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We address the problem of classifying a signal that has been corrupted by an unknown linear time-invariant filter. This problem is common in remote-sensing and non-destructive evaluation applications wheremultipath and spreading are prevalent. A traditional approach is blind deconvolution to estimate the original signal, followed by classification of the estimated signal. Blind deconvolution is an ill-posed estimation problem, and if only a classification is needed, then we hypothesize it is an unnecessary step. We present an alternative maximum likelihood classifier that uses second-order probability models for the original signal and the unknown corrupting filter. The resulting quadratic discriminant analysis classifier is shown to perform well over a range of signal-to-noise ratios for two different models of multipath, and in all cases performs consistently better than a standard blind deconvolution method followed by a quadratic discriminant analysis classifier.