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The amount of the data storage in signal processing systems, whose behavior is described by loop-organized algorithmic specifications, has an important impact on the overall energy consumption, chip area, as well as system performance. This paper presents a non-scalar approach for computing exactly the minimum data storage for high-level procedural specifications, where the main data structures are multi-dimensional arrays. In contrast, all the previous works are only estimation methods. In addition, the paper discusses two applications of this technique in the memory management of signal processing systems: (1) the evaluation of the impact of loop transformations on the data storage, and (2) the assessment of different models of mapping multi-dimensional signals into the physical memory.