Dynamic voltage and frequency scaling (DVFS) offers great potential for optimizing the energy efficiency of Multiprocessor Systems-on-Chip (MPSoCs). The conventional approaches for processor voltage and frequency adjustment are not suitable for streaming multimedia applications due to the cyclic nature of dependencies in the executing tasks which can potentially violate the throughput constraints. In this paper, we propose a methodology that applies DVFS for such cyclic dependent tasks. The methodology involves an off-line analysis that assumes worst-case execution times of tasks to identify the executions that can be slowed down and an on-line analysis to utilize the slacks arising from tasks that finish their execution before the worst-case execution times. Thus, the methodology minimizes energy consumption during both off-line and on-line analysis while satisfying the throughput constraints. Experiments based on models of real-life streaming multimedia applications show that the proposed methodology reduces the overall energy consumption by 43% when compared to existing approaches.