  Through numerical simulations, it is predicted that the gravitational waves
(GWs) reflect the characteristics of the core-collapse supernova (CCSN)
explosion mechanism. There are multiple GW excitation processes that occur
inside a star before its explosion, and it is suggested that the GWs
originating from the CCSN have a mode for each excitation process in terms of
time-frequency representation. Therefore, we propose an application of the
Hilbert-Huang Transform (HHT), which is a high-resolution time-frequency
analysis method, to analyze these GW modes for theoretically probing and
increasing our understanding of the explosion mechanism. The HHT defines
frequency as a function of time, and is not bound by the trade-off between time
and frequency resolutions. In this study, we analyze a gravitational waveform
obtained from a three-dimensional general-relativistic CCSN model that showed a
vigorous activity of the standing-accretion-shock-instability (SASI). We
succeed in extracting the SASI induced GWs with high resolution on a
time-frequency representation using the HHT and we examine their instantaneous
frequencies.
