The manipulation of dynamic Brillouin gratings in optical fibers is demonstrated to be an extremely flexible technique to achieve, with a single experimental setup, several all-optical signal processing functions. In particular, all-optical time differentiation, time integration and true time reversal are theoretically predicted, and then numerically and experimentally demonstrated. The technique can be exploited to process both photonic and ultra-wide band microwave signals, so enabling many applications in photonics and in radio science.