Reflections from movable, dynamic acoustic gratings in polarization maintaining (PM) fibers are employed in the long variable delay of periodic, isolated pulses. The gratings are introduced by stimulated Brillouin scattering (SBS) interaction between two counter-propagating pump waves, which are spectrally detuned by the Brillouin frequency shift of the PM fiber and are both polarized along one of its principal axes. The gratings are interrogated by the reflections of read-out signals that are polarized along the orthogonal principal axis. High-rate phase modulation of both pump waves by a pseudo-random binary sequence introduces dynamic gratings that are both localized and stationary, at specific locations in which the modulated pumps are correlated. The separation between adjacent correlation peaks can be made arbitrarily long. Long variable delays are readily obtained by scanning the grating along the fiber, via changing either the length or the rate of the modulation sequence. At the same time, the short length of the gratings, on the order of a cm, accommodates the delay of broadband pulses. The technique is therefore free of the delay-times-bandwidth product limitation that undermines the performance of SBS-based 'slow light' delay: we report the delay 1-ns long pulses by as much as 770 ns. In addition, the combined reflections from two dynamic gratings with a variable separation are used to implement radio-frequency photonic filters of tunable free spectral range. At the current stage, the technique is restricted by noise from residual scattering that takes place outside of the correlation peaks. Hence, it is thus far limited to the processing of repetitive signals, for which the noise may be effectively averaged out.