Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: searchforperiod
Posted:
Sep 19, 1999 2:17 AM


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 longdrawnout 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.mathematicajournal.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@smc.vnet.net>, Andre Hautot <ahautot@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 rmodvalues 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 PhysiqueB5 >SartTilman >4000 Liege >Belgium > >Tel: 32 4 366 36 21 >Fax: 32 4 366 45 16 >Email: ahautot@ulg.ac.be >
 from  John Tanner home  john@janacek.demon.co.uk mantra  curse Microsoft, curse... work  john.tanner@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.



