相关论文: Uncertainty Principles for Signal Concentrations
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
The short-time linear canonical transform (STLCT) can be identified as a generalization of the short-time Fourier transform (STFT). It is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty…
The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…
It is proved that the width of a function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is demonstrated for…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
Let $G$ be a finite abelian group. Let $f: G \to {\mathbb C}$ be a signal (i.e. function). The classical uncertainty principle asserts that the product of the size of the support of $f$ and its Fourier transform $\hat f$, $\text{supp}(f)$…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
Donoho and Stark have shown that a precise deterministic recovery of missing information contained in a time interval shorter than the time-frequency uncertainty limit is possible. We analyze this signal recovery mechanism from a physics…
Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us…
The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than $1/(4\pi)$. We study human ability to simultaneously judge the frequency and the timing of a sound.…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…
The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…