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A programmable broadband Radio Frequency (RF) filter is designed using a Digital Micromirror Device (DMD), an Acoustooptic Tunable Filter (AOTF), and a Chirped Fiber Bragg grating (CFBG). This hybrid analog-digital optical design enables implementation of RF filters with higher number of taps in comparison with an AOTF-only RF filter design and improved RF tunability in comparison with a DMD-only design. A 3-tap RF filter is theoretically analyzed and experimentally demonstrated using a combination of analog and digital optical tap selection. Filter nulls recorded at 6.90, 6.945, and 6.99 GHz show the tunability improvement with the hybrid design. Implementation of higher tap count filters can lead to similar improvements in filter tunability and pass-band and stop-band characteristics.