A novel fractional wavelet transform and its applications

The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing. However, the signal analysis capability of the former is limited in the time-frequency plane. Although the latter has overcome such limitation and can provide signal representations in the fractional domain, it fails in obtaining local structures of the signal. In this paper, a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT. The proposed transform not only inherits the advantages of multiresolution analysis of the WT, but also has the capability of signal representations in the fractional domain which is similar to the FRFT. Compared with the existing FRWT, the novel FRWT can offer signal representations in the time-fractional-frequency plane. Besides, it has explicit physical interpretation, low computational complexity and usefulness for practical applications. The validity of the theoretical derivations is demonstrated via simulations.

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