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Some recognizers for stochastic time-varying patterns with additive noise are studied. As in binary communication channels with fading, it is supposed that the fluctuation of a pattern (or signal) may be approximated by a stationary Gaussian autoregressive process with known parameters. Each measurement belongs to either of two classes: the pattern plus noise or noise alone. Under these assumptions, optimum dichotomizers with supervized learning are discussed. To the nonsupervised problems, the decision-directed approach and the modified-decision-directed approach are applied. Also some experimental results are presented.