Generalized joint signal representations extend the scope of joint time-frequency representations to a richer class of nonstationary signals. Cohen's marginal-based generalized approach is canonical from a distributional viewpoint, whereas, in some other applications, for example, in a signal detection framework, a covariance-based formulation is needed and/or more attractive. In this note, we present a canonical covariance-based recipe for generating generalized joint signal representations. The method is highlighted by its simple characterization and interpretation, and naturally extends the concept of the corresponding linear representations.