Characteristic Vectors in p/q-Channel Orthonormal Wavelet
Applied and Computational Mathematics
Volume 8, Issue 3, June 2019, Pages: 65-69
Received: Jul. 8, 2019; Published: Aug. 27, 2019
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Zhaofeng Li, College of Science, China Three Gorges University, Yichang, China; Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China
Hongying Xiao, College of Science, China Three Gorges University, Yichang, China; Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China
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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.
Orthonormal Wavelet Base, Rational Dilation Factor, Perfect Reconstruction Condition
To cite this article
Zhaofeng Li, Hongying Xiao, Characteristic Vectors in p/q-Channel Orthonormal Wavelet, Applied and Computational Mathematics. Vol. 8, No. 3, 2019, pp. 65-69. doi: 10.11648/j.acm.20190803.13
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