
The fast Fourier transformFourier techniques are widely used in science. The basic idea of these techniques is that just about any variation can be expressed as the sum of regular sine waves with different periods. This is true even if the variation is not periodic. However, for a periodic signal, only relatively few frequencies will be present (frequency is the inverse of period here). Using Fourier transforms does have complications, however, because we really need continuous data. The basic "compromise" technique is the fast Fourier transform (FFT), which settles for equally spaced data points. The output of an FFT is normally called a periodogram or power spectrum, because it gives the "power" at any particular frequency (period). The program powerts calculates the power spectrum of a single time series taken from a Ginga data file. The results are written to a file so they can be displayed or analysed further. An example of powerts is given below:
qcl>powerts ** POWERTS Version 1.1 Mon Oct 6 20:58:37 1997 ** POW_DATIN Data file name =mkn335_91a.time Number of time samples 393 Number of PHA samples 1 Number of IDENTs 2 Sample duration : 128 POW_IPHA PHA subscript = 1 = POW_IDENT Ident subscript = 1 = Number of missing samples 305 Mean data value 0.0005417928438295 Dimension chosen for DFT 1024 Noise power estimated from variances 172.33609260212 (cts/sec)**2/Hz Average power in spectrum 153.3974091716 (cts/sec)**2/Hz qcl> The program powerts writes the results to a file with the same root name as the input time series, but with an extension ".pspe" (i.e. mkn335_91a.pspe in the above example). The QCL procedure pl_power.qcl can be used display the power spectrum. The following is an example of its use:
qcl>.pl_power QCL_CL Power spectrum file name = mkn335_91a.pspe = QCL_CL graphics device = xw = QCL_CL Title for plot = mkn335_91a.pspe = Starting /soft1/xanadu/OSF1_4.0_alpha/bin/pgxwin_server. Graphics device /xw open HDS_NODE mkn335_91a.pspe GRP_XMODE 0 GRP_XNAM1 FREQUENCY GRP_XNAM2 DUMMY1 GRP_YMODE 0 GRP_YNAM1 POWERSPECTRUM GRP_YNAM2 DUMMY2 LABX X LABY Y Number of data points 512 Range of data points X 0.762939E05 to 0.390625E02 Y 0.221402 to 1188.87 QCL_CL Bottom of Y axis = 86.168046301060 = QCL_CL Top of Y axis = 4755.4800000000 = QCL_CL Low X = 7.62939453125000E06 = QCL_CL High X = 3.90625000000000E03 = Mapping 7.6293945E06 3.9062500E03 86.16805 4755.480 Position 0.762940E05 172.336 Position 0.390625E02 172.336 Device still open ... Type CLOSE to finish qcl> Note that periods of ~96 minutes (frequency of ~1.7 x 10^{4} Hz) are spurious; that is about the orbital period of the Ginga satellite. [Next: Miscellaneous Apps.] [Previous: DisplayFolded] [Back to Timing Analysis] 


