关于小波包的消失矩、小波的卷积和互相关的一些结果

Q2 Mathematics Arab Journal of Mathematical Sciences Pub Date : 2019-07-01 DOI:10.1016/j.ajmsc.2018.07.001

A.M. Jarrah , Nikhil Khanna

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引用次数: 10

摘要

导出了小波包矩的计算公式，得到了小波包矩消失的充分条件。并证明了小波希尔伯特变换的卷积定理和互相关定理。最后，利用L2(R)的MRA，给出了二维尺度函数、小波及其卷积的消失矩的一些结果。

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Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets

A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of $L^{2} (R)$ , some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.

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