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##

Example: `snr` program

0
As mentioned in Sec. , an interesting
question to ask in regard to stochastic background searches is:
``What is the theroretically predicted signal-to-noise ratio after a total
observation time , for a given pair of detectors, and for a given
strength of the stochastic background?''
The following example program show how one can combine the functions
`detector_site()`, `noise_power()`, `overlap()`, and
`calculate_var()` to answer this question for the case of a
stochastic background having a constant frequency spectrum:
for
.
Specifically, we calculate and display the theoretical SNR after
approximately 4 months of observation time (
seconds),
for the initial Hanford, WA and Livingston, LA LIGO detectors, and for
for
.
(The answer is
, which means that we could say, with greater
than 95% confidence, that a stochastic background has been detected.)
By changing the parameters in the `#define` statements listed
at the beginning of the program, one can calculate and display the
signal-to-noise ratios for different observation times , for different
detector pairs, and for different strengths of the stochastic
background.

Note: Values of and should be chosen so that the whole
frequency range (from DC to the Nyquist critical frequency) is included,
and that there are a reasonably large number of discrete frequency values
for approximating integrals by sums.
The final answer, however, is independent of the choice of and
, for sufficiently large and sufficiently small.

Includes/snr.tex

** Next:** Example: omega_min program
** Up:** GRASP Routines: Stochastic background
** Previous:** Function: calculate_var()
** Contents**
Bruce Allen
2000-11-19