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A hybrid phase-time shifter structure is proposed, for the first time, for widely tunable microwave photonic filters and phased array antennas. It is based on an optical frequency comb in conjunction with a diffraction-based spatial light modulator, which can simultaneously form true time delays and radio-frequency (RF) phase shift functions within one device. Experimental results verify the new concept by synchronously demonstrating the tunable hybrid phase-time shifts over a range of 360° and up to 64 ps. A 17-tap microwave bandpass filter, based on the hybrid shifter structure, is also presented. It is shape-invariantly tuned across the free spectral range of 7.92 GHz, and operates at up to 20 GHz without any RF distortion.