New Insights into Wigner Distributions of Deterministic and Random Analytic Signals

We present a new insight into studying the properties of deterministic and random analytic signals basing on even and odd parts of their Wigner distributions (WDs). For random processes, our research is focused on the properties of WDs of single sample functions and of ensemble averages. If we accept negative energies, the WD of a single sample function can be regarded as the energy distribution in the time-frequency plane. Using positive and negative energies, we propose to define new notions of active and reactive energies of WDs. It has been shown that averaging process reduces the reactive energy of WDs of pure noise signals