  Recent core-collapse supernova (CCSN) simulations have predicted several
distinct features in gravitational-wave (GW) spectrograms, including a ramp-up
signature due to the g-mode oscillation of the proto-neutron star (PNS) and an
excess in the low-frequency domain (100-300 Hz) potentially induced by the
standing accretion shock instability (SASI). These predictions motivated us to
perform a sophisticated time-frequency analysis (TFA) of the GW signals, aimed
at preparation for future observations. By reanalyzing a gravitational waveform
obtained in a three-dimensional general-relativistic CCSN simulation, we show
that both the spectrogram with an adequate window and the quadratic TFA
separate the multimodal GW signatures much more clearly compared with the
previous analysis. We find that the observed low-frequency excess during the
SASI active phase is divided into two components, a stronger one at 130 Hz and
an overtone at 260 Hz, both of which evolve quasi-statically during the
simulation time. We also identify a new mode whose frequency varies from 700 to
600 Hz. Furthermore, we develop the quadratic TFA for the Stokes I, Q, U, and V
parameters as a new tool to investigate the GW circular polarization. We
demonstrate that the polarization states that randomly change with time after
bounce are associated with the PNS g-mode oscillation, whereas a slowly
changing polarization state in the low-frequency domain is connected to the PNS
core oscillation. This study demonstrates the capability of the sophisticated
TFA for diagnosing the polarized CCSN GWs in order to explore their complex
nature.
