Analysis of gravitational waves from binary neutron star merger by Hilbert-Huang transform

Using the Hilbert-Huang transform (HHT), we analyze gravitational waves from late inspiral, merger, and post-merger phases of binary neutron stars coalescence, computed by a general relativistic numerical simulation. The HHT analysis has been developed as a method for time series analysis of nonlinear and nonstationary data, and it enables us to perform a high resolution time frequency analysis of signals with strong frequency modulation by evaluating the instantaneous variation of amplitude and frequency of data. We find that we can clearly observe the time evolution of the instantaneous frequency of the post-merger waveforms. It is found that temporal variation of frequency of post-merger waveforms can be evaluated within 5% error if BNS coalescences occur within 10 Mpc. This accuracy allows us to constrain the equation of state of neutron stars and to evaluate the radius of a fiducial neutron star of $1.8{M}_{\ensuremath{\bigodot}}$ with a few hundred meters accuracy.