相关论文: Uncertainty Principles for Signal Concentrations
The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and…
The role of the Uncertainty Principle is examined through the examples of squeezing, information capacity, and position monitoring. It is suggested that more attention should be directed to conceptual considerations in quantum information…
In the analysis of the on-axis intensity for a highly focused optical field it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure…
The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
This paper investigates performance limitations and tradeoffs in the control design for linear time-invariant systems. It is shown that control specifications in time domain and in frequency domain are always mutually exclusive determined…
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…
A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…
We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some interesting specific cases, and discuss consequences for…
Some aspects of application of the Uncertainty Principle in the range of interaction radiation with matter surveyed. The procedure of adjustment is proposed at calculation of values of an electromagnetic energy in a quantum theory of a…
In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse…
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then…
In this paper, the uncertainty principle of discrete signals associated with Quaternion Fourier transform is investigated. It suggests how sparsity helps in the recovery of missing frequency.
The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal…
Several uncertainty principles are proved for the Fock space.
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an…
The aim of this paper is to establish a few uncertainty principles for the Fourier and the short-time Fourier transforms. Also, we discuss an analogue of Donoho--Stark uncertainty principle and provide some estimates for the size of the…