       searchforperiod

• To: mathgroup at smc.vnet.net
• Subject: [mg19759] searchforperiod
• From: Andre Hautot <ahautot at ulg.ac.be>
• Date: Wed, 15 Sep 1999 03:53:08 -0400
• Organization: ULg
• Sender: owner-wri-mathgroup at wolfram.com

```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

```

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