:17Z | |
dc.date.issued | 2003-10-13 | |
dc.identifier.citation | LIM ZHI YUAN (2003-10-13). Wavelet frames of dilation factor M. ScholarBank@NUS Repository. | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/13470 | |
dc.description.abstract | Based on a frame multiresolution analysis (FMRA) of dilation factor M, we establish quantitative criteria in the frequency domain for the construction of a tight wavelet frame generated by a minimum number of M-1 mother wavelets. We utilize the concept of fibres of closed shift-invariant subspaces in the frequency domain to show the existence of tight frames in the wavelet spaces and also to provide a method of constructing the mother wavelets. It is shown that M mother wavelets would always be sufficient to generate a tight wavelet frame. We also provide an alternative way of constructing the mother wavelets for the elementary case of M=2 based on the analysis of the Gramian. Finally, we extend our construction techniques to creating a sequence space FMRA which is related to periodic wavelet frames and show that the fibres of multiresolution subspaces in L<sup>2</sup>(R) also form a FMRA in l<sup>2</sup>(Z) and that the wavelets constructed for L<sup>2</sup>(R) can be used to construct wavelets for l<sup>2</sup>(Z). | |
dc.language.iso | en | |
dc.subject | frame multiresolution analysis, fibres, wavelet frames | |
dc.type | Thesis | |
dc.contributor.department | MATHEMATICS | |
dc.contributor.supervisor | GOH SAY SONG | |
dc.description.degree | Master's | |
dc.description.degreeconferred | MASTER OF SCIENCE | |
dc.identifier.isiut | NOT_IN_WOS | |
Appears in Collections: | Master's Theses (Open) |
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