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Recently, a multidimensional detector for magnetic recording channels has been proposed in order to better exploit the high media noise due to jitter and pulse broadening. The ideal scheme implementation is based on a bank of receiver filters matched to a Taylor approximation of the reading channel model. In this paper, the performance of a sub-optimal Baud-spaced multidimensional detector is evaluated for perpendicular channel systems, where the matched filters are replaced by partial response equalizers. Simulation results look promising, showing that the proposed detector may outperform the standard monodimensional linear predictor detector despite its suboptimal realization.