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A new efficient decision feedback equalizer (DFE) appropriate for channels with long and sparse impulse response (IR) is proposed. Such channels are encountered in many high-speed wireless communications applications. It is shown that, in cases of sparse channels, the feedforward and feedback (FB) filters of the DFE have a particular structure, which can be exploited to derive efficient implementations of the DFE, provided that the time delays of the channel IR multipath components are known. This latter task is accomplished by a novel technique, which estimates the time delays based on the form of the channel input-output cross-correlation sequence in the frequency domain. A distinct feature of the resulting DFE is that the involved FB filter consists of a reduced number of active taps. As a result, it exhibits considerable computational savings, faster convergence, and improved tracking capabilities as compared with the conventional DFE. Note that faster convergence implies that a shorter training sequence is required. Moreover, the new algorithm has a simple form and its steady-state performance is almost identical to that of the conventional DFE.