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Reducing the number of states is a possible solution for complexity reduction of trellis-based equalization. It has been often proposed that such approaches profit from a near minimum phase target channel which may be obtained by prefiltering the incoming sequence appropriately. A possible finite length solution of such a prefilter is given by the optimal settings of the decision feedback equalizer with a finite length constraint on its feedforward and feedback filter. We focus on the limiting behavior of this solution with respect to the unconstrained solution which is obtained by spectral factorization.