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.

小波变换（WT）在频域中可以看作是不同比例的带通滤波器，因此对于那些在频域中不受频带限制的信号，WT并不是最佳的时频表示方法。提出了一种新颖的分数小波变换（FRWT），打破了WT的局限性，它在时分频率（TFF）平面上共同显示时间和分数频率信息。首先研究了FRWT的定义和基本性质。此外，探索了与FRWT相关的多分辨率分析和正交分数小波。最后，讨论了FRWT在LFM信号TFF分析中的应用，并通过仿真进行了验证。实验结果表明，所提出的FRWT代表LFM信号的能量集中度优于某些现有方法。更好的能量集中度使其可以进一步应用于LFM信号的去噪，检测，参数估计和分离。