The Cohen Class

J.C. O'Neill, William J. Williams

Cohen's (see Prentice Hall, Englewood Cliffs, NJ, 1995) class of time-frequency distributions for continuous signals has been to extended to discrete signals using both an axiomatic approach and an operator theory approach. We investigate the formulation of several classical time-frequency distributions (Wigner, Rihaczek, Margenau-Hill, Page, Levin, Born-Jordan, spectrogram) in the discrete Cohen's classes. The main result of this paper concludes that there does not exist a formulation of the Wigner distribution in all of the discrete Cohen's classes.

Paolo Boggiatto, Evanthia Carypis, Alessandro Oliaro

In this paper we study the relationships between general quantization rules which yield Cohen operators and the signal time-frequency representations in the Cohen class. After defining a suitable functional setting, we focus on the particular case of the concentration operators which, as the multipliers and Fourier multipliers in the Donoho-Stark uncertainty principle, furnish estimates of the energy concentration on subsets of the time-frequency space. Finally we study the case of positive representations in the Cohen class.

Dominik Hangleiter, Jacques Carolan, Karim P. Y. Thébault

Franz Hlawatsch, Helmut Bölcskei

We propose classes of quadratic time-frequency distributions that retain the inner structure of Cohen's class. Each of these classes is based on a pair of conjugate unitary operators producing time-frequency displacements. The classes satisfy covariance and marginal properties corresponding to these operators. For each class, we define a central member generalizing the Wigner distribution and the Q-distribution, and we specify a transformation by which the class can be derived from Cohen's class.

R. F. Streater