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In this paper, we employ the widely linear adaptive processing technique in digital communication channel equalization. We present two new techniques for supervised and unsupervised equalization. In the supervised technique the multi-split transform is aggregated to the widely linear processing, using a power normalized and time-varying step-size LMS algorithm. The unsupervised technique consists of a widely linear adaptive prediction-error filter using the time-varying step-size LMS algorithm proposed by Kwong and Johnston. We show that this technique can invert non-minimum phase channels. The main advantages of the proposed equalizers are the low computational complexity and better performance in terms of convergence rate and accuracy, when compared to the conventional equalization techniques. Simulation results show that the widely linear equalizers have a good performance.