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We demonstrate a millimeter-wave (mm-wave) synthesizer based on spectral filtering of the plusmn2 harmonics of a phase-modulated (PM) laser. Optical filters with narrow passband, good extinction ratio and tunable peak wavelengths are obtained by introducing distributed phase-shifts in a chirped fiber Bragg grating (CFBG) using current-controlled heating elements. Detailed modeling and analysis of the filter is performed using the effective index model and coupled-mode theory. We present several optimization criteria to customize the grating design and two experimental configurations are tested. The more flexible approach is based on a fiber Mach-Zehnder structure with a tunable phase-shifted CFBG in each arm. We show generation of mm-wave from 33 GHz to 48 GHz, with a maximum frequency limited by the bandwidth of the photodetector.