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BicoMon

BicoMon. Steve Penn, Hobart and William Smith Colleges LSC Meeting — August 2002 LIGO Hanford Observatory LIGO-G020390-00-Z. Synopsis. Introduction to Higher Order Statistics 1D: Correlation, Coherence, Power Spectra 2D: Bicorrelation, Bicoherence, Bispectrum Monitor Update Future work.

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BicoMon

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  1. BicoMon Steve Penn, Hobart and William Smith Colleges LSC Meeting — August 2002 LIGO Hanford Observatory LIGO-G020390-00-Z

  2. Synopsis • Introduction to Higher Order Statistics • 1D: Correlation, Coherence, Power Spectra • 2D: Bicorrelation, Bicoherence, Bispectrum • Monitor Update • Future work HWS LIGO Group

  3. What are Higher Order Statistics? • 1D Statistics: • Correlation: • Power Spectral Density: • Coherence: • Tells us power and phase coherence at a given frequency HWS LIGO Group

  4. Second Order Statistics • 2D Statistics: • Bicumulant: • Bispectral Density: • Bicoherence: • Tells us power and phase coherence at a coupled frequency HWS LIGO Group

  5. Zero-lag Cumulants Mean Variance Skewness Kurtosis 0 if Symmetric 0 if Gaussian Useful statictical values, but… Skewness = 0 does not prove symmetry Kurtosis = 0 does not prove Gaussianity Variations in skew and kurtosis not well quantified. HWS LIGO Group

  6. Why Higher Order Statistics? • For a Gaussian process: • For independent processes: • Allows for separation of Gaussian process for n>2 • Visual check of frequency coupling and phase noise • Statistical test for the probability of gaussianity and linearity • Iterative process to reconstruct nongaussian signal from the higher order cumulants HWS LIGO Group

  7. Auto-Bispectrum Unique Area fN f1=f2 f2=2fN-f1 0 fN HWS LIGO Group

  8. Monitor Features • Plots (cross-)bicoherence, (cross-)bispectrum, & PSD’s • Operates on 1–3 channels • User-specified Bispectrum method (Direct / InDirect) • Automatically decimates to the lowest channel rate. • User selected fmax and Df Limited to factor 2n • User specifies the accuracy • Monitor Outputs the Time span (gives user the update time) • User-specified Bispectrum method (Direct / InDirect) • Windowing: Optimized Rao-Gabr windowing • Outputs GIF files of the plots • Help facility HWS LIGO Group

  9. HWS LIGO Group

  10. HWS LIGO Group

  11. Improvements / Future Directions • GUI, frequency-selection method, freq. resolution • Vijay Chickarmane and I are working together to monitor the time variation of regions of high bicoherence. --> Background monitoring - we are devising a method to fit the bilinear features for tracking of coefficients and/or subtraction HWS LIGO Group

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