Anal. Theory Appl., 28 (2012), pp. 385-396.
Published online: 2012-12
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In this paper, the notion of $p$-wavelet packets on the positive half-line $\mathbb{R}^+$ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the low-pass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor $p > 2$.
}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.04.007}, url = {http://global-sci.org/intro/article_detail/ata/4572.html} }In this paper, the notion of $p$-wavelet packets on the positive half-line $\mathbb{R}^+$ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the low-pass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor $p > 2$.