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In this paper, we investigate the differential channel state information (CSI) feedback problem for a general multiple input multiple output(MIMO) system over time-correlated Rayleigh block-fading channels. Specifically, we first derive the analytical minimum differential feedback rate in the presence of channel estimation errors and quantization distortion. With the feedback-channel capacity constraint, in the periodic feedback system, we further study the relationship between the ergodic capacity and the feedback interval. We find that there exists an optimal feedback interval to maximize the ergodic capacity. Analytical results are verified by simulations in a practical differential feedback system employing Lloyd's quantization algorithm.