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A novel equalisation scheme, based on parametric channel estimation, is presented. The proposed scheme is appropriate for channels with a long and sparse impulse response, such as those encountered in high-definition digital video-transmission systems. The main feature of the channel estimation is that instead of seeking the whole channel impulse response only the unknown time delays and attenuation factors of the physical channel multipath components are efficiently estimated. The equalisation consists of an adaptive decision-feedback equaliser (DFE), whose initialisation is properly designed for sparse channels. The information needed in the initialisation procedure is provided by the channel estimation part. The DFE converges much faster compared to a conventional DFE, and the whole scheme utilises a very short training sequence and hence a significant saving in bandwidth is achieved.