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Example: optimal_filter program

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The following example program shows one way of combining the functions detector_site(), noise_power(), overlap(), and optimal_filter() to calculate the spectrum $\tilde Q(f)$ of the optimal filter function for a given pair of detectors. Below we explictly calculate $\tilde Q(f)$ for the initial Hanford, WA and Livingston, LA LIGO detectors. (We also choose to normalize the magnitude of the spectrum $\tilde Q(f)$ to 1, for later convenience when making plots of the output data.) Noise power information for these two detectors is read from the input data file noise_init.dat. This file is specified by the information contained in detectors.dat. (See Sec. [*] for more details.) The resulting optimal filter function data is stored as two columns of double precision numbers ($f_i$ and ) in the file LIGO_filter.dat, where $f_i=i\Delta f$ and $i=0,1,\cdots,N-1$. A plot of this data is shown in Fig. [*].

As usual, the user can modify the parameters in the #define statements listed at the beginning of the program to change the number of frequency points, the frequency spacing, etc. used when calculating $\tilde Q(f)$. Also, by changing the site location identification numbers and the output file name, the user can calculate and save the spectrum of the optimal filter function for any pair of detectors. For example, Fig. [*] is a plot of the optimal filter function for the advanced LIGO detectors.

Includes/optimal_filter.tex

Figure: Optimal filter function $\tilde Q(f)$ (normalized to 1) for the initial LIGO detectors.

Figure: Optimal filter function $\tilde Q(f)$ (normalized to 1) for the advanced LIGO detectors.
\begin{figure}\begin{center}
{\epsfig{file=Figures/f4b_sb.ps,angle=-90,width=5in}}
\end{center}\end{figure}


next up previous contents
Next: Discussion: Theoretical signal-to-noise ratio Up: GRASP Routines: Stochastic background Previous: Function: optimal_filter()   Contents
Bruce Allen 2000-11-19