Proposed and experimentally demonstrated is a new class of optimal fibre Bragg grating (FBG) filters for pulse temporal differentiation, which is suited to process waveforms with a spectral extent up to 100 GHz. In particular, high-quality first- and second-order differentiation of 20 and 12.5 Gbit/s pulse trains are demonstrated using first- and second-order 50 GHz bandwidth FBG filters, synthesised by a layer-peeling algorithm and fabricated by continuous writing in hydrogen-loaded standard telecommunication optical fibres.