How to filter pulse like jumps in a signal?
I think that you will not be able to get acceptable results with linear filtering because the impulse noise covers the whole frequency range. You may want to look into nonlinear filtering techniques. As a first (and simple) approach try median filtering: http://en.wikipedia.org/wiki/Median_filter

I think if you optimize the window size of the median filter you should get better results than with purely linear filtering.