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.