TY - JOUR
T1 - Non-Orthogonal $p$-Wavelet Packets on the Half-Line
AU - F. A. Shah
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 - <p style="text-align: justify;">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 $p &gt; 2$.</p>