Burst detection in time frequency space
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Burst detection in time-frequency space. Unfolding signal structure. Starting point unbiased toward specific signals. Aim at timing and frequency band accuracy. Nb: all results based on Virgo-type simulated data (LIGO-VIRGO joint group). AC Clapson. GWDAW 9, Annecy, December 2004.

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Burst detection in time-frequency space

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Burst detection in time frequency space

Burst detection in time-frequency space

  • Unfolding signal structure.

  • Starting point unbiased toward specific signals.

  • Aim at timing and frequency band accuracy.

    Nb: all results based on Virgo-type simulated data (LIGO-VIRGO joint group).

AC Clapson

GWDAW 9, Annecy, December 2004


S transform

S transform

  • Gaussian shaped complex exponential template.

    (applied in frequency domain)

  • Resolution defined by Gaussian width and centre

    • Linear centre frequency spacing.

    • Width increases with frequency.

  • Colored spectrum issue

    • Spectrum reproduced in TF map.

    • Noise / signal discrimination based on excess energy: adaptive criterion.

  • Spectral lines issue

    • Line coupling with successive templates gives wide frequency profile.

    • Locally, line energy much larger than signal.


Initial analysis chain

Initial analysis chain

  • Preprocessing

    • Line removal (Kalman filters).

    • High pass filter.

    • Segment edges Hann-shaped.

  • Transform

    • 215 bins long, exclude edges from map.

    • Output power.

    • Band 30 – 500 Hz.

    • Normalize mean and standard deviation

      (for each frequency).

  • Event extraction

    • Bin energy cut.

    • Clusterize bins.

    • Cluster energy cut.


Results

Results

  • Satisfying efficiency for sine Gaussians and short Gaussian peaks.

    • Energy well localized in TF map (compacity and frequency band)

  • Lower detectability for long Gaussian peak and DFM.

    • Energy reduction by preprocessing.

    • Spread out energy: secondary clusters.

    • Map frequency cut : high frequency component missed.


First improvement

Signals

First improvement

Map size increase:

  • Statistics more accurate.

  • Better frequency separation by template.


Improvement under study

(Preliminary results)

Improvement under study

  • Non-linear list of template frequency centres.

    • Gaussian templates overlap set by equal s rule.

    • Reduces template number (1/3 here).

    • Requires energy renormalization (restore time-frequency atom integral)


Summary

Summary

  • Core transform promising.

  • Compact signals efficiently extracted.

  • Complex signals require finer treatment.

  • Noise spectral features rapidly detrimental.

  • Series of modifications under study.

    • Alternative S transform

      • Implement “à la Welch” windowing (discard high pass).

      • Use non-linear frequency spacing (constant s spacing).

      • Avoid self-normalization.

    • Elaborate clustering / thresholding

      • Time coincidence before cluster energy cut.

      • Additional cluster parameter cuts (noise discrimination).

AC Clapson


Kalman filters for line removal

Measure

Prediction

Correction

Model

Kalman filters for line removal

  • Relies on model of the feature to be extracted.

  • Discrete time first order recursive model => fast.

  • Optimal filter in Wiener sense (minimal reconstruction error)

  • Model mismatch detection

    and correction required.

  • Model:

  • Thermally excited violin modes

    • Viscous damping oscillator equation

    • Parameters : m, Q, T, w0 , x0, x’0


Template spacing

Template spacing

  • Balance centre frequency distance / template overlap.

    • fn+1 = fn + df

    • fn+1 = fn * sf


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