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Flat-top sharp optical filters of gigahertz bandwidth are realized using stimulated Brillouin scattering (SBS). Pump chirp control of the SBS process enables versatile programming of the filter shape and bandwidth. The operating wavelength of the filters is tunable, and their frequency response is inherently aperiodic. Full widths at half maximum of 1.3-2.5 GHz are demonstrated, with a filtering selectivity up to 30 dB and an rms ripple of 0.5-1 dB. The filters are used to convert double sideband to single sideband (SSB) modulations for 1-GHz-wide linear-frequency-modulated (LFM) signals of arbitrary radio-frequency carrier. Such SSB modulation is highly instrumental for photonic implementations of true time delay, for example, in antenna beam-forming. The peak-side-lobe ratio of the processed LFM signal was -32 dB; its main lobe was broadened by only 4%. The integrated side-lobe ratio, which is limited by noise from spontaneous Brillouin scattering, was better than 21 dB, which is a sufficient value for most systems. The technique results in a large modulation index and does not lead to harmonic distortions.