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A Tunable optoelectronic oscillator (OEO) implemented employing a high-Q spectrum sliced photonic microwave transversal filter without using any electronic microwave filters is proposed and experimentally demonstrated for the first time to our knowledge. The high-Q photonic microwave transversal filter is implemented using a sliced broadband optical source and a dispersive element, to perform frequency-tunable microwave frequency selection. The central frequency of the microwave filter is a function of the wavelength spacing of the sliced optical source and the chromatic dispersion of the dispersive element, therefore, the oscillation frequency can be tuned by changing the channel spacing or the chromatic dispersion of the dispersive element. A theoretical analysis is provided, which is verified by a proof-of-concept experiment. The phase noise performance and the frequency tunability are both experimentally investigated.