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Below you will see a measurement of a human heart beat interval as a function of time. I take the Fourier transform of this data (but a much longer measurement, obviously). However, notice that the wave form is not symmetric on the upward path and the downward path. This is related to Respiratory Sinus Arrhythmia (RSA), which is perfectly health, although the exact relationship between RSA and the data points here escapes me right now. Anyway, if I take the Fourier Transform of this kind of data, what artifact will this asymmetry create? Suppose I don't want to look at the RSA but only the frequency. Will the RSA distort the central frequency of the Fourier transform? Could it create the bimodal peak in the frequency domain that I sometimes see? Should I correct the data and somehow even out this waveform before I take the transform?

Thanks.

heart beat

Chris
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  • I think that you should try to find some books and articles about pseudo-periodic time series. – md2perpe Sep 22 '20 at 21:59
  • How many "periods" do you have in your data? Has the frequency been relatively constant or varied a lot? Such things will probably affect how easy it is to do frequency analysis. – md2perpe Sep 22 '20 at 22:02
  • @md2perpe In a 40 minute measurement, there are hundreds of these periods. I can run the Fourier transform on the data in a few seconds, so computation time isn't a limit. I will look up pseudo-periodic. Thanks. However, maybe you could give me the quick story. Will this asymmetry lead to a separation of the fourier peak into two peaks? This would explain a lot. – Chris Sep 22 '20 at 22:12
  • I'm not at all worried about computation time. What I'm worried about is what it will mean doing Fourier analysis on a pseudo-periodic time series and how it's done best. – md2perpe Sep 22 '20 at 23:15
  • The data I showed is a small clip. The rest of the 40 minute measurement goes through some beats that are well behaved, and then it gets messy, and then it seems to lock back on to a well behaved pattern again. There is something very complex going on. If you want to know a little more neurology, look up Mayer waves. Someone suggested I read up on autocorrelation, which I did, but I found autocorrelation to be a difficult subject. I could send you a data set? and my Mathematica code. – Chris Sep 22 '20 at 23:44
  • I have no experience in analyzing time series and little experience with Mathematica, so I don't think that I'm the best person to help you. – md2perpe Sep 23 '20 at 00:13

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