We describe a procedure to identify and remove a class of interference lines
from gravitational wave interferometer data. We illustrate the usefulness of
this technique applying it to prototype interferometer data and removing all
those lines corresponding to the external electricity main supply and related
features.Comment: Latex 6 pages, 5 figures. To appear in: "Gravitational Wave Detection
  II". Edt. Rie Sasaki; Universal Academy Press, Inc, Tokyo, Japa

Schutz, B. F.

Sintes, A. M.

English

arXiv

We describe a procedure to identify and remove a class of interference lines from gravitational wave interferometer data. We illustrate the usefulness of this technique applying it to prototype interferometer data and removing all those lines corresponding to the external electricity main supply and related features

Sintes, A.

Schutz, B.

MPG.PuRe

arXiv:gr-qc/0005071 v1   16 May 2000Removing Line Interference from Gravi-tational Wave Interferometer DataAlicia M. SINTES and Bernard F. SCHUTZMax-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)Am Mühlenberg 1. 14476 Golm. Germany, sintes@aei-potsdam.mpg.deAbstractWe describe a procedure to identify and remove a class of interference linesfrom gravitational wave interferometer data. We illustrate the usefulness of thistechnique applying it to prototype interferometer data and removing all thoselines corresponding to the external electricity main supply and related features.1. IntroductionIn the measured noise spectrum of the different gravitational wave inter-ferometer prototypes, we observe peaks due external interference [1,2]. The mostnumerous are powerline frequency harmonics. We have shown how to model andremove these lines very effectively using a technique we call coherent line removal(clr) [3]. In addition to those lines appearing at multiples of 50 (or 60) Hz,there are other interference lines whose frequencies change in step with the sup-ply frequency, but not at the harmonic frequencies. The easiest way to detecttheir presence is by studying in detail the spectrogram (see figure 1). These lines,although they are not as powerful as the harmonics, are spread over the wholespectrum. From a data analysis point of view, we try to develop a techniqueable to remove this interference while producing a minimum disturbance to theunderlying noise background [4].In this paper, we illustrate the usefulness of these techniques by applyingthem to the data produced by the Glasgow laser interferometer in March 1996.As a result the interference is attenuated or eliminated by cancellation in the timedomain and the power spectrum appears completely clean allowing the detectionof signals that were buried in the interference. Therefore, these new methodsappear to be good news as far as searching for continuous waves is concerned.The removal reduces the level of non-Gaussian noise, improving the sensitivity ofthe detector to short bursts of gravitational waves as well.12Time [s]Frequency [Hz]0 500 1000 1500 2000 2500 3000 3500440445450455Fig. 1. Zoom of the spectrogram of the prototype data. The line near 450 Hzcorresponds to the 9th harmonic of the external electricity supply. The weakerline near 443 Hz is one example of the many lines present in the spectrum thathave a similar time-frequency evolution to that of the harmonics of 50 Hz.2. Line removalclr is an algorithm able to remove interference present in the data whilepreserving the stochastic detector noise. clr works when the interference ispresent in many harmonics, as long as they remain coherent with one another.It can remove the external interference without removing any ‘single line’ sig-nal buried by the harmonics. The algorithm works even when the interferencefrequency changes. clr can be used to remove all harmonics of periodic or broad-band signals (e.g., those which change frequency in time), even when there is noexternal reference source. It assumes that the interference has the formy(t) =∑nanm(t)n + (anm(t)n)∗ , (1)where an are complex amplitudes and m(t) is a nearly monochromatic functionnear a frequency f0. The idea is to use the information in the different harmonicsof the interference to construct a function M(t) that is as close a replica as pos-sible of m(t) and then construct a function close to y(t) which is subtracted fromthe output of the system cancelling the interference. The key is that real gravita-tional wave signals will not be present with multiple harmonics and that M(t) isconstructed from many frequency bands with independent noise. Hence, clr willlittle affect the statistics of the noise in any one band and any gravitational wavesignal masked by the interference can be recovered without any disturbance.3745 750 755−35−34−33−32−31Frequency [Hz]Log10 periodogram(a)745 750 755−35−34−33−32−31Frequency [Hz]Log10 periodogram(b)445 450 455 460−34−33−32−31−30Frequency [Hz]Log10 periodogram(c)445 450 455 460−34−33−32−31−30Frequency [Hz]Log10 periodogram(d)Fig. 2. Decimal logarithm of the periodogram of 219 points of the prototypedata. (a) One of the harmonics near 754 Hz. (b) The same data after theremoval of the interference using clr. (c) The same experimental data withan artificial signal added at 452 Hz. (d) The data in (c) after the removal ofthe interference, revealing that the signal remains detectable.In figure 2, we show the performance of clr on two minutes of data. Wecan see how clr leaves the spectrum clean of the interference and keeps theintrinsic detector noise.For the non-harmonic lines, after examining them in detail and rejectingthe possibility of the beats, we assume a noninteger harmonic of the supplyy(t) = α(t)M(t)q , (2)where α(t) is a slowly varying complex amplitude, M(t) is a reference wave formcorresponding the fundamental harmonic (that can be obtained using clr), butq is a real number, not only an integer as in the case of the harmonics (and it canalso drift in time q(t) = q0 + δq(t), where δq(t) is small in comparison to q0). See[4] for details. The justification for this model is simply the success we have inremoving the interference as we show in figures 3 and 4.498 99 100 101 102−31−30−29−28−27−26−25Frequency [Hz]Log10 periodogram98 99 100 101 102−31−30−29−28−27−26−25Frequency [Hz]Log10 periodogram237 238 239 240 241−35−34−33−32−31−30Frequency [Hz]Log10 periodogram442 443 444 445 446 447−36−35−34−33−32Frequency [Hz]Log10 periodogram237 238 239 240 241−35−34−33−32−31−30Frequency [Hz]Log10 periodogram442 443 444 445 446 447−36−35−34−33−32Frequency [Hz]Log10 periodogramFig. 3. Decimal logarithm of the periodogram of 219 points of the prototypedata. (Left) Details of the lines near 99.5, 100.5, 239 and 445 Hz. (Right) Thesame data after removing the electrical interference.In figure 4, we compare zooms of the spectrogram. There we can see theperformance of both algorithms on the whole data stream, showing how the linesdue to electrical interference in the initial data are removed.We are interested in studying possible side effects of the line removal onthe statistics of the noise in the time domain. For the Glasgow data, the stan-dard deviation value is around 1.50 Volts. After the line removal, the standarddeviation is reduced to 1.05 Volts. This indicates that a huge amount of powerhas been removed. Further analysis reveals that values of skewness and kurtosisare getting closer to zero after the line removal. Values of skewness and kurtosisnear zero suggest a Gaussian nature. Therefore, we are interested in studyingthe possible reduction of the level of non-Gaussian noise. To this end, we take a5time [s]frequency [Hz](a)0 500 1000 1500 2000 2500 3000 3500740745750755760time [s]frequency [Hz](b)0 500 1000 1500 2000 2500 3000 3500740745750755760Time [s]Frequency [Hz](a)0 500 1000 1500 2000 2500 3000 3500110112114116118120Time [s]Frequency [Hz](b)0 500 1000 1500 2000 2500 3000 3500110112114116118120Fig. 4. Comparison of a zoom of the spectrogram. (Left) (a) is obtained fromthe prototype data. We can observe the wandering of the incoming electricalsignal. The other two remaining lines at constant frequency correspond to vi-olin modes. (b) The same spectrogram as in (a) after applying clr, showinghow the electrical interference is completely removed. (Right) (a) The pro-totype data with two anomalous lines near 114 and 116 Hz. (b) The samespectrogram as in (a) after removing the interference.piece of data and we study their histogram, calculating the number of events thatlie between different equal intervals. If we plot the logarithm of the number ofevents versus (x− µ)2, where x is the central position of the interval and µ is themean, in case of a Gaussian distribution, all points should fit on a straight lineof slope −1/2σ2, where σ is the standard deviation. We observe that this is notthe case. See figure 5. Although, both distributions seem to have a linear regime,they present a break and then a very heavy tail. The two distributions are verydifferent. This is mainly due to the change of the standard deviation. We canzoom the ‘linear’ regime and change the scale in the abscissa to (x − µ)2/(2σ2).Then, any Gaussian distribution should fit into a straight line of slope -1. We ob-serve that after removing the interference, it follows a Gaussian distribution quitewell up to 4σ. The original Glasgow data does not fit a straight line anywhere.60 20 40 60 80 100 120 140024681012(x−µ)2  [Volts2]log N0 2 4 624681012(x−µ)2/(2σ2)log NFig. 5. Comparison of the logarithm plot of the histogram for 3.2 × 219 pointsas a function of (x − µ)2. The circles correspond to the Glasgow data andthe stars to the same data after removing the electrical interference. In theright-hand corner, there is zoom of the original figure, but rescaled so that theabscissa corresponds to (x − µ)2/2σ2.We have also applied two statistical tests to the data: the chi-squaretest that measures the discrepancies between binned distributions, and the one-dimensional Kolmogorov-Smirnov test that measures the differences between cu-mulative distributions of a continuous data. In both tests, the significance prob-ability increased after removing the electrical interference, showing that theseprocedures suppress some non-Gaussian noise, although, generally speaking, thedistribution was still non-Gaussian in character. See [3] for details.3. References1. Abramovici A. et al. 1996, Phys. Lett. A 218, 1572. Robertson D.I. et al. 1995, Rev. Sci. Instrum. 66, 44473. Sintes A. M., Schutz B.F. 1998, Phys. Rev. D, 58, 1220034. Sintes A. M., Schutz B.F. 1999, Phys. Rev. D, 60, 062001

Removing Line Interference from Gravitational Wave Interferometer Data

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