Piotr Jaranowski
Institute of Theoretical Physics
University of Białystok
Lipowa 41
15-424 Białystok, Poland
Andrzej Królak
Max-Planck-Institut für Gravitationsphysik
Am Mühlenberg 1
D-14476 Golm, Germany
on leave of absence from:
Institute of Mathematics
Polish Academy of Sciences
Śniadeckich 8
00-950 Warsaw, Poland
The article reviews the
statistical theory of signal detection in application to
analysis of
deterministic gravitational-wave
signals in the noise of a detector. Statistical foundations
for
the theory of signal detection
and parameter estimation are presented. Several tools
needed
for both theoretical evaluation
of the optimal data analysis methods and for their
practical
implementation are introduced.
They include optimal signal-to-noise ratio, Fisher matrix,
false
alarm and detection
probabilities,
-statistic, template placement,
and fitting factor. These
tools apply to the case of
signals buried in a stationary and Gaussian noise. Algorithms
to
efficiently implement the optimal
data analysis techniques are discussed. Formulas are
given
for a general gravitational-wave
signal that includes as special cases most of the
deterministic
signals of interest.
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