I am not understanding your terminology but after reading it the gist of seem to be (without having specifically stated it) is that you want to AMPLIFY the signal. I really don't know what you mean by SIMPLIFY. There are basically only two terms that apply here, neither of which you have used. The first is AMPLIFICATION. This is what you need to do before applying the second term which is
SIGNAL CONDITIONING. After doing that , you could go on and apply an FFT , but let's keep it SIMPLE for the moment. You are
wasting your time trying to read the signal with the ADC on the arduino , unless you use the
analogReference(INTERNAL);
statement which will immediately limit your analog range to 0 to 1.1 volts, which it would seem is more appropriate for your signal.
Without any amplitude data for your signal (while you image looks nice, it has no amplitude data) there is no way to know what you are receiving in terms of analog values. Your code has Serial prints but you did not attach a serial monitor terminal capture file showing what you received. If you do that , we will have a better idea of what we are dealing with. It would seem that you need an analog input amplifier (op amp). We can talk about that , when we know more about the level of your signal.