English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Analysis of signals with oscillatory modes with crossover instantaneousfrequencies is a challenging problem in time series analysis. One way to handlethis problem is lifting the 2-dimensional time-frequency representation to a3-dimensional representation, called time-frequency-chirp rate (TFC)representation, by adding one extra chirp rate parameter so that crossoverfrequencies are disentangled in higher dimension. The chirplet transform is analgorithm for this lifting idea, which leads to a TFC representation. However,in practice, we found that it has a strong ``blurring'' effect in the chirprate axis, which limits its application in real-world data. Moreover, to ourknowledge, we have limited mathematical understanding of the chirplet transformin the literature. Motivated by the need for the real-world data analysis, inthis paper, we propose the synchrosqueezed chirplet transform (SCT) thatenhances the TFC representation given by the chirplet transform. The resultingconcentrated TFC representation has high contrast so that one can betterdistinguish different modes with crossover instantaneous frequencies. The basicidea is to use the phase information in the chirplet transform to determine areassignment rule that sharpens the TFC representation determined by thechirplet transform. We also analyze the chirplet transform and providetheoretical guarantees of SCT.

Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application