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The implementation of multidimensional systems in embedded devices is a major design challenge due to the high algorithmic complexity of the applications. The authors suggest a novel application-level synthesis methodology for those parts of the embedded application which are characterized by being Lebesgue measurable (the computation involved in signal and image processing systems is Lebesgue measurable). The synthesis methodology, based on perturbation analysis, supports the design of analog, digital, or mixed implementations at the very high level of the system design cycle. The outputs of the methodology are quantitative indications regarding the maximum performance loss tolerable by the subsystems composing the application. Such information, augmented with a stochastic description of the tolerated perturbations, can be related to lower synthesis levels and guide the designer toward the final implementation of the embedded device. The perturbation analysis is based on randomized algorithms for an effective evaluation of the performance loss of the computational flow once affected by behavioral perturbations and a Tabu-search-inspired optimizing algorithm for distributing the tolerable performance loss at the system output along the computational subsystems composing the possibly multidimensional processing.