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<https://discovery.ucl.ac.uk/id/eprint/1477576> <http://purl.org/dc/terms/title> "Enhanced B-Wavelets via Mixed, Composite Packets"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/1477576> <http://purl.org/ontology/bibo/abstract> "A modified B-wavelet construction with enhanced\r\nfilter characteristics is considered. The design comprises a superposition\r\nof tessellated, integer dilated, ‘sister’ wavelet functions.\r\nWe here propose a cascaded filter-bank realisation of this wavelet\r\nfamily together with some notable extensions. We prove that\r\nmodifications of low-order members exist in the multiresolution\r\nsubspace spanned by the half-translates of the original wavelets\r\nand hence that the resulting modified wavelet coefficients can be\r\ncomputed as convolutions of the undecimated original wavelet\r\ncoefficients. Finite impulse response filters are thus designed and\r\nincorporated into a B-wavelet packet architecture such that the\r\nmainlobe-to-sidelobe ratio of the resulting wavelet filter characteristic\r\nis improved. This is achieved by designing the filters so\r\nthat zeros are introduced near to the maxima of the harmonics.\r\nIt is shown that the numbers of zeros can be balanced with the\r\nlength of the corresponding filters by controlling the ‘modification\r\norder’. Several constructions are presented. We prove that two\r\nsuch constructions satisfy the perfect reconstruction property for\r\nall orders. The resulting modified wavelets preserve many of the\r\nproperties of the original B-wavelets such as differentiability,\r\nnumber of vanishing moments, symmetry, anti-symmetry, finite\r\nsupport, and the existence of a closed form expression."^^<http://www.w3.org/2001/XMLSchema#string> .
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