Minimum entropy time-frequency distributions

Re´nyi entropy has been proposed as an effective measure of signal information content and complexity on the time-frequency plane. The previous work concerning Re´nyi entropy in the time-frequency plane has focused on measuring the complexity of a given deterministic signal. In this paper, the properties of Re´nyi entropy for random signals are examined. The upper and lower bounds on the expected value of Re´nyi entropy are derived and ways of minimizing the entropy of time-frequency distributions by putting constraints on the time-frequency kernel are explored. It is proven that the quasi-Wigner kernel has the minimum entropy among all positive time-frequency kernels with finite time-support and correct marginals. A general class of minimum entropy kernels is presented. The performance of minimum entropy kernels in signal representation and component counting is also demonstrated.