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Qualitative and quantitative performances of adaptive filters can significantly vary when they are implemented in finite precision arithmetic. Analyzing theoretically such performances is very complex. In this paper, we present a new approach which simplifies both transient and steady state analysis of implemented adaptive filters. Indeed, the finite precision adaptive identification scheme in a stationary context is replaced by an equivalent simple infinite precision scheme in a specific non stationary context; where the channel to be identified has stochastic time-variations.