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This paper studies the relation between the performances of digital filters and some inherent characteristics of the latest microprocessors. The implementation of digital filters on micro-processor(s) offers some indisputable advantages, but at the same time imposes limits on the speed, accuracy or even stability of digital filters. The approach taken here is to establish some mathematical relations between the computation time, accuracy and the order of the filter on one hand, and the addition and multiplication time, and the number of bits of the microprocessor on the other hand. Such relations lead to the feasibility study of the implementation and open the possibility of trade-offs between various parameters. Parallel processing technique implemented on multi-microprocessor structures is considered as an alternative to significantly improve the filter performances.