An Explicit Algorithm for the Construction of 3-Band Wavelet Frames Based on FMRA
Applied and Computational Mathematics
Volume 7, Issue 3, June 2018, Pages: 155-160
Received: Aug. 9, 2018; Published: Aug. 13, 2018
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Authors
Zhaofeng Li, College of Science, China Three Gorges University, Yichang, China; Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China
Yuanyuan Zhang, College of Science, China Three Gorges University, Yichang, China; Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China
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Abstract
In 1974, an French engineer, J. Morlet raised the concept of wavelet transform and established the inversion formula through the experience of physical intuition and signal processing and in 1986, the famous mathematician, Y. Meyer, created a real small wave base. From then on, Wavelet transform is a rapidly developing new subfield in mathematics and is used in more and more fields, such as signal analysis, image processing, quantum mechanics and theoretical physics etc. Multiresolution analysis is a systematic method for constructing orthonormal wavelet bases and most of the current dilation is M=2 With the development of wavelet transform, M>2 -band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing. However, there are relatively less results for the case of M>2. Based on this fact and inspired by other similar papers, this paper studies the 3-band wavelets and wavelet frames associated with a given refinable function based on frame multiresolution analysis. In this paper, firstly, a sufficient and necessary condition which the refinable function should satisfy for the existence of wavelet frames is showed. Further, an explicit algorithm to construct this frames is worked out and finally, several designed examples are constructed to illustrate this algorithm.
Keywords
Frame Multiresolution Analysis, Polyphase Decomposition, Unitary Matrix Extension
To cite this article
Zhaofeng Li, Yuanyuan Zhang, An Explicit Algorithm for the Construction of 3-Band Wavelet Frames Based on FMRA, Applied and Computational Mathematics. Vol. 7, No. 3, 2018, pp. 155-160. doi: 10.11648/j.acm.20180703.21
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