Wavelet analysis is a newly rapidly developing subject in the late twentieth century. As a time-frequency analysis tool, wavelet analysis has many advantages over other time-frequency tools, such as in signal processing, image processing, speech processing, pattern recognition, quantum physics and other fields. Multiresolution analysis (MRA for short) is an important method for studying wavelet orthonormal wavelet bases with rational dilation 2. However, p/q-band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing and attracted more and more interest in recent years. But there are relatively less results for the case of p/q-band. This paper studies the orthonormal wavelet bases with rational dilation factor p/q based on multiresolution analysis by a polyphase decomposition technique. First, we gave the concept of Multiresolution analysis with rational dilation p/q and deduced an identity of the masks matrix. Also, a perfect reconstruction condition in terms of masks was presented. Further, we gave the refinement and wavelet matrices respectively and derived the characteristic roots and the corresponding orthonormal characteristic vectors of the wavelet matrix, and then a method with characteristic vectors was reduced to achieve the orthonormal wavelet bases with rational dilation factor p/q. In the end, an example is offered to verify this theory.
| Published in | Applied and Computational Mathematics (Volume 8, Issue 3) |
| DOI | 10.11648/j.acm.20190803.13 |
| Page(s) | 65-69 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Orthonormal Wavelet Base, Rational Dilation Factor, Perfect Reconstruction Condition
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APA Style
Zhaofeng Li, Hongying Xiao. (2019). Characteristic Vectors in p/q-Channel Orthonormal Wavelet. Applied and Computational Mathematics, 8(3), 65-69. https://doi.org/10.11648/j.acm.20190803.13
ACS Style
Zhaofeng Li; Hongying Xiao. Characteristic Vectors in p/q-Channel Orthonormal Wavelet. Appl. Comput. Math. 2019, 8(3), 65-69. doi: 10.11648/j.acm.20190803.13
AMA Style
Zhaofeng Li, Hongying Xiao. Characteristic Vectors in p/q-Channel Orthonormal Wavelet. Appl Comput Math. 2019;8(3):65-69. doi: 10.11648/j.acm.20190803.13
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Download@article{10.11648/j.acm.20190803.13,
author = {Zhaofeng Li and Hongying Xiao},
title = {Characteristic Vectors in p/q-Channel Orthonormal Wavelet},
journal = {Applied and Computational Mathematics},
volume = {8},
number = {3},
pages = {65-69},
doi = {10.11648/j.acm.20190803.13},
url = {https://doi.org/10.11648/j.acm.20190803.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20190803.13},
abstract = {Wavelet analysis is a newly rapidly developing subject in the late twentieth century. As a time-frequency analysis tool, wavelet analysis has many advantages over other time-frequency tools, such as in signal processing, image processing, speech processing, pattern recognition, quantum physics and other fields. Multiresolution analysis (MRA for short) is an important method for studying wavelet orthonormal wavelet bases with rational dilation 2. However, p/q-band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing and attracted more and more interest in recent years. But there are relatively less results for the case of p/q-band. This paper studies the orthonormal wavelet bases with rational dilation factor p/q based on multiresolution analysis by a polyphase decomposition technique. First, we gave the concept of Multiresolution analysis with rational dilation p/q and deduced an identity of the masks matrix. Also, a perfect reconstruction condition in terms of masks was presented. Further, we gave the refinement and wavelet matrices respectively and derived the characteristic roots and the corresponding orthonormal characteristic vectors of the wavelet matrix, and then a method with characteristic vectors was reduced to achieve the orthonormal wavelet bases with rational dilation factor p/q. In the end, an example is offered to verify this theory.},
year = {2019}
}
TY - JOUR T1 - Characteristic Vectors in p/q-Channel Orthonormal Wavelet AU - Zhaofeng Li AU - Hongying Xiao Y1 - 2019/08/27 PY - 2019 N1 - https://doi.org/10.11648/j.acm.20190803.13 DO - 10.11648/j.acm.20190803.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 65 EP - 69 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20190803.13 AB - Wavelet analysis is a newly rapidly developing subject in the late twentieth century. As a time-frequency analysis tool, wavelet analysis has many advantages over other time-frequency tools, such as in signal processing, image processing, speech processing, pattern recognition, quantum physics and other fields. Multiresolution analysis (MRA for short) is an important method for studying wavelet orthonormal wavelet bases with rational dilation 2. However, p/q-band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing and attracted more and more interest in recent years. But there are relatively less results for the case of p/q-band. This paper studies the orthonormal wavelet bases with rational dilation factor p/q based on multiresolution analysis by a polyphase decomposition technique. First, we gave the concept of Multiresolution analysis with rational dilation p/q and deduced an identity of the masks matrix. Also, a perfect reconstruction condition in terms of masks was presented. Further, we gave the refinement and wavelet matrices respectively and derived the characteristic roots and the corresponding orthonormal characteristic vectors of the wavelet matrix, and then a method with characteristic vectors was reduced to achieve the orthonormal wavelet bases with rational dilation factor p/q. In the end, an example is offered to verify this theory. VL - 8 IS - 3 ER -
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