Multiwindow Nonharmonic Analysis Method for Gravitational Waves

Abstract

The frequency of the observed gravitational wave (GW) signal GW150914 changes slowly over a long time in the low frequency band and then increases rapidly from low to high frequency band, the frequency variance over time of such signals cannot be analyzed and visualized accurately using current analytical methods due to their fixed analytical window lengths or low time-frequency resolutions. To obtain high-accuracy GW representations, we propose the use of multiwindow nonharmonic analysis (NHA); in this method, NHA is performed using different window lengths for each subband after a band division procedure. A simulated signal was used to compare the results obtained using NHA and multiwindow NHA in this paper. The results distinctly show that the error of multiwindow NHA is 6.311 Hz which is lower than NHA. We also compared the results of multiwindow NHA with those of state-of-the-art methods by using actual GW150914 data and verified the analytical precision of these techniques. We found that the high timefrequency resolution of multiwindow NHA and its low sensitivity to analysis window variations enable it to analyze more accurately with 6.021 Hz errors in the extracted interval than the state-of-the-art methods even with the presence of significant noise. In addition, only multiwindow NHA can accurately represent GW signals at amplitudes down to the noise limit and achieve correct low-frequency range representation, due to its ability to assign the appropriate window length for each subband.

Keywords

• Gravitational wave
• band division
• analytical window length
• nonharmonic analysis (NHA)
• multiwindow NHA