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Excess Power Trigger Generator for Gravitational Wave Detection

This document outlines the Excess Power method developed by Patrick Brady and Saikat Ray-Majumder at the University of Wisconsin-Milwaukee, in collaboration with the LIGO Scientific Collaboration. The method involves analyzing detector data to detect gravitational wave bursts by calculating power in specified frequency bands and assessing the probability of observing such power in Gaussian noise. It details optimal tuning parameters, implementation techniques, and efficiency measurements, contributing significantly to the field of gravitational wave astronomy.

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Excess Power Trigger Generator for Gravitational Wave Detection

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  1. Excess power trigger generator Patrick Brady and Saikat Ray-Majumder University of Wisconsin-Milwaukee LIGO Scientific Collaboration

  2. Excess power method:the basic idea • The basic idea: • Pick a start time, a duration (dt), and a frequency band (df) • Fourier transform detector data with specified start time and duration • Sum the power in the frequency band • Calculate probability of obtaining the summed power from Gaussian noise using a c2 distribution with (2 x dt x df) degrees of freedom • If the probability is small, record a trigger • Repeat procedure for all start times, frequency bands and durations • For Gaussian noise, the method is optimal to detect bursts of specified duration and frequency bandwidh • Details are in Anderson, Brady, Creighton and Flanagan [PRD 63, 042003. (2001)] GWDAW - Dec 2003

  3. Excess-power method:time-frequency decomposition • Using N data points corresponding to maximum duration of signal to be detected • Construct time-frequency planes at multiple resolutions • Each plane is constructed to have pixels of unit time-frequency volume • Time resolution improves by factor of 2 from plane to plane GWDAW - Dec 2003

  4. Excess-power method:Implementation • Calculate time-frequency planes as described above’ • Compute power in tiles defined by a start-time, duration, low-frequency, frequency band • Output is sngl_burst trigger if probability of obtaining power from Gaussian noise is less than user supplied threshold GWDAW - Dec 2003

  5. Tuning the search code • Parameters available for tuning • Lowest frequency to search • Maximum and minimum time duration of signals • Maximum bandwidth • Confidence threshold • Number of events recorded for each 1 second of data • Tuning procedure • Lowest frequency decided based on high glitch rate below 130 Hz • Max duration is 1 second; Min duration is 1/64 seconds • Max bandwidth of a tile 64Hz, but allows for broader band signals by clustering • Tuned confidence threshold and number of events recorded to allow trigger rate ~ 1 Hz GWDAW - Dec 2003

  6. Running the search on large data sets • Excess power runs standalone using Condor batch scheduler • Directed Acyclic Graph describes workflow • Use LALdataFind to locate data • Interrogation of replica catalog maintained by LDR (S. Koranda) • All search code in • LAL and LALApps (many contributors) • Power code • Generates triggers from each interferometer • Coincidence stage of the search is part of the jobs we run • Coincidence needs to be tuned within burst group (See talk by Cadonati) GWDAW - Dec 2003

  7. Performance on interferometer data 600s: uncalibrated data Same data with Sine-Gaussians at 250Hz, h0 = 6e-20 GWDAW - Dec 2003

  8. 800 Triggers 800 Triggers Frequency Dependence of Triggers Hanford 4km: # of triggers in various freq. bands Livingston 4km: # of triggers in various freq. bands Frequency Frequency GWDAW - Dec 2003

  9. Measuring the efficiency of algorithm • Sine Gaussian waveform • h+(t) = h0 Sin[ 2 p f0 (t-t0) ] exp[ - (t – t0)2/t2 ] • hx(t) = 0 • Signal parameters used: • Frequencies: 235, 319, 434, 590, 801 • Q = sqrt(2) p f0t = 8.89 • h0 = [10-21,10-17] uniform on log scale • Location on sky for single detector tests: • Zenith of each detector • Linearly polarized w.r.t. that detector • That is F+=1, Fx=0 GWDAW - Dec 2003

  10. Efficiencies to Q=9 Sine-Gaussians4km Interferometers GWDAW - Dec 2003

  11. Parameter accuracy: peak time and central frequency Q=9 Sine-Gaussian at 235Hz Peak time Central frequency GWDAW - Dec 2003

  12. Continuing work as part of LSC burst analysis group • Tune the coincidence step to best utilize triggers from excess power • Extend efficiency measurements to all sky for sine-Gaussians • Extend efficiency measurements to include supernova waveforms • Implement multi-detector extension of excess power discussed in Anderson, Brady, Creighton and Flanagan [PRD 63, 042003. (2001)] • Test alternative statistic involving over-whitened data [See ABCF and/or Vicere PRD 66, 062002. (2002)] GWDAW - Dec 2003

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