Complex Autoregressive Time-Frequency Analysis: Estimation of Time-Varying Periodic Signal Components

Time-frequency representations of nonstationary signals have a wide range of geophysical applications, including seismics, seismology, volcanology, and astrophysics. In this article, we estimate a complex autoregressive (AR) model from a short time window of the analytic signal. The local power spectrum is the inverse of the spectrum of this AR model. Since the coefficients are complex, the time window can be shorter than for the real AR model, which requires more coefficients. This results in higher time-frequency resolution, as seen in a synthetic data examples with different signal components. The new technique also gives good results when computing the instantaneous average frequency (IAF) of marine seismic data. Applied to digitized and downloaded data from the Laser Interferometer Gravitational-Wave Observatory (LIGO) in Hanford, Washington, the result clearly shows the linear chirp associated with the merger of two black holes.