Next: Example: calibrateF program
Up: GRASP Routines: Reading/using FRAME
Previous: Function: GRnormalize()
Contents
Example: power_spectrumF program
0
This example uses the function GRnormalize() to produce a
normalized, properly calibrated power spectrum of the interferometer
noise, using the gravitywave signal and the sweptsine calibration information
from the frames.
The output of this program is a 2column file; the first column is
frequency and the second column is the noise in units of
.
To run this program, and display a graph, type
setenv GRASP_FRAMEPATH /usr/local/GRASP/18nov94.1frame
power_spectrumF > outputfile
xmgr log xy outputfile
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 meterssec and is
given by
, where
is the sample interval. The (onesided) power spectrum of
in
is
where is the total length of the
observation interval, in seconds. Hence one has

(4.11.26) 
This is the reason for the factor which appears in
this example.
 3. To get a spectrum with decent frequency resolution, the timedomain
data must be windowed (see the example program calibrate and the function
avg_spec() to see how this works).
A sample of the output from this program is shown in Figure .
Figure:
An example of a power spectrum curve produced
with power_spectrumF. The spectrum produced off a data tape
(with 100 point smoothing) is compared to that produced by the HP
spectrum analyzer in the lab.

Includes/power_spectrumF.tex
 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
multitaper methods of David J. Thompson [39], or the textbook
by Percival and Walden [40]). Using methods such as the
Ftest to remove line features from the timedomain 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 .
Next: Example: calibrateF program
Up: GRASP Routines: Reading/using FRAME
Previous: Function: GRnormalize()
Contents
Bruce Allen
20001119