Time-frequency representations (TFRs) provide a powerful and flexible structure for designing optimal detectors in a variety of nonstationary scenarios. In this paper, we describe a TFR-based framework for optimal detection of arbitrary second-order stochastic signals, with certain unknown or random nuisance parameters, in the presence of Gaussian noise. The framework provides a useful model for many important applications including machine fault diagnostics and radar/sonar. We emphasize a subspace-based formulation of such TFR detectors which can be exploited in a variety of ways to design new techniques. In particular, we explore an extension based on multi-channel/sensor measurements that are often available in practice to facilitate improved signal processing. In addition to potentially improved performance, the subspace-based interpretation of such multi-channel detectors provides useful information about the physical mechanisms underlying the signals of interest.