A new ultrawide continuously tunable single-passband microwave photonic filter with very high resolution, is presented. It is based on a stimulated Brillouin scattering technique using a phase modulated optical signal and a dual-sideband suppressed-carrier pump. Results are presented which demonstrate a 1- to 20-GHz measured tuning range, together with continuous tuning, extremely high resolution with a 3-dB bandwidth of only 20 MHz, a single passband, shape-invariant tuning, and a high out-of-band rejection of 31 dB.