A time-frequency analysis of gravitational wave signals with non-harmonic analysis

We apply non-harmonic analysis (NHA) to analyze gravitational wave signals from compact binary coalescences. After investigating the general properties of NHA by using several test signals with amplitude and frequency modulation, we analyze gravitational wave signals from the inspiraling of compact binary coalescences. We find that the time-frequency property of the signal can be reproduced accurately. We analyze the signals from inspiraling binary black holes injected into simulated Gaussian noise.We find that we can identify the signal even if the signal-To-noise ratio in the sense of a matched filter is as low as 10.We investigate the accuracy of the instantaneous amplitude and frequency of the signal recovered with NHA. We analyze gravitational wave events detected by LIGO and Virgo, and find that gravitational wave signals with strong amplitude like GW150914 can be shown clearly on the time-frequency map by NHA. We also find that even in the case of a low-Amplitude signal like GW170817, the signal can be clearly seen by choosing an appropriate window size that depends on the frequency band.