Asymptotic Time Averages and Frequency Distributions

Invariant Distributions and Time Averages for Horocycle Flows

There are infinitely many obstructions to the existence of smooth solutions of the cohomological equation Uu = f , where U is the vector field generating the horocycle flow on the unit tangent bundle SM of a Riemann surface M of finite area and f is a given function on SM. We study the Sobolev regularity of these obstructions, construct smooth solutions of the cohomological equation, and derive...

Robust time-frequency distributions

Study of the additive Gaussian noise influence on time-frequency (TF) distributions is an important issue [Article 9.1]. However, in many practical applications, especially in communications, signals are disturbed by a kind of impulse noise. These noises are commonly modeled by heavy-tailed (long-tailed) probability density functions (pdfs) [6]. It is well known fact that the conventional TF di...

On Asymptotic Differentiability of Averages

Asymptotic Measures and Distributions of Birkhoff Averages with Respect to Lebesgue Measure

Blind source separation using time-frequency distributions: algorithm and asymptotic performance

This paper addresses the problem of the blind source separation which consists of recovering a set of signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting the di erence in the time-frequency (t-f) signatures of the sources is considered. The approach is based on the diagonalization of a combined set of `spatial time-frequency distributi...