Related papers: Signal Analysis using Born-Jordan-type Distributio…
The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions…
One of the most popular time-frequency representation is certainly the Wigner distribution. To reduce the interferences coming from its quadratic nature, several related distributions have been proposed, among which the so-called…
The quadratic nature of the Wigner distribution causes the appearance of unwanted interferences. This is the reason why engineers, mathematicians and physicists look for related time-frequency distributions, many of them are members of the…
Wigner-type distributions have shown their effectiveness in classification problems of sonar and radar. We present an overview of applications where resonance features in echoes scattered from targets insonified or illuminated with short…
Time-frequency analysis have played a crucial role in the development of localization operators in the last twenty years. We present its applications to the study of boundedness and Schatten Class property for such operators. In particular,…
We investigate the $\tau$-quantizations and Cohen's class distributions of a suitable class of trace-class operators, called Feichtinger's operators, and show that it is a convenient substitute for the class of Schwartz operators. Many…
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literature. Some of these are recalled in the Introduction. In this…
The usefulness of time-frequency analysis methods in the study of quasicrystals was pointed out in a previous paper, where we proved that a tempered distribution $\mu$ on ${\mathbb R}^d$ whose Wigner transform is a measure supported on the…
Born-Jordan operators are a class of pseudodifferential operators arising as a generalization of the quantization rule for polynomials on the phase space introduced by Born and Jordan in 1925. The weak definition of such operators involves…
We show that there is a way to unify distribution functions that describe simultaneously a signal in space and (spatial) frequency. Probably the most known of them is the Wigner distribution function. Here we show how to unify functions of…
It is shown how the optimal detector of Gaussian signals can be represented in terms of Bertrand's class of time-frequency distributions. In this representation, the detector is a correlation between the corresponding time-frequency…
We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related, and in fact in competition, with the possibility of damping the…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this…
We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and…
We study nonlinear concentration problems for time-frequency distributions in the Cohen class. Using recent techniques from quantum harmonic analysis (QHA) we provide both positive and negative results, such as sufficient conditions for the…
We study mixed-state localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced…