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In many applications, it is necessary to retrieve the sub-signal buildingblocks of a multi-component signal, which is usually non-stationary inreal-world and real-life applications. Empirical mode decomposition (EMD),synchrosqueezing transform (SST), signal separation operation (SSO), anditerative filtering decomposition (IFD) have been proposed and developed forthis purpose. However, these computational methods are restricted by thespecification of well-separation of the sub-signal frequency curves formulti-component signals. On the other hand, the chirplet transform-based signalseparation scheme (CT3S) that extends SSO from the two-dimensional"time-frequency" plane to the three-dimensional "time-frequency-chirp rate"space was recently proposed in our recent work to remove thefrequency-separation specification, and thereby allowing "frequency crossing".The main objective of this present paper is to carry out an in-depth erroranalysis study of instantaneous frequency estimation and component recovery forthe CT3S method.

Analysis of a Direct Separation Method Based on Adaptive Chirplet Transform for Signals with Crossover Instantaneous Frequencies