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A class of second-order complex domain blind source extraction algorithms is introduced to cater for signals with noncircular probability distributions, which is a typical case in real-world scenarios. This is achieved by employing the so-called augmented complex statistics and based on the temporal structures of the sources, thus permitting widely linear (WL) predictability to be the extraction criterion. For rigor, the analysis of the existence and uniqueness of the solution is provided based on both the covariance and the pseudocovariance and for both noise-free and noisy cases, and serves as a platform for the derivation of the algorithms. Both direct solutions and those requiring prewhitening are provided based on a WL predictor, thus making the methodology suitable for the generality of complex signals (both circular and noncircular). Simulations on synthetic noncircular sources support the uniqueness and convergence study, followed by a real-world example of electrooculogram artifact removal from electroencephalogram recordings in real time.