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In cyber-physical systems where sensors measure the temporal evolution of a given phenomenon of interest and radio communication takes place over short distances, the energy spent for source acquisition and compression may be comparable with that used for transmission. Additionally, in order to avoid limited lifetime issues, sensors may be powered via energy harvesting and thus collect all the energy they need from the environment. This work addresses the problem of energy allocation over source acquisition/compression and transmission for energy-harvesting sensors. At first, focusing on a single-sensor, energy management policies are identified that guarantee a minimum average distortion while at the same time ensuring the stability of the queue connecting source and channel encoders. It is shown that the identified class of policies is optimal in the sense that it stabilizes the queue whenever this is feasible by any other technique that satisfies the same average distortion constraint. Moreover, this class of policies performs an independent resource optimization for the source and channel encoders. Suboptimal strategies that do not use the energy buffer (battery) or use it only for adapting either source or channel encoder energy allocation are also studied for performance comparison. The problem of optimizing the desired trade-off between average distortion and backlog size is then formulated and solved via dynamic programming tools. Finally, a system with multiple sensors is considered and time-division scheduling strategies are derived that are able to maintain the stability of all data queues and to meet the average distortion constraints at all sensors whenever it is feasible.