On positivity of time-frequency distributions

This correspondence addresses the problem of how to regard the fundamental impossibility with time-frequency energy distributions of Cohen´s class always to be nonnegative and, at the same time, to have correct marginal distributions. It is shown that the Wigner distribution is the only member of a large class of bilinear time-frequency distributions that becomes nonnegative after smoothing in the time-frequency plane by means of Gaussian weight functions with BT product equal to unity.