  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.
