Positivity of time-frequency distribution functions

V. Canivell, Pere Seglar

Leon W. Cohen

Joint positive distributions of time and frequency which satisfy the correct marginals exist and can be readily obtained. In this presentation we generalize the continuous case previously considered to the discrete time case and the two dimensional situation.

Leon W. Cohen, Patrick J. Loughlin

Theo A. C. M. Claasen, W. Mecklenbräuker

This contribution addresses the implications of Heisenberg's uncertainty relation on time-frequency energy distribution functions depending bilinearly on the signal. It is indicated that all these distribution functions must have a certain minimum spread in the time-frequency plane. Further-more such distribution functions can either have correct marginal distributions or be positive, but not both. Therefore a local interpretation of these energy distributions must be taken with care. Some facts determining the choice of an appropriate distribution function will be discussed. A comparison will be made between the spectrogram and the Wigner distribution.

Leon W. Cohen

The general equation for joint time - frequency distribution functions is reformulated to make it more tractible for the study of the recently found positive distributions.