Enhanced B-Wavelets via Mixed, Composite Packets


A changed $B$-wavelet construction with enhanced filter characteristics is taken into account. The look comprises a superposition of tessellated, integer dilated, “sister” wavelet functions. We tend to here propose a cascaded filter-bank realization of this wavelet family along with some notable extensions. We have a tendency to prove that modifications of low-order members exist in the multiresolution subspace spanned by the 0.5-translates of the original wavelets and, hence, that the ensuing modified wavelet coefficients can be computed as convolutions of the undecimated original wavelet coefficients. Finite impulse response filters are so designed and incorporated into a $B$-wavelet packet design such that the mainlobe-to-sidelobe ratio of the resulting wavelet filter characteristic is improved. This is often achieved by coming up with 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 2 such constructions satisfy the perfect reconstruction property for all orders. The resulting changed wavelets preserve several of the properties of the initial $B$-wavelets, such as differentiability, range of vanishing moments, symmetry, anti-symmetry, finite support, and therefore the existence of a closed kind expression.

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