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# 6. How does Einstein@Home search for a signal?

Our gravitational-wave detectors are remarkably sensitive instruments. In fact they are the most sensitive detectors ever built, and incorporate cutting-edge technology. But their output is still dominated by "noise" arising from many different effects. These include seismic ground motion, thermal vibrations of the atoms making up the detector optics and suspensions, and the particle-like quantum behavior of the laser light. (This last type of noise is often called "shot noise"). The problem of gravitational-wave data analysis has been described as 'trying to hear a single flute in the middle of a heavy-metal concert' because we need to identify a 'known' waveform hidden in the noise of the detector.

The standard method used to search for signals in noise is known as 'matched filtering' or 'optimal filtering' [29]. One can prove mathematically that matched filtering is the optimal linear technique to search for a known signal embedded in additive noise. The idea is a simple one. If we know the exact waveform of the signal, we multiply the output of the detector by this waveform, and average over time T. The resulting integral has two terms. There is a term whose expected value grows like the square root of time T, arising from random noise in the instrument. (This process is known as a a random walk 6.1 [30,31].) Then there is another term which grows in proportion to time T, which is due to the pulsar signal. So if we have enough data, and enough computing power, and knew the exact sky position and frequency of the pulsar, we could always choose T big enough that the term due to the source dominates the term due to the instrument noise. Of course, T is limited to the amount of time we actually collect data, so the pulsar signal needs to have a certain minimum strength to be detectable in this finite time.

In summary, matched filtering permits us to find a very small signal buried in noise, provided that (1) we have a long enough data set and (2) we know the exact waveform of the signal that we are searching for. However, Einstein@Home searches for signals from unknown sources, and therefore the exact waveform is not known: its shape depends on the sky-position (as discussed in the previous section) and on the intrinsic frequency evolution of the source. As a consequence, a search for unknown sources needs to try matched-filtering for many different waveforms, covering the full range of possible sky-positions and intrinsic frequency evolutions. This is reason why such 'wide-parameter' searches are extremely expensive in required computational power.

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 Einstein@Home S3 Analysis Summary Last Revised: 2007.03.28 08:59:23 UTC Copyright © 2005 Bruce Allen for the LIGO Scientific Collaboration Document version: 1.132