psd

Power Spectral Density Fast Method (Application).

Application psd calculates the power spectral density of a time series, by using a FFT algorithm. It requires one input series. It is run in the Question/Answer user interface by typing:

[n]Xronos> psd

[n]Xronos> psd [series1]

[n]Xronos> psd[/qualifier1/qual2/... etc]  [series1]

More on psd

The newbin time must correspond to an integer multiple of the maximum bin time. The default newbin time is either the maximum bin time (if fewer than 4096 newbins are expected) or the integer multiple of it which will produce a single interval with number of newbins <4096. The FFT algorithm requires that the number of newbins per interval be a power of 2. The average count rate in each interval is subtracted from all newbins, and gaps and rejected newbins are replaced with zeroes, before the power spectrum is calculated.

The power spectrum error bars are obtained either by propagating the theoretical error bars of the spectra from individual intervals (from the relevant chi-square distribution) or by evaluating directly the standard deviation of the average of the power in each frequency bin from different intervals. This depends on whether the specified number of intervals per frame is, respectively, smaller or larger than the value of global parameter number 9 (default =5).

Error bars are plotted by default only if two or more power spectra are averaged. Sidelobes and other effects introduced by windows, data gaps etc. can be studied by analysing the exposure profile of the time series. This is done by setting global parameter number 10 to 1.

Normalisations

The analysis normalisation flag, specified by global parameter number 11, has the following meaning for application psd:

• =0 power spectra are normalised by dividing by the number of good newbins in each interval.
• =1 (d/f); power spectra are normalised such that the (white) noise level expected from the data errors, corresponds to a power of 2 (note that a correction of the data errors for instrument dead time effect might be necessary to bring the expected noise level to 2; See e.g. the EXOSAT ME light curves)
• =2 power spectra are normalised such that their integral gives the squared rms fractional variability (therefore the power spectrum is in units of (rms)/Hz). The expected (white) noise level must be subtracted to obtain the rms fractional variability of the series. This level is written out by psd (note that it might be necessary to correct the white noise level: see e.g. EXOSAT ME light curve. Other corrections for instrumental dead time effects, e.g. the energy dependent correction of the source rms in EXOSAT ME light curves, must be handled separately). The squared rms is normalised by (avg); if the light curves are not background subtracted, to get the source squared rms fractional variability the power spectrum must be multiplied by (avg)/(avg-bkgd). Alternatively the background can be subtracted from the light curves by using input file option sd.
• =-1 as =1, but the expected white noise level is subtracted
• =-2 as =2, but the expected white noise level is subtracted