You have a signal with a small amplitude but in almost the same frequency as a noise with a large amplitude. Then the signal to be measured is destroyed - except you have additional knowledge, e.g. that the breathing is periodic, while the movement is not. Then a Fourier analysis will help you to tell the different parts of the signals.
Please post some examples to let the readers guess an impression, what the actual problem is. "Bring out the breathing" is not completely clear, and what exactly are "large swings".
