Skip to main content

Periodicity Detection with DCT

6 posts / 0 new
Last post
tcalderw
tcalderw's picture
Periodicity Detection with DCT

 

I am working on an analysis project involving check stars in the AAVSO PEP program.  Check stars and their associated comps are supposed not to vary, but, inevitably, some do.  For this work, I want to screen out the variables.  I have been using the discrete cosine transform in VStar to look for periodic variation. The variability is obvious many times, but not always, and I am looking for some pointers as to how to interpret the DCT output.  In particular, I am unsure how high a power spike must be, relative to any others, to give confidence of a signal.  Obviously, the quantity and "cleanliness" of the data are factors. Attached are some light curves and DC transforms.

V441 Her appears to experince a regular variation, and the DCT has one nice power spike.  With rho Cas, the situation gets more complicated.  Is there real periodicity, or just noise?  CE Tau appears to have a smorgasboard of modest variations, and V1339 Cyg is somewhere in between.

Tom

 

David Benn
David Benn's picture
DC DFT

Hi Tom

Let me begin with a few initial comments.

  1. If you haven't yet, you may find some use from the user manual, from page 55.
  2. Grant Foster's Analyzing Light Curves: A Practical Guide is well worth getting a hold of if you haven't read it.
  3. There's a VStar CHOICE coming up in July. Like minded people getting together to talk and learn about light curve analysis has always seemed fruitful in previous courses. I've learned a lot from participants and other instructors during such courses myself.

​Let me quote Grant Foster (Analyzing Light Curves: A Practical Guide, p 125), as I often find myself doing:

Proper evaluation of statistical significance for periodogram analysis can be risky business. What power level is significant? That's a very thorny issue which for a long time was not properly appreciated.

Grant goes on to talk about significance in terms of chi square statistics, problems associated with treating these as indepedendent in the presence of different frequencies in irregularly sampled data, and that even with high power peaks on a periodogram (p 127), he reminds us that:

Significance doesn't demonstrate periodcity, it just negates the null hypothesis...

where the null hypothesis is that nothing but white noise is represented by the data. Also (on p 127), Grant says that:

...when we have a trend, it leads to exaggerated power in the periodogram at low frequencies. This is yet another reason to distrust periodogram peaks at low frequencies; they can be a sign, not of periodic fluctuation, but of long-term trend.

So given the above and declaring myself to still be a student of period analysis myself (it's a big topic!), I'll make some other comments in subsequent posts.

David

David Benn
David Benn's picture
A couple of comments and a question

Hi Tom

A couple of comments and a question.

Comments:

  1. Even before using DCDFT, its useful to look at the light curve on small and large scales. For example, what happens when you zoom in on the discrete blocks of data separated by a lack (e.g. seasonal) of observations? Can you observe periodicity on the small scale? The Mean time between observations plug-in (see Tool -> Plug-in Manager) can help with this.
  2. If you select a high power period, create a phase plot with that period. What does that look like (again, on different scales).

Questions:

  1. The V441 HER light curve is actually a check star that can be used for V441 HER photometry, right? The other light curves show "CHECK" at the end of each title.
  2. Can you supply data files for these datasets? Having the same data as you would allow us to carry out the same experiments.

Thanks.

David

tcalderw
tcalderw's picture
data files

 

David:

Yes, V441 Her is the check star - my oversight in labelling.  The data for all four stars may be found at

http://cantordust.net/CHK/

The four files were created by massaging a standard AAVSO ascii download.  In PEPHQ data, the check star magnitude is placed in the comment field.  I wrote a script to extract the check magnitude and put it in the place of the program star magnitude.  Be aware that check star magnitudes are not transformed or corrected for differential extinction.  I have already found one check star that has very interesting extinction symptoms in a year's time frame.

Will get to your comments in another post.

Tom

tcalderw
tcalderw's picture
New files

I found a problem in some of the files so they have been regenerated.  These are my "sf" or "standard filtered" files.  Observations with an uncetrtainty greater than 20mmag have been removed, and all data points more than three sigma from the mean have also been removed.  The ce_tau file was further prefiltered to remove observations with a different comp/check pair.

The power spike in v441_her is clearly the 1 year artifact.

Tom

 

 

 

 

David Benn
David Benn's picture
Periodicity in CHK star data

Hi Tom

I've been trying to get back this thread for awhile.

Being busy at work, having a couple of rounds of non-trivial dental work and family commitments have left less free time than I'd like lately. Also, I've been preparing a new VStar release (should be out within a week), which, by the way, will include the filter-from-current-plot-view feature you asked about and that has been on my list for quite awhile.

Here are some thoughts on the CHK star data after taking a further look:

  • V441 Her
    • I agree that the power spectrum spike aligns with the observation gaps. AoV period analysis (also to be formally released soon) backs this up. You can also see this with the Mean time between selection plug-in.
    • Visually, a long-term trend does appear to be evident. A polynomial fit (e.g. 3 degrees) highlights this. I don't think it's clear from DCDFT though. It's not just some sort of long term periodic trend; there appears to be an upward trend superimposed.
  • rho Cas
    • The highest DCDFT (with period range 1..500) spikes seem to be consistent with the "observation block" frequency here also but the power spectrum is certainly messy, as you say.
    • Grant's comment (above) about suspicion re: spikes at low frequencies may be relevant here (with DCDFT with frequency range).
  • CE Tau
    • The ~360 period again seems to align with the frequency of observation blocks.
    • The other low frequency spikes (with slightly lower power) don't produce phase plots with obvious periodicity. That's probably true for the other stars but I haven't checked yet.
  • 1339 Cyg
    • The yearly gap artifact comment applies here as well.
    • A longer term trend is apparent visually. It's not made more obvious with a polynomial fit of 3 degrees and 6 may be too much here. Looking at this with the Mean time between selection plug-in gives a period similar to the highest peak on the DCDFT Standard Scan.

David

Log in to post comments
AAVSO 49 Bay State Rd. Cambridge, MA 02138 aavso@aavso.org 617-354-0484