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The paper considers the design of the equaliser and the desired overall system impulse response (d.i.r.) for various types of detection algorithms used to recover digital data which has suffered intersymbol interference. The joint optimisation of the equaliser and desired response is formulated using a mean-square error cost. A constraint on the desired response is introduced which enables simple adaptive algorithms to be derived for determining the optimum equalizer and d.i.r. One of the algorithms considered has been found to converge rapidly and is thus ideally suited for application where fast start-up is required. Simulation results of the probability of error performance of various detection algorithms, using the equaliser and d.i.r. designed according to the approach developed in the paper, are presented. These results show that the performance obtained is comparable to that achieved with systems in which the equaliser and d.i.r. are designed according to other techniques. The disadvantage of these other techniques is that they usually lead to algorithms which are difficult to make adaptive and are slow to converge.