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We analyze an echo canceller structure which has dispersion and/or delay in the tap adjustment loop. Such a structure has the potential of providing a savings in the analog filtering requirements when the cancellation is performed in the sampled-data domain. We derive the optimal coefficient vector, in the mean-square error sense, and we derive conditions for a unique solution. It is observed that this problem is somewhat similar, but not equivalent, to the mean-square equalizer problem. Similarities and differences between the two are discussed. We also propose an adaptive algorithm which is well suited for this canceller structure. It is shown that the computational complexity of this algorithm is significantly greater than that of the conventional updating algorithm.