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It is increasingly important to structure signal processing algorithmsand systems to allow for trading off between the accuracy of results and theutilization of resources in their implementation. In any particular context,there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential fordeveloping a more formal approach, including utilizing current research inComputer Science on Approximate Processing and one of its central concepts,Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computerscience community. We then present four examples of signal processingalgorithms/systems that are structured with these goals in mind. These examplesmay be viewed as partial inroads toward the ultimate objective of developing,within the context of signal processing design and implementation, a more general and rigorous framework for utilizing and expanding upon approximate processing concepts and methodologies.