# FFT returns large low-frequency power - probably because signal is interpreted as containing cycles that do not fit. How is this called?

So I have a large number of signals like the one in the first picture below and I would like to extract and compare the frequencies within them. I applied a Fourier transform which resulted in results like those shown in the second picture. The large power of very low frequencies suggests to me that the signals include something that is interpreted as being of such low frequency that one cycle does not fit into the time window (which is 1.2 seconds). I hence applied a High pass filter with different cut-offs and the pattern is gone after using a HPF with 2Hz (last picture).

I have two questions about this: 1) Does my reasoning make sense? 2) How is such an effect / pattern called?

I need to include this in a paper I am currently drafting and hence am especially unsure about question 2). My supervisor's first reaction was that these are edge-effects, but looking into them I feel like that is not really what is at work here.

Thank you!!

1) Yes, your reasoning makes sense.

2) The usual way to get rid of this is called "detrending". Generally, the best fit line is subtracted from the data. This zeroes out your DC bin and reduces the "power" in the lower frequencies.

I have a different suggestion for you to try. Apply the smoothed difference technique described in my blog article Exponential Smoothing with a Wrinkle. This will zero out the DC, greatly reduce any of the low frequency components, leave your midrange pretty much alone, and greatly dampen your high frequency/noise. The pure tones will be phase shifted, but their frequencies will be unaltered. Their amplitude will also be somewhat attenuated but the article gives your the formula to recover the original amplitude.

• Thank you! I tried detrending using the Matlab function for it, it pulled my signal to be around zero, but it did not change the results of the Fourier transform. Thanks also for suggesting and directing me to the exponential smoothing technique - however I do not think that it would be the best fit for my issue because I am interested in the full frequency range and it sounds like the technique modulates for example high frequencies (which are of interest). May I ask how you would call the 'issue' I am experiencing? – Mah1510 Feb 11 '19 at 12:15
• @Mah1510,What would you say your "issue" is? A visual inspection of your data shows there seems to be sort of a sine wave swoop to it. Maybe a cycle and quarter. This would explain a high value in bins 1 and 2. Likewise, a detrending is as if you are removing just a partial cycle, it should not affect the higher bins much so I am puzzled by your comment "but it did not change the results of the Fourier transform". It's not supposed to, only remove distortion at the lower end when an oscillating process is riding a linear trend. – Cedron Dawg Feb 11 '19 at 21:48
• (continued) If you want to accentuate higher frequencies, you can use a simple difference filter, $y[n] = x[n] - x[n-1]$. This will kill your DC and amplify your high frequencies compared to the low ones. – Cedron Dawg Feb 11 '19 at 21:48

Your reasoning sounds correct. It is impossible to see from your example what frequency that low frequency is.

If the frequency of the phenomenon is 0 Hz, then it is simply a direct current (DC) bias that affects the first bin of the discrete Fourier transform (DFT). If none of your signal of interest is in that bin then you can simply ignore it in your analyses or set it to zero. If your signal never goes to negative values, then you have DC bias (although there could be other low frequencies).

• Thank you! So if I understand this correctly DFT results might be just due to the fact that the signal is not 'centered' at zero, but at 0.5? It has practical meaning that it is at 0.5, hence I'd like to keep it this way. So I would just apply the HPF and argue that the 'baseline' at 0.5 led the DFT to treat it as a DC bias and hence we needed to apply the filter - does this make sense? – Mah1510 Feb 11 '19 at 12:15
• @Mah1510 yes that sounds correct. – Olli Niemitalo Feb 11 '19 at 14:08