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A new adaptive equaliser for the minimisation of mean-square error has been developed for use over a wide range of transmission channels. The equaliser comprises a transversal filter (with variable tap gains) and a processor. Using the processor, the tap-gain-adjustment information is derived from blocks of samples taken from the channel output. The processor operates independently of the channel speed and can provide variable step size for adjusting the tap gains of the transversal filter and flexibility in the implementation of the equaliser in terms of the channel speed and the equaliser realisation. Analytical and computer-simulation results are presented showing the equaliser performance.