How detect and filter noise from signal
Just "eyeballing" your signal, it looks like the interesting things are all down below 1Hz.  The peaks in your signal browser diagramm seem to be spaced at every 5 to 10 Seconds, which would be 0.1 to 0.2 Hz.  Your spectrum plot goes from zero to 25 Hz, and doesn't show anything really interesting.

Try zooming in on the spectrum and see what lies below 1 Hz.  Yo may well find that the signal itself lives down in the very low frequencies, and that separating the noise from the signal is as simple as using a low pass filter.