Application of bispectral techniques to Virgo Data G
![Application of bi-spectral techniques to Virgo Data G. Vedovato Padova Trento Group Virgo Week Application of bi-spectral techniques to Virgo Data G. Vedovato Padova Trento Group Virgo Week](https://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-1.jpg)
Application of bi-spectral techniques to Virgo Data G. Vedovato Padova Trento Group Virgo Week Meeting 29 Jan 2008 1
![Summary • • • When & Why ? What is the Bicoherence ? The Summary • • • When & Why ? What is the Bicoherence ? The](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-2.jpg)
Summary • • • When & Why ? What is the Bicoherence ? The Bicoherence Tool The Virgo Data Set The Virgo Bicoherence Next Steps Virgo Week Meeting 29 Jan 2008 2
![When & Why • When : non Gaussian noise, non-linear response… , non stationary When & Why • When : non Gaussian noise, non-linear response… , non stationary](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-3.jpg)
When & Why • When : non Gaussian noise, non-linear response… , non stationary noise… • Why : because of bilinear couplings of noise sources / signal disturbances. • Consider a physical process, which puts out the value of the product of two signals at two different frequencies • The output signal will then be • where k is a coupling factor which in general could be frequency dependent. As we can expect, there will be two additional frequencies at Virgo Week Meeting 29 Jan 2008 3
![What is the bicoherence ? • The bicoherence is a normalized form of the What is the bicoherence ? • The bicoherence is a normalized form of the](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-4.jpg)
What is the bicoherence ? • The bicoherence is a normalized form of the bispectrum : • and is defined as • where Xk , Xl and Xm are the Fourier components of the signal at the frequencies k, l and m=l+k, If the signal at m=l+k arises due to the product of the signal at k and l, then for the phase of the numerator will average out to a nonzero value and hence the bispectrum will be nonzero Virgo Week Meeting 29 Jan 2008 4
![Example F 1=16. 5 Hz, F 2=918 Hz F 2 -F 1=901. 5 Hz, Example F 1=16. 5 Hz, F 2=918 Hz F 2 -F 1=901. 5 Hz,](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-5.jpg)
Example F 1=16. 5 Hz, F 2=918 Hz F 2 -F 1=901. 5 Hz, F 2+F 1=934. 5 Hz F 1=16. 5 Hz F 2=918 Hz Virgo Week Meeting 29 Jan 2008 5
![The Bicoherence Tool • Our bicoherence tool is embedded in the AURIGA Data Analysis, The Bicoherence Tool • Our bicoherence tool is embedded in the AURIGA Data Analysis,](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-6.jpg)
The Bicoherence Tool • Our bicoherence tool is embedded in the AURIGA Data Analysis, which works in the ROOT framework, reads frame format data files, includes some LAL libraries… • It has been extremely useful in AURIGA to identify the “bad” low frequency resonances to design the additional suspension stage • The analysis reported in this talk has been implemented with a ROOT macro • Performances : Intel Xeon CPU 3. 4 GHz – – – Sample Rate : 20 KHz Analyzed Frequency Area : 5 Hz x 50 Hz Frequency Resolution : 0. 03125 Hz # average : 250 Speed : 44 x (8000 sec of data analyzed in 186 sec) Virgo Week Meeting 29 Jan 2008 6
![Virgo Data Set Run 5941 : Channel : V 1: Pr_B 1_ACp : 2007 Virgo Data Set Run 5941 : Channel : V 1: Pr_B 1_ACp : 2007](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-7.jpg)
Virgo Data Set Run 5941 : Channel : V 1: Pr_B 1_ACp : 2007 -09 -22 17: 00 Time : 0 -700 sec Frequency : 0 -1250 Hz Virgo Week Meeting 29 Jan 2008 7
![Bilinear Coupling in Virgo Low frequencies Virgo Week Meeting 29 Jan 2008 Coupling High Bilinear Coupling in Virgo Low frequencies Virgo Week Meeting 29 Jan 2008 Coupling High](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-8.jpg)
Bilinear Coupling in Virgo Low frequencies Virgo Week Meeting 29 Jan 2008 Coupling High frequencies 8
![Bicoherence @ 444 Hz Virgo Week Meeting 29 Jan 2008 9 Bicoherence @ 444 Hz Virgo Week Meeting 29 Jan 2008 9](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-9.jpg)
Bicoherence @ 444 Hz Virgo Week Meeting 29 Jan 2008 9
![Bicoherence @ 444 Hz 0. 5847 Hz 0. 2 Hz Virgo Week Meeting 29 Bicoherence @ 444 Hz 0. 5847 Hz 0. 2 Hz Virgo Week Meeting 29](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-10.jpg)
Bicoherence @ 444 Hz 0. 5847 Hz 0. 2 Hz Virgo Week Meeting 29 Jan 2008 10
![Bicoherence @ 50 -100 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 50 -100 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-11.jpg)
Bicoherence @ 50 -100 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 11
![Bicoherence @ 100 -150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 100 -150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-12.jpg)
Bicoherence @ 100 -150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 12
![Bicoherence @ 200 -250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 200 -250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-13.jpg)
Bicoherence @ 200 -250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 13
![Bicoherence @ 250 -300 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 250 -300 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-14.jpg)
Bicoherence @ 250 -300 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 14
![Bicoherence @ 300 -350 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 300 -350 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-15.jpg)
Bicoherence @ 300 -350 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 15
![Bicoherence @ 350 -400 Hz x 0 -3 Hz +/- 2 Hz Virgo Week Bicoherence @ 350 -400 Hz x 0 -3 Hz +/- 2 Hz Virgo Week](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-16.jpg)
Bicoherence @ 350 -400 Hz x 0 -3 Hz +/- 2 Hz Virgo Week Meeting 29 Jan 2008 16
![Bicoherence @ 400 -450 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 400 -450 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-17.jpg)
Bicoherence @ 400 -450 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 17
![Bicoherence @ 1000 -1150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 1000 -1150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-18.jpg)
Bicoherence @ 1000 -1150 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 18
![Bicoherence @ 1200 -1250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan Bicoherence @ 1200 -1250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-19.jpg)
Bicoherence @ 1200 -1250 Hz x 0 -3 Hz Virgo Week Meeting 29 Jan 2008 19
![Next Steps • Feedback from HW Virgo peoples • Analysis of data set with Next Steps • Feedback from HW Virgo peoples • Analysis of data set with](http://slidetodoc.com/presentation_image_h2/7411fbdd080f4e041b64a9f388cfcefa/image-20.jpg)
Next Steps • Feedback from HW Virgo peoples • Analysis of data set with different setup – Comparisons could highlight the origin of the non linearities • Implementation of an offline tool under ROOT framework (? if useful) Virgo Week Meeting 29 Jan 2008 20
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