# Determining Periodicity with Fourier?

Note: This question has previously 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!

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?

• I am at a wedding at the moment and won't be able to help for a few days. However what you need is a harmonic cursor. This will show if your peaks in the spectrum are multiples of a fundamental frequency. By eye your data does not look like it is periodic. Do you have other reasons to think it is? – Hugh May 20 '17 at 7:04
• I suggest you try first with some made up data that has a strong, known periodicity. This will let you get familiar with the analysis before trying it on your real data. – Simon Woods May 20 '17 at 9:18