Parameter analysis of chirplet transform and high-resolution time-frequency representation via chirplets combination

The standard chirplet transform (CT) with the chirp-modulated Gaussian window provides a valuable tool for analyzing linear chirp signals. The parameters present in the window determine the performance of the CT and play a vital role in high-resolution time-frequency (TF) analysis. In this paper, we give the window shape analysis of the CT and compare it with the extension that employs a rotating Gaussian window by the fractional Fourier transform. The given parameters analysis provides theoretical guidance for developing high-resolution CT. We then propose a multi-resolution chirplet transform (MrCT) by combining multiple CTs with different parameter combinations. These are combined geometrically to obtain an improved TF resolution by overcoming the limitations of any single representation of the CT. We further develop a TF post-processing approach to enhance the readability of the MrCT by deriving a combined instantaneous frequency equation, which can characterize the mixture of the chirp-like and impulse-like signals. Numerical experiments on simulated and real signals verify the effectiveness of the proposed approaches.