Re: searchforperiod

• To: mathgroup at smc.vnet.net
• Subject: [mg19866] Re: searchforperiod
• From: John Tanner <john at janacek.demon.co.uk>
• Date: Sun, 19 Sep 1999 01:20:48 -0400
• Organization: Peace with the World
• References: <7rnkao\$elp@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

There is a very nice illustration of "Spectral Analysis of Irregularly
Sampled Data" in the In And Out section of Mathematica Journal vol 7
issue 1 (winter 1997), with a real case of pulsar data with not only
irregular spacing but also large gaps.

Unfortunately this issue was immediately prior to the long-drawn-out
break in publication of this extremely useful publication.  The later
issues (vol 6 and vol 7 no 1) have not yet reached MathSource, even
though vol 7 no. 2 is directly available on the Web page

http://www.mathematica-journal.com

I am not sure what the copyright status is so I will not will not post
here...

Good luck.
John

In article <7rnkao\$elp at smc.vnet.net>, Andre Hautot <ahautot at ulg.ac.be>
writes
>Hello,
>Is Mathematica able to solve the following kind of problem?
>I have computed the time evolution of a certain quantity, say rmod, (the
>details of the physical problem which leads to them are unimportant).
>The results are contained in a list like this :
>Table[{t[i],rmod[i]},{i,0,5000}]
>To fix the ideas here is the beginning of a typical list :
>{{0,1.},{2.02484567313,1.30384048104},{5.44775639416,2.34594834824},
>{11.921842635,4.27850743029},{23.2431295354,7.13760085727},
>{41.2272127052,10.9087937072},{67.6554674978,15.562780576},
>{104.248787003,21.0622014538},{152.649762838,27.3628881652},
>{214.407985645,34.4143233727},{290.966976416,42.1600354445},
>{383.652320768,50.53803291},{493.660902853,59.4812881541},
>{622.051243359,68.918265984},{769.734982324,78.7734911707},...}
>The rmod-values increase during 35 steps and they decrease during the 35
>next steps, returning near the initial value of one after 70 steps, and
>so on. Similarly, the time spacing increases during 35 steps, decreases
>during the 35 next steps and so on.
>The coordinates are known with arbitrary high precision (50 figures for
>example or more if you need)
>The graph of rmod versus t is obtained, as usual, by
>ListPlot[Table[{t[i],rmod[i]},{i,0,5000}]]
>It seems to be periodic. How can verify such a conjecture and obtain a
>high precision value for the period?
>Since 70 points are contained within a period one understands that 5000
>points approximatively correspond to 71 full periods. Note however, and
>this seems to be the main difficulty, that the time abscissas of the
>points are not equally spaced. Otherwise discrete Fourier transform
>should be convenient.
>The classical litterature generally deals with equally spaced abscissas.
>Has somebody heard of a generalized algorithm?
>Of course I could interpolate the function, rmod versus t, but the
>accuracy of the period obtained in that way is ridicoulusly low compared
>to the, say 50 figures, injected in the data. Thanks in advance.
>--
>Andre Hautot
>Universite de Liege
>Physique Generale
>Institut de Physique-B5
>Sart-Tilman
>4000 Liege
>Belgium
>
>Tel: 32 4 366 36 21
>Fax: 32 4 366 45 16
>Email: ahautot at ulg.ac.be
>

--
from -   John Tanner                 home -  john at janacek.demon.co.uk
mantra - curse Microsoft, curse...   work -  john.tanner at gecm.com
I hate this 'orrible computer,  I really ought to sell it:
It never does what I want,      but only what I tell it.

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