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

Abstract

We analyze the gravitational wave signals with a model-independent time-frequency analysis, which is improved from the Hilbert–Huang transform (HHT) and optimized for characterizing the frequency variability on the time-frequency map. Instead of the regular HHT algorithm, i.e., obtaining intrinsic mode functions with ensemble empirical mode decomposition and yielding the instantaneous frequencies, we propose an alternative algorithm that operates the ensemble mean on the time-frequency map. We systematically analyze the known gravitational wave events of the compact binary coalescence observed in the first gravitational-wave transient catalog, and in the simulated gravitational wave signals from core-collapse supernovae (CCSNe) with our method. The time-frequency maps of the binary black hole coalescence cases show much more detail compared to those wavelet spectra. Moreover, the oscillation in the instantaneous frequency caused 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 standing accretion shock instability can be precisely determined with the HHT in great detail. More importantly, the initial stage of different modes of oscillations can be clearly separated. These results provide new hints for further establishment of the detecting algorithm and new probes to investigate the underlying physical mechanisms.