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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 L2(R), some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.
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Jarrah et al. (2018) studied this question.
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