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Some physicists are in the habit of calling this optimal filtering method simply “Wiener filtering.” However, in the larger signal processing community, “Wiener filtering” refers to an altogether different technique. In order to avoid confusion we call this method “matched filtering.”
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Some physicists are in the habit of calling this optimal filtering method simply “Wiener filtering.” However, in the larger signal processing community, “Wiener filtering” refers to an altogether different technique. In order to avoid confusion we call this method “matched filtering.”
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13
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One might try to avoid using a large family of templates by finding a set of basis functions on which to expand the signal. However, this technique does not work very well for inspiral chirps (and many other types of signals) because the number of basis functions required to achieve nearly optimal signal-to-noise ratio is comparable to the number of templates
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One might try to avoid using a large family of templates by finding a set of basis functions on which to expand the signal. However, this technique does not work very well for inspiral chirps (and many other types of signals) because the number of basis functions required to achieve nearly optimal signal-to-noise ratio is comparable to the number of templates.
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B. F. Schutz, in The Detection of Gravitational Radiation, edited by D. Blair (Cambridge University Press, Cambridge, England, 1991), p. 406
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Strictly speaking, the upper limit of integration in the noise moments should be the lesser of the sampling frequency and the “coalescence frequency” (Formula presented) which represents (roughly) the point where adiabatic inspiral of the bodies ends. Both of these frequencies are much greater than (Formula presented) and thus our approximation is quite good, except on the high-mass end of template parameter space where (Formula presented) becomes comparable to (Formula presented). Since most templates populate the low-mass end of parameter space, the effect on the total number of templates is small. However, detailed algorithms for placing high-mass templates will have to take (Formula presented) into account—which may be problematic since (Formula presented) is poorly known when the binary components have comparable masses. Using an infinite upper frequency is safe in the sense that the errors cause us to space templates slightly more closely than needed, i.e., we slightly overestimate the loss of signal-to-noise ratio
-
Strictly speaking, the upper limit of integration in the noise moments should be the lesser of the sampling frequency and the “coalescence frequency” (Formula presented) which represents (roughly) the point where adiabatic inspiral of the bodies ends. Both of these frequencies are much greater than (Formula presented) and thus our approximation is quite good, except on the high-mass end of template parameter space where (Formula presented) becomes comparable to (Formula presented). Since most templates populate the low-mass end of parameter space, the effect on the total number of templates is small. However, detailed algorithms for placing high-mass templates will have to take (Formula presented) into account—which may be problematic since (Formula presented) is poorly known when the binary components have comparable masses. Using an infinite upper frequency is safe in the sense that the errors cause us to space templates slightly more closely than needed, i.e., we slightly overestimate the loss of signal-to-noise ratio.
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