Volume 28, Issue 4
Non-Orthogonal $p$-Wavelet Packets on the Half-Line

Anal. Theory Appl., 28 (2012), pp. 385-396.

Published online: 2012-12

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• Abstract

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 $p > 2$.

• Keywords

$p$-Multiresolution analysis, $p$-wavelet packets, Riesz basis, Walsh function, Walsh-Fourier transform.

42C40, 42C10, 42C15

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@Article{ATA-28-385, author = {}, title = {Non-Orthogonal $p$-Wavelet Packets on the Half-Line}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {4}, pages = {385--396}, abstract = {

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} }
TY - JOUR T1 - Non-Orthogonal $p$-Wavelet Packets on the Half-Line JO - Analysis in Theory and Applications VL - 4 SP - 385 EP - 396 PY - 2012 DA - 2012/12 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.04.007 UR - https://global-sci.org/intro/article_detail/ata/4572.html KW - $p$-Multiresolution analysis, $p$-wavelet packets, Riesz basis, Walsh function, Walsh-Fourier transform. AB -

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 $p > 2$.

F. A. Shah. (1970). Non-Orthogonal $p$-Wavelet Packets on the Half-Line. Analysis in Theory and Applications. 28 (4). 385-396. doi:10.3969/j.issn.1672-4070.2012.04.007
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