Math @ Duke
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Publications [#361464] of Hau-Tieng Wu
Papers Published
- Chen, Z; Wu, H-T, Disentangling modes with crossover instantaneous frequencies by
synchrosqueezed chirplet transforms, from theory to application
(December, 2021)
(last updated on 2024/04/24)
Abstract: Analysis of signals with oscillatory modes with crossover instantaneous
frequencies is a challenging problem in time series analysis. One way to handle
this problem is lifting the 2-dimensional time-frequency representation to a
3-dimensional representation, called time-frequency-chirp rate (TFC)
representation, by adding one extra chirp rate parameter so that crossover
frequencies are disentangled in higher dimension. The chirplet transform is an
algorithm for this lifting idea, which leads to a TFC representation. However,
in practice, we found that it has a strong ``blurring'' effect in the chirp
rate axis, which limits its application in real-world data. Moreover, to our
knowledge, we have limited mathematical understanding of the chirplet transform
in the literature. Motivated by the need for the real-world data analysis, in
this paper, we propose the synchrosqueezed chirplet transform (SCT) that
enhances the TFC representation given by the chirplet transform. The resulting
concentrated TFC representation has high contrast so that one can better
distinguish different modes with crossover instantaneous frequencies. The basic
idea is to use the phase information in the chirplet transform to determine a
reassignment rule that sharpens the TFC representation determined by the
chirplet transform. We also analyze the chirplet transform and provide
theoretical guarantees of SCT.
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