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In variable-bit-rate video coding, the video is preprocessed to collect sequence-level statistics, which are used for global bit allocation in the actual encoding stage to obtain a smoothed video presentation quality. However, in real-time video recording and network streaming, this type of two-pass encoding scheme is not allowed because the access to future frames and global statistics is not available. To address this issue, we introduce the concept of low-pass filtering of rate-distortion functions and develop a smoothed rate control (SRC) framework for real-time video recording and streaming. Theoretically, we prove that, using a geometric averaging filter, the SRC algorithm is able to maintain a smoothed video presentation quality while achieving the target bit rate automatically. We also analyze the buffer requirement of the SRC algorithm in real-time video streaming, and propose a scheme to seamlessly integrate robust buffer control into the SRC framework. The proposed SRC algorithm has very low computational complexity and implementation cost. Our extensive experimental results demonstrate that the SRC algorithm significantly reduces the picture quality variation in the encoded video clips.