Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform
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The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform, has been shown to be potentially useful for signal processing. Many fundamental results of this transform are already known, but the theory of multiresolution analysis and orthogonal wavelets is still missing. In this paper, we first develop multiresolution analysis associated with the FRWT and then derive a construction of orthogonal wavelets for the FRWT. Several fractional wavelets are also presented. Moreover, some applications of the derived results are discussed.
KeywordsTime-frequency analysis Multiresolution analysis Orthogonal wavelets Fractional wavelet transform
This work was completed in parts while Shi J. was visiting the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA. The work was supported in part by the National Basic Research Program of China (Grant No. 2013CB329003), and the National Natural Science Foundation of China (Grant No. 61171110).
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