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.