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We describe an optical Fourier transform pulse shaper based on a combination of a diffraction grating and a reconfigurable array of digital micromirrors. The pulse shaper allows for adjustment of separation between consecutive pulses within a pulse burst and the length of the burst. Pulse separation, burst length, and number of pulses can be dynamically reconfigured by changing the periodic pattern imposed to the array of digital micromirrors. Experimental results on binary intensity modulation are in excellent agreement with basic design relations describing the spectral and temporal characteristics of the pulse shaper.