Time-Frequency Analysis of Gravitational Waves

The instantaneous frequency (IF) is a vital parameter for time-frequency analysis of a nonstationary signal such as gravitational wave. In this paper, IF of gravitational waves, recorded by the Laser Interferometer Gravitational-Wave Observatory detectors, is estimated by applying the energy preserving empirical mode decomposition and the Fourier decomposition method. The frequency values corresponding to minimum inspiral strain, maximum strain that indicates the merger of binary black holes, and the subsequent ringdown are obtained as (a) GW150914: 30-160-264 Hz, and (b) GW151226: 19-164-265 Hz. The proposed methods demonstrate a superior performance in terms of better time-frequency resolution as compared to the widely used continuous wavelet transform.