Filter of differentiated responses

I'm trying to filter out the noise in a displacement response. I typically do a 0-50 Hz filter to get rid of all the noise. This gets rid of some 60 Hz shit as well as some other noise past 100 Hz. The problem is with this project, I need to differentiate the response to get velocity and when I do so, all that small amplitude noise looks way worse.

Do I filter it before I differentiate and after? Just after? Just before? If I differentiate after, I can't use the 0-50 Hz range because the frequency domain looks much different. Any advice would be very helpful.

Sample rate is normally 1024 Hz by the way.

>>1
Disclaimer: I have no idea of what is a displacement response. I imagine a spring going up and down.

care to give a sample?

And, if you need to get velocity, why do you filter the noise? Wouldn't that be helpful to determine velocity? Do you filter noise just because you don't like it or it is because a measuring error?

It is too complex for you to use brownian motion to determine what noise is really noise?
http://arxiv.org/pdf/1302.5324v2