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Example: snr program

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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 $T$, 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: $\Omega_{\rm gw}(f)=\Omega_0$ for $f_{\rm low}\le f \le f_{\rm high}$. Specifically, we calculate and display the theoretical SNR after approximately 4 months of observation time ( $T=1.0\times 10^7$ seconds), for the initial Hanford, WA and Livingston, LA LIGO detectors, and for $\Omega_0=3.0\times 10^{-6}$ for $5\ {\rm Hz}\le f\le 5000\ {\rm Hz}$. (The answer is ${\rm SNR}=1.73$, 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 $T$, for different detector pairs, and for different strengths $\Omega_0$ of the stochastic background.

Note: Values of $N$ and $\Delta f$ 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 $N$ and $\Delta f$, for $N$ sufficiently large and $\Delta f$ sufficiently small.

Includes/snr.tex


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