Bio-signal discontinuity after FIR filtering I'm filtering respiration signal. I have a signal of duration equal to 10 minutes, so I decided to divided it into period of 10 s. I filtered each epoch with FIR filter, but I have discontinuities each 10s.
I attached an example.
I can not filter all the signal at once by the theory, so how can avoid discontinuity?
You need to maintain the filter state. For an FIR filter that's fairly easy since the state are just the last $N-1$ samples if your previous input, where $N$ is the FIR filter length.
Most filter functions have a built in option for doing this. If you don't have it just do the following:

Prepend you current frame with the $N-1$ last samples of the previous frame
Run the filter
Throw away the first $N-1$ samples of the output.