A high-resolution low-noise single-laser photonic filter that can operate to high frequencies is presented. It is based on the single-sideband suppressed carrier electro-optic modulator frequency shifter that enables high frequency shifts to be realised in a frequency shifting amplified recirculating delay line loop structure. Designs to minimise the unwanted spurious harmonic frequencies generated by the single-sideband suppressed carrier modulator are presented. Simulations are presented to investigate the gain spectrum limitations that arise from the bandwidth narrowing of the erbium-doped fibre amplifier due to the important self-filtering effects that occur when the signals circulate inside the frequency shifting amplified recirculating delay line loop, and new techniques to counter this effect and to realise a large number of taps is presented. Experimental results demonstrate a high-resolution microwave photonic filter with a Q of 107 and with low-noise performance.