High-resolution chirplet transform: from parameters analysis to parameters combination

The standard chirplet transform (CT) with a 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. By deriving a combined instantaneous frequency equation, we further develop a high-concentration TF post-processing approach to improve the readability of the MrCT. Numerical experiments on simulated and real signals verify the effectiveness of the proposed methods.