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The finite alphabet approach is a method proposed to analyze exactly adaptive algorithms/structures. The performances are related to the choice of the transition matrix, corresponding to the Markov chain that models the inputs. When increasing the alphabet cardinality, the algebraic method uses matrices with prohibitive dimensions, so the definition of the corresponding transition matrix becomes complicated, and the determination of signal statistics becomes rather unfeasible. The contribution of this paper deals with proposition of a method allowing to generate finite alphabet sets, at any cardinality, operating on certain characteristics of the finite alphabet set (correlation, high order statistics), in order to carry out exact analytical results.