Novel fractional wavelet transform: Principles, MRA and application

Wavelet transform (WT) can be viewed as a differently scaled bandpass filter in the frequency domain, so WT is not the optimal time-frequency representation method for those signals which are not band-limited in the frequency domain. A novel fractional wavelet transform (FRWT) is proposed to break the limitation of WT, it displays the time and fractional frequency information jointly in the time-fractional-frequency (TFF) plane. The definition and basic properties of FRWT are studied firstly. Furthermore, the multiresolution analysis and orthogonal fractional wavelets associated with FRWT are explored. Finally, the application of FRWT in the LFM signal TFF analysis is discussed and verified by simulations. The experimental results show that the energy concentration of LFM signal representation by proposed FRWT is better than that of some existing methods. The better energy concentration makes it can be further applied to the denoising, detection, parameter estimation and separation of LFM signal.