Interpreting FFT graph of a time serie

I've been trying to understand Fourier transform for some time now and I think I've perhaps finally got the idea now. I would like to check if the FFT can help me to determine the optimum lenght of the smoothing filter. For this reason , I have represented an example of a time series signal (measured at 5.9GHz) and I am struggling to interpret the results.

I know that the measured signal is a supperposition of large scale fading + small scale fading + noise. These component are equivalent in frequency domain to low frequency zone, middle frequency zone, and high frequency zone, repectively. The figure on the right is the FFT of the measured signal (bleu), FFT of the filtered signal with a filter of 135 ms (red) and FFT of the filtered signal with a filter of 294 ms (green). Can anybody help me to interpret the figure on the right? thank you in advance.

[Jakob B. Nielsen]

Interpretation of graphs is perhaps more a question relevant for a dedicated physics or math forum... You are right, however, that your received signal consists of your true signal (which can have contributions all over the frequency domain, not just low and middle), as well as some noise (which can also have contributions all over the frequency domain, although mostly its high frequency).

Your figure on the right confirms this. When you apply both filters, everything beyond 10 Hz goes close to 0; all high frequency signals are killed. However, you also seem to lose some of your signal between 1 and 10 Hz with the F=135 filter, and most of that same signal with your F=294 filter. This also comes into play on your original signal graph; around t=1400 ms ish, you have some modulation in your power, and your F=294 filter seems to "mean that out" so to speak, whereas the f=135 filter retains the "up down" look of your signal. I would be very hesistant before making any interpretation based on your green line - I would take the F=135 filter, or perhaps an even lower threshhold, maybe 100 ms, and work from there, unless you are very, very sure that the 1-10 Hz peaks are mostly noise.

[yusra Ch]

First thanks for the clarrification I really apreciate it

The filter is a moving average filter. I have a signal of 5000 ms and I have applied a filter of 135 ms. this means that the first 134 filtered data are iniciating the filter and the real filtered data start form 135 ms to 5000 ms (check this to get what I mean). So for example in case of filter F=135, I did plot(filteredsignal(135:end)). I have represented the graph you asked for.

Apart from this, I would like to tell you that the filtered signal correspond to large scale component. So how could its FFT have few values in low frequency zone?

Do you lnow any references which can help me to interpret these results correctly?

[Jakob B. Nielsen]

Yep, I get the moving average. That is also why you see the "shift" in the green curve on your original graph. I think a 100 ms filter gives a more accurate filtering of the high frequency noise while retaining the middle frequency data.

Another approach to this type of filtering that is a little more "crude" is, lets say if you have Y=fft(X) then go into your transformed data, find the indexes corresponding to the frequency axis and simply set everything above 10 Hz to 0. Then use ifft(Y) to get a "smoothed" version of your time domain signal. (I misread the x axis in my first response. Where I said 10 to 100 Hz I meant 1 to 10 Hz :) It makes plenty of sense that, if your component is large, then its frequencies are low. (Bigger things tend to move slower, and all).

In regards to further reading, I dont know... I mostly 'just' read a book and then did some trial and error.