Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Conference on Acoustics Speech and Signal Processing

Properties of the positive time-frequency distribution functions

Leon W. Cohen

Published Mar 23, 2005• 2 citations
Publisher

Abstract

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.
DOI
10.1109/icassp.1985.1168363

Related papers

Marginals vs. covariance in joint distribution theory

Richard G. Baraniuk

Cohen (1966, 1995) has proposed a method for constructing joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. We investigate the covariance properties of this procedure and caution that in its present form it cannot generate all possible distributions. Using group theory, we extend Cohen's construction to a more general form that can be customized to satisfy specific marginal and covariance requirements.

IEEE International Conference on Acoustics Speech and Signal Processing•Nov 19, 2002•13 citations

Positive quantum joint distributions

Leon W. Cohen, Yu. I. Zaparovanny

We demonstrate the existence of positive phase space density functions which yield the quantum mechanical marginal distributions of position and momentum.

Journal of Mathematical Physics•Apr 1, 1980•121 citations

Distributions in signal theory

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.

IEEE International Conference on Acoustics Speech and Signal Processing•Mar 24, 2005•7 citations

Entropic Inequalities and Marginal Problems

Tobias Fritz, Rafael Chaves

A marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables. Here, we point out that the existence of such a joint distribution imposes nontrivial conditions already on the level of Shannon entropies of the given marginals. These entropic inequalities are necessary (but not sufficient) criteria for the existence of a joint distribution. For every marginal problem, a list of such Shannon-type entropic inequalities can be calculated by Fourier-Motzkin elimination, and we offer a software interface to a Fourier-Motzkin solver for doing so. For the case that the hypergraph of given marginals is a cycle graph, we provide a complete analytic solution to the problem of classifying all relevant entropic inequalities, and use this result to bound the decay of correlations in stochastic processes. Furthermore, we show that Shannon-type inequalities for differential entropies are not relevant for continuous-variable marginal problems; non-Shannon-type inequalities are both in the discrete and in the continuous case. In contrast to other approaches, our general framework easily adapts to situations where one has additional (conditional) independence requirements on the joint distribution, as in the case of graphical models. We end with a list of open problems. A complementary article discusses applications to quantum nonlocality and contextuality.

arXiv:1112.4788•IEEE Transactions on Information Theory•Oct 22, 2012•97 citations

Generalized Phase-Space Distribution Functions

Leon W. Cohen

A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.

Journal of Mathematical Physics•May 1, 1966•1,105 citations

Positivity of time-frequency distribution functions

Augustus J. E. M. Janssen

Signal Processing•Apr 1, 1988•15 citations
A marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables. Here, we point out that the existence of such a joint distribution imposes nontrivial conditions already on the level of Shannon entropies of the given marginals. These entropic inequalities are necessary (but not sufficient) criteria for the existence of a joint distribution. For every marginal problem, a list of such Shannon-type entropic inequalities can be calculated by Fourier-Motzkin elimination, and we offer a software interface to a Fourier-Motzkin solver for doing so. For the case that the hypergraph of given marginals is a cycle graph, we provide a complete analytic solution to the problem of classifying all relevant entropic inequalities, and use this result to bound the decay of correlations in stochastic processes. Furthermore, we show that Shannon-type inequalities for differential entropies are not relevant for continuous-variable marginal problems; non-Shannon-type inequalities are both in the discrete and in the continuous case. In contrast to other approaches, our general framework easily adapts to situations where one has additional (conditional) independence requirements on the joint distribution, as in the case of graphical models. We end with a list of open problems. A complementary article discusses applications to quantum nonlocality and contextuality.
A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.