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- Title
Dual wavelet frame packets with non-square iterative matrices.
- Authors
Zhang, Zhihua
- Abstract
Traditional wavelet frame packets are based on square iterative matrices and frame scaling functions. Since the Fourier transform of frame scaling functions are discontinuous, the resulting wavelet frame packets do not possess time-frequency localization. In this study, we will develop the new construction of wavelet frame packets by using non-square iterative matrices: one is to construct wavelet frame packets directly from known non-GMRA wavelet frames to obtain finer time-frequency structure, the other is based on GMRA wavelet frames constructed from smooth generalization scaling functions, the corresponding quasi-projection formula and fast algorithm are also given.
- Subjects
DISCONTINUOUS functions; MATRICES (Mathematics); FOURIER transforms; WAVELET transforms; NONSMOOTH optimization
- Publication
International Journal of Wavelets, Multiresolution & Information Processing, 2024, Vol 22, Issue 2, p1
- ISSN
0219-6913
- Publication type
Article
- DOI
10.1142/S0219691323500418