Time-frequency methods for coherent spectroscopy

Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed

On the Signal Processing Operations in LIGO signals

This article analyzes the data for the five gravitational wave (GW) events detected in Hanford(H1), Livingston(L1) and Virgo(V1) detectors by the LIGO collaboration. It is shown that GW170814, GW170817, GW151226 and GW170104 are very weak signals whose amplitude does not rise significantly during the GW event, and they are indistinguishable from non-stationary detector noise. LIGO software implements cross-correlation funcion(CCF) of H1/L1 signals with the template reference signal, in frequency domain, in a matched filter, using 32 second windows. It is shown that this matched filter misfires with high SNR/CCF peaks, even for very low-amplitude, short bursts of sine wave signals and additive white gaussian noise(AWGN), all the time. It is shown that this erratic behaviour of the matched filter, is due to the error in signal processing operations, such as lack of cyclic prefix necessary to account for circular convolution. It is also shown that normalized CCF method implemented in time domain using short windows, does not have false CCF peaks for sine wave and noise bursts. It is shown that the normalized CCF for GW151226 and GW170104, when correlating H1/L1 and template, is indistinguishable from correlating detector noise and the template. It is also shown that the normalized CCF for GW151226 and GW170104, when correlating H1/L1 and template, is indistinguishable from correlating H1/L1 and bogus chirp templates which are frequency modulated(FM) waveforms which differ significantly from ideal templates. Similar results are shown with LIGO matched filter, which misfires with high Signal to Noise Ratio(SNR) for bogus chirp templates.Comment: Corrected typographical errors, updated names, references and acknowledgement section. Added a subsection on an improved whitening procedur

An excess power statistic for detection of burst sources of gravitational radiation

We examine the properties of an excess power method to detect gravitational waves in interferometric detector data. This method is designed to detect short-duration (< 0.5 s) burst signals of unknown waveform, such as those from supernovae or black hole mergers. If only the bursts' duration and frequency band are known, the method is an optimal detection strategy in both Bayesian and frequentist senses. It consists of summing the data power over the known time interval and frequency band of the burst. If the detector noise is stationary and Gaussian, this sum is distributed as a chi-squared (non-central chi-squared) deviate in the absence (presence) of a signal. One can use these distributions to compute frequentist detection thresholds for the measured power. We derive the method from Bayesian analyses and show how to compute Bayesian thresholds. More generically, when only upper and/or lower bounds on the bursts duration and frequency band are known, one must search for excess power in all concordant durations and bands. Two search schemes are presented and their computational efficiencies are compared. We find that given reasonable constraints on the effective duration and bandwidth of signals, the excess power search can be performed on a single workstation. Furthermore, the method can be almost as efficient as matched filtering when a large template bank is required. Finally, we derive generalizations of the method to a network of several interferometers under the assumption of Gaussian noise.Comment: 22 pages, 6 figure