Reducing interference in stochastic time-frequency analysis without losing information

The analytic signal is commonly used in stochastic time-frequency analysis in Cohen's class to reduce interference terms. However, we show that the usual time-frequency representation (TFR) based on the analytic signal gives only an incomplete signal description. This is because the analytic signal constructed from a non-stationary real signal is in general improper, which means that it has non-zero complementary correlation. We show how to augment the standard TFR by a complementary TFR to obtain a complete second-order characterization of the signal while still reducing interference terms compared to the TFR of the real signal.