Positive time-frequency distributions based on joint marginal constraints

Abstract

Abstract-This correspondence studies the formulation of members of the Cohen-Posch class of positive time-frequency energy distributions. Minimization of cross-entropy measures with respect to different priors and the case of no prior or maximum entropy were considered. It is concluded that, in general, the information provided by the classical marginal constraints is very limited, and thus, the final distribution heavily depends on the prior distribution. To overcome this limitation, joint time and frequency marginals are derived based on a "direction invariance" criterion on the time-frequency plane that are directly related to the fractional Fourier transform.

Fractional Fourier Transformation-Based Blind Chromatic Dispersion Estimation for Coherent Optical Communications

“…Therefore, it can be used to analyze the signal both in the time and frequency domains. Thanks to its unique properties, the FrFT has been used in multiple applications such as solving differential equations [7], quantum mechanics [7], optical image processing [8] and signal processing [9]- [11]. It has advantages in dealing with linear frequency modulated (LFM) or chirped signals and has been deployed for detecting and estimating LFM signal's characteristics [12].…”

CT Image Reconstruction Approaches Applied to Time-Frequency Representation of Signals

“…In practical applications, this separability simplifies the mathematical derivation and decreases the computational complexity, but unfortunately the solution obtained is not sufficiently general to express complex TFR. This drawback arises mainly in the case of uniform prior distribution and can be compensated by imposing additional constraints based on FrFT and line integrals along paths not parallel to either the time or frequency axes [7].…”

“…The constraint of correct marginals when combined with optimization procedures (e.g., least squares method, entropy maximization, and cross-entropy minimization) provides a tool for time-frequency distribution construction [6,7,11,12]. In the case of Shannon entropy maximization with generalized marginals as constraints, Lagrange multipliers technique with nonlinear Gauss-Seidel-type iteration procedure may be advantageously used [13].…”