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In nature and engineering world, the acquired signals are usually affected bymultiple complicated factors and appear as multicomponent nonstationary modes.In such and many other situations, it is necessary to separate these signalsinto a finite number of monocomponents to represent the intrinsic modes andunderlying dynamics implicated in the source signals. In this paper, weconsider the mode retrieval of a multicomponent signal which has crossinginstantaneous frequencies (IFs), meaning that some of the components of thesignal overlap in the time-frequency domain. We use the chirplet transform (CT)to represent a multicomponent signal in the three-dimensional space of time,frequency and chirp rate and introduce a CT-based signal separation scheme(CT3S) to retrieve modes. In addition, we analyze the error bounds for IFestimation and component recovery with this scheme. We also propose amatched-filter along certain specific time-frequency lines with respect to thechirp rate to make nonstationary signals be further separated and moreconcentrated in the three-dimensional space of CT. Furthermore, based on theapproximation of source signals with linear chirps at any local time, wepropose an innovative signal reconstruction algorithm, called the group  filter-matched CT3S (GFCT3S), which also takes a group of components intoconsideration simultaneously. GFCT3S is suitable for signals with crossing IFs.It also decreases component recovery errors when the IFs curves of differentcomponents are not crossover, but fast-varying and close to one and other.Numerical experiments on synthetic and real signals show our method is moreaccurate and consistent in signal separation than the empirical modedecomposition, synchrosqueezing transform, and other approaches

A Chirplet Transform-based Mode Retrieval Method for Multicomponent Signals with Crossover Instantaneous Frequencies