The output of this program is a 2-column file; the first column is frequency and the second column is the noise in units of .

A couple of comments are in order here:

- 1. Even though we only need the modulus, for pedagogic reasons, we explicitly calculate both the real and imaginary parts of .
- 2.
The fast Fourier transform of , which we denote
, has the same units (meters!) as . As can be
immediately seen from
*Numerical Recipes*equation (12.1.6) the Fourier transform has units of meters-sec and is given by , where is the sample interval. The (one-sided) power spectrum of in is where is the total length of the observation interval, in seconds. Hence one has

(3.13.13) - 3. To get a spectrum with decent frequency resolution, the time-domain
data must be windowed (see the example program
`calibrate`and the function`avg_spec()`to see how this works).

- Author: Bruce Allen, ballen@dirac.phys.uwm.edu
- Comments: The IFO output typically consists of a number of strong line sources (harmonics of the 60 Hz line and the 180 Hz laser power supply, violin modes of the suspension, etc) superposed on a continuum background (electronics noise, laser shot noise, etc) In such situations, there are better ways of finding the noise power spectrum (for example, see the multi-taper methods of David J. Thompson [39], or the textbook by Percival and Walden [40]). Using methods such as the F-test to remove line features from the time-domain data stream might reduce the sidelobe contamination (bias) from nearby frequency bins, and thus permit an effective reduction of instrument noise near these spectral line features. Further details of these methods, and some routines that implemen them, may be found in Section .