0

Note: This question has been marked as a duplicate of What do the X and Y axis stand for in the Fourier transform domain?. While the answer will likely have an overlap, so the question should be linked, I see the context and background as sufficiently different to warrant a separate question for anyone who is having a similar issue to what I'm having; and it has been noted that some additional information may be useful in answering this question.

I'm trying to find the periods of time series and was directed toward Fourier analysis. I am having a hard time understanding what is going on in ref/Fourier > Applications > Frequency Identification. Would anyone be able to explain, or direct me to an explanation somewhere? Thank you!

EDIT: Here is some sample data. It is a list representing a 55-year time series with one measurement per year, for a total of 56 points. What I have been doing is subtracting off the seventh-order polynomial regression and running the absolute value of the fourier on both the raw data and the data with the overall trend removed.

{0.,0.,0.,0.00118064,0.,0.00437956,0.,0.,0.0035461,0.00107875,0.00715015,0.00501505,0.0040568,0.00294985,0.00514933,0.00609137,0.0047619,0.00100806,0.00196464,0.000882613,0.00187793,0.00282486,0.00172563,0.000807754,0.00318218,0.00233645,0.0015528,0.00149365,0.000776398,0.000688705,0.00198151,0.00236593,0.00225904,0.00149589,0.,0.00332889,0.00179748,0.00126743,0.00289352,0.00218103,0.00265675,0.00104275,0.00509495,0.00292887,0.00161616,0.00327869,0.00413793,0.00223928,0.00502067,0.00434075,0.00392465,0.00469373,0.00595745,0.00521147,0.00567752,0.00293255}

Note, for the Fourier graphs below, the data have not been padded to the right; should I do that?

enter image description here

enter image description here

enter image description here

enter image description here

user3769181
  • 153
  • 1
  • 7
  • 1
    related – andre314 May 14 '17 at 19:50
  • 2
    I have put some basic information on Fourier here. Let me know if this helps of if you need more. – Hugh May 14 '17 at 21:02
  • @Hugh: Thank you, that's some very helpful information; though one thing I'm actually still not clear on is, what do each of the axes represent with standard Fourier in Mathematica? – user3769181 May 15 '17 at 22:13
  • @andre: That looks like exactly what I'm looking for. Is it necessary to pad to the right? And I'm not clear on how you converted the position of the peak to the period. Thank you! – user3769181 May 15 '17 at 22:14
  • I have tried to add some extra information to the article here. However, I think you need to describe your difficulty more precisely for me to help you. Try to give us an example of your problem. – Hugh May 16 '17 at 11:30
  • @Hugh, I'll update with some sample data as soon as I'm able, but I think I've mostly got it. If my Fourier results have many (6+) peaks, does that mean there's no specific period to the function? And is there a way to convert a given peak to a trig function that can be overlaid on the graph of the source data? – user3769181 May 17 '17 at 20:46
  • I think we need to see your spectra. Are your peaks harmonics I.e. multiples of a fundamental frequency. ? A trig representation is possible. – Hugh May 17 '17 at 20:51
  • @Hugh: Okay, I just updated my post to include a sample series (I'm working with well over 50 series, so I promise, you don't want them all), and I'm about to upload graphs for that sample. – user3769181 May 18 '17 at 02:29
  • I had a look at the data. I do not see a strong periodic behaviour either in the original data or in the Fourier transform of the data. If you look at your second plot what period do you think you see in the data? If you have 1) reason to suspect a periodicity 2) other evidence for periodic behaviour or 3) wish to force a periodic behaviour into the data then you probably could. This question has been marked as a duplicate so I can't show my investigation. If you wish to continue along these lines then I suggest you start a new question with a new heading. – Hugh May 18 '17 at 15:29
  • @Hugh, I just made a new question here: https://mathematica.stackexchange.com/questions/146456/determining-periodicity-with-fourier – user3769181 May 20 '17 at 00:45

0 Answers0