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.
The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. W
e analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.
