In 1974, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing. In 1986, Y. Meryer created a real small wave base, and the wavelet analysis began to flourish after a multi scale analysis of the same method of constructing the small wave base with S. Mallat. In order to analyze and deal with non-stationary signals, a series of new signal analysis theories are proposed.: Short Time Fourier Transform, time-frequency analysis, wavelet transform, and fractional Fourier transform and so on. In this paper, an explicit algorithm is given to construct the minimum-energy frames based on frame multiresolution analysis via characteristic vectors of the mask matrix. In section 2, we show the structure of minimum-energy wavelet frames in terms of their masks (Lemma 1) and discuss that we should eliminate the correlation of the rows of the mask matrix by the polyphase decomposition technique. Based on FMRA, an explicit algorithm is given to construct this frames. By this method, all the minimum-energy wavelet frames can be obtained. As an application, several examples are showed to explain this method in section 3. This method can also be applied in other fields of wavelet analysis.
| Published in | Applied and Computational Mathematics (Volume 7, Issue 3) |
| DOI | 10.11648/j.acm.20180703.22 |
| Page(s) | 161-166 |
| 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. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Frame Multiresolution Analysis, Polyphase Decomposition, Minimum-Energy Frames
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APA Style
Yuanyuan Zhang, Zhaofeng Li. (2018). The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA. Applied and Computational Mathematics, 7(3), 161-166. https://doi.org/10.11648/j.acm.20180703.22
ACS Style
Yuanyuan Zhang; Zhaofeng Li. The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA. Appl. Comput. Math. 2018, 7(3), 161-166. doi: 10.11648/j.acm.20180703.22
AMA Style
Yuanyuan Zhang, Zhaofeng Li. The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA. Appl Comput Math. 2018;7(3):161-166. doi: 10.11648/j.acm.20180703.22
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Download@article{10.11648/j.acm.20180703.22,
author = {Yuanyuan Zhang and Zhaofeng Li},
title = {The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA},
journal = {Applied and Computational Mathematics},
volume = {7},
number = {3},
pages = {161-166},
doi = {10.11648/j.acm.20180703.22},
url = {https://doi.org/10.11648/j.acm.20180703.22},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20180703.22},
abstract = {In 1974, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing. In 1986, Y. Meryer created a real small wave base, and the wavelet analysis began to flourish after a multi scale analysis of the same method of constructing the small wave base with S. Mallat. In order to analyze and deal with non-stationary signals, a series of new signal analysis theories are proposed.: Short Time Fourier Transform, time-frequency analysis, wavelet transform, and fractional Fourier transform and so on. In this paper, an explicit algorithm is given to construct the minimum-energy frames based on frame multiresolution analysis via characteristic vectors of the mask matrix. In section 2, we show the structure of minimum-energy wavelet frames in terms of their masks (Lemma 1) and discuss that we should eliminate the correlation of the rows of the mask matrix by the polyphase decomposition technique. Based on FMRA, an explicit algorithm is given to construct this frames. By this method, all the minimum-energy wavelet frames can be obtained. As an application, several examples are showed to explain this method in section 3. This method can also be applied in other fields of wavelet analysis.},
year = {2018}
}
TY - JOUR T1 - The Application of Eigenvectors for the Construction of Minimum-Energy Wavelet Frames Based on FMRA AU - Yuanyuan Zhang AU - Zhaofeng Li Y1 - 2018/08/13 PY - 2018 N1 - https://doi.org/10.11648/j.acm.20180703.22 DO - 10.11648/j.acm.20180703.22 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 161 EP - 166 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20180703.22 AB - In 1974, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing. In 1986, Y. Meryer created a real small wave base, and the wavelet analysis began to flourish after a multi scale analysis of the same method of constructing the small wave base with S. Mallat. In order to analyze and deal with non-stationary signals, a series of new signal analysis theories are proposed.: Short Time Fourier Transform, time-frequency analysis, wavelet transform, and fractional Fourier transform and so on. In this paper, an explicit algorithm is given to construct the minimum-energy frames based on frame multiresolution analysis via characteristic vectors of the mask matrix. In section 2, we show the structure of minimum-energy wavelet frames in terms of their masks (Lemma 1) and discuss that we should eliminate the correlation of the rows of the mask matrix by the polyphase decomposition technique. Based on FMRA, an explicit algorithm is given to construct this frames. By this method, all the minimum-energy wavelet frames can be obtained. As an application, several examples are showed to explain this method in section 3. This method can also be applied in other fields of wavelet analysis. VL - 7 IS - 3 ER -
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