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In this paper, we first propose a simple but general analytical channel model for bit-patterned media (BPM) systems. It facilitates the generation of accurate readback signals with a large amount of media noise, as well as the analytical design of equalizer and channel partial response (PR) target. We further propose an analytical approach to jointly design the two-dimensional (2-D) equalizer with one-dimensional (1-D) channel PR target for BPM systems with media noise, according to the minimum mean square error (MMSE) criterion with monic constraint. Simulation results show that the proposed 2-D equalizer with 1-D target based approach achieves significant performance gain over the system designed without considering media noise.