Comparison of Signals from Gravitational Wave Detectors with Instantaneous Time-Frequency Maps

TL;DR

This paper demonstrates that comparing instantaneous time-frequency maps from the Hilbert-Huang Transform can effectively determine relative timing, discriminate real signals from noise, and classify gravitational wave signals based on their time-frequency trajectories.

Contribution

It introduces a novel method using HHT-based maps and chi-square goodness-of-fit for signal comparison in gravitational wave detection, especially for frequency-modulated signals.

Findings

Effective discrimination between coincident signals and noise.

Accurate relative timing of gravitational wave signals.

Classification of signals based on time-frequency trajectories.

Abstract

Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of sources. We show that the comparison of instantaneous time-frequency and time- amplitude maps provided by the Hilbert-Huang Transform (HHT) can be used effectively for relative signal timing of common signals, to discriminate between the case of identical coincident signals and random noise coincidences, and to provide a classification of signals based on their time-frequency trajectories. The comparison is done with a chi-square goodness-of-fit method which includes contributions from both the instantaneous amplitude and frequency components of the HHT to match two signals in the time domain. This approach naturally allows the analysis of waveforms with strong frequency modulation.