Nelson, JDB;
(2015)
Enhanced B-Wavelets via Mixed, Composite Packets.
IEEE Transactions on Signal Processing
, 63
(12)
pp. 3191-3203.
10.1109/TSP.2015.2419185.
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Abstract
A modified B-wavelet construction with enhanced filter characteristics is considered. The design comprises a superposition of tessellated, integer dilated, ‘sister’ wavelet functions. We here propose a cascaded filter-bank realisation of this wavelet family together with some notable extensions. We prove that modifications of low-order members exist in the multiresolution subspace spanned by the half-translates of the original wavelets and hence that the resulting modified wavelet coefficients can be computed as convolutions of the undecimated original wavelet coefficients. Finite impulse response filters are thus designed and incorporated into a B-wavelet packet architecture such that the mainlobe-to-sidelobe ratio of the resulting wavelet filter characteristic is improved. This is achieved by designing the filters so that zeros are introduced near to the maxima of the harmonics. It is shown that the numbers of zeros can be balanced with the length of the corresponding filters by controlling the ‘modification order’. Several constructions are presented. We prove that two such constructions satisfy the perfect reconstruction property for all orders. The resulting modified wavelets preserve many of the properties of the original B-wavelets such as differentiability, number of vanishing moments, symmetry, anti-symmetry, finite support, and the existence of a closed form expression.
| Type: | Article |
|---|---|
| Title: | Enhanced B-Wavelets via Mixed, Composite Packets |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TSP.2015.2419185 |
| Publisher version: | http://dx.doi.org/10.1109/TSP.2015.2419185 |
| Language: | English |
| Additional information: | © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | B-wavelets, filter characteristic, wavelet packets |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1477576 |
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