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We analyze the gravitational wave signals with a model-independenttime-frequency analysis, which is improved from the Hilbert-Huang transform(HHT) and optimized for characterizing the frequency variability on thetime-frequency map. Except for the regular HHT algorithm, i.e., obtainingintrinsic mode functions with ensemble empirical mode decomposition andyielding the instantaneous frequencies, we propose an alternative algorithmthat operates the ensemble mean on the time-frequency map. We systematicallyanalyze the known gravitational wave events of the compact binary coalescenceobserved in LIGO O1 and O2, and in the simulated gravitational wave signalsfrom core-collapse supernovae (CCSNe) with our method. The time-frequency mapsof the binary black hole coalescence cases show much better details compared tothose wavelet spectra. Moreover, the oscillation in the instantaneous frequencycaused by mode-mixing could be reduced with our algorithm. For the CCSNe data,the oscillation from the proto-neutron star and the radiation from the standingaccretion shock instability can be precisely determined with the HHT in greatdetail. More importantly, the initial stage of different modes of oscillationscan be clearly separated. These results provide new hints for furtherestablishment of the detecting algorithm, and new probes to investigate theunderlying physical mechanisms.

A Comprehensive Analysis of the Gravitational Wave Events with the Hilbert-Huang Transform: From Compact Binary Coalescence to Supernova