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A general theoretical model for spectrum-sliced microwave-photonic filter design is presented. It is applicable to arbitrary variable time-delay characteristics, and to both double- and single-sideband modulation formats. Based on this model, dispersion-induced RF characteristics are investigated theoretically and experimentally. The results show that apart from the carrier suppression effect, the performance of spectrum-sliced microwave-photonic filters is limited by a dispersion-induced RF distortion that is related to the sliced spectrum character, and which is modulation format independent. The model provides data for designing the optimum grating optical slicing bandwidth and shape, and for determining the required spectral slice matching tolerance, to overcome nonideal RF characteristics and to enhance the filter frequency response.