Enhanced B-Wavelets via Mixed, Composite Packets
Enhanced B-Wavelets via Mixed, Composite Packets
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DOI：
10.1109/tsp.2015.2419185
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发表时间：
2015-06
影响因子：
5.4
通讯作者：
J. Nelson
中科院分区：
文献类型：
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作者：
J. Nelson
提出了一种改进的b -小波结构，增强了滤波特性。该设计包括镶嵌、整数展开、“姐妹”小波函数的叠加。本文提出了该小波族的级联滤波器组实现，并进行了一些值得注意的扩展。我们证明了在原始小波的半平移所跨越的多分辨率子空间中存在低阶元的修改，因此，由此得到的修改小波系数可以计算为未消去的原始小波系数的卷积。因此，有限脉冲响应滤波器被设计并集成到b小波包结构中，从而提高了小波滤波器特性的主瓣副瓣比。这是通过设计滤波器来实现的，以便在谐波最大值附近引入零。结果表明，通过控制“修改顺序”，零的数量可以与相应滤波器的长度相平衡。提出了几种结构。我们证明了这两个结构对所有阶都满足完全重构性质。所得到的修正小波保留了原b小波的许多性质，如可微性、消失矩数、对称性、反对称性、有限支持和闭形式表达式的存在性。
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 realization 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.