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A class of multivariate spectral representations for real-valuednonstationary random variables is introduced, which is characterised by ageneral complex Gaussian distribution. In this way, the temporal signalproperties -- harmonicity, wide-sense stationarity and cyclostationarity -- aredesignated respectively by the mean, Hermitian variance and pseudo-variance ofthe associated time-frequency representation (TFR). For rigour, the estimatorsof the TFR distribution parameters are derived within a maximum likelihoodframework and are shown to be statistically consistent, owing to thestatistical identifiability of the proposed distribution parametrization. Byvirtue of the assumed probabilistic model, a generalised likelihood ratio test(GLRT) for nonstationarity detection is also proposed. Intuitive examplesdemonstrate the utility of the derived probabilistic framework for spectralanalysis in low-SNR environments.

A Probabilistic Spectral Analysis of Multivariate Real-Valued Nonstationary Signals