Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform

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.