Analysis of gravitational waves from binary neutron star coalescence using improved Hilbert–Huang transform based on Steffen interpolation

Abstract

Analyzing the post-merger phase of gravitational waves from observed binary neutron star coalescences is expected to provide constraints on the neutron star equation of state (EOS), which remains theoretically uncertain. Achieving this objective requires a method capable of simultaneously attaining high temporal and frequency resolutions at a local level. The Hilbert–Huang transform (HHT) has been proposed as a suitable approach for this purpose. Previous studies demonstrated that replacing the conventional cubic spline interpolation of extrema in the HHT with the Akima spline suppresses interpolation-induced overshoot and improves analytical accuracy. In this study, we investigate whether the accuracy can be further improved by employing the Steffen interpolation, an interpolation scheme that inherently prevents overshoot. The results confirm that the HHT implemented with the Steffen interpolation achieves the highest performance.