Synchrosqueezed Fractional Wavelet Transform: A New High-Resolution Time-Frequency Representation

The synchrosqueezed wavelet transform (SSWT) has been proven to be a powerful time-frequency analysis tool. However, this transform is unable to deal with signals with fast varying instantaneous frequencies. The objective of this paper is to overcome this deficiency using the fractional wavelet transform (FRWT), which is a generalization of the conventional wavelet transform. We first propose a synchrosqueezed FRWT (SSFRWT), which shares many properties of its SSWT counterpart while offering attractive new features. Then, we present a theoretical analysis of the SSFRWT, including the derivation of its basic properties. Moreover, we show that the discrete form of the SSFRWT admits efficient numerical implementation akin to that of the SSWT. Finally, the theoretical derivations are validated via simulations.