scholarly journals Heisenberg uncertainty principles for an oscillatory integral operator

2017 ◽  
Author(s):  
L. P. Castro ◽  
R. C. Guerra ◽  
N. M. Tuan
Keyword(s):  
Integral Operator ◽  
Oscillatory Integral ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty ◽  
Oscillatory Integral Operator

scholarly journals A fast butterfly algorithm for generalized Radon transforms

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. U41-U51 ◽  
Author(s):  
Jingwei Hu ◽  
Sergey Fomel ◽  
Laurent Demanet ◽  
Lexing Ying
Keyword(s):  
Integral Operator ◽  
Radon Transform ◽  
Model Space ◽  
Oscillatory Integral ◽  
Fourier Integral ◽  
Low Rank ◽  
Radon Transforms ◽  
Low Rank Approximation ◽  
Data Set ◽  
Generalized Radon Transforms

Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We have devised a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator and to construct a blockwise low-rank approximation of the kernel function. The overall structure follows the Fourier integral operator butterfly algorithm. For 2D data, the algorithm runs in complexity [Formula: see text], where [Formula: see text] depends on the maximum frequency and offset in the data set and the range of parameters (intercept time and slowness) in the model space. From a series of studies, we found that this algorithm can be significantly more efficient than the conventional time-domain integration.

Some shaper uncertainty principles for multivector-valued functions

2016 ◽  
Vol 14 (06) ◽  
pp. 1650043
Author(s):  
Minggang Fei ◽  
Yubin Pan ◽  
Yuan Xu
Keyword(s):  
Fourier Transform ◽  
Clifford Algebra ◽  
Uncertainty Principle ◽  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Heisenberg Uncertainty Principle ◽  
Clifford Fourier Transform ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform ◽  
Adjoint Operators

The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.

scholarly journals On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Ahmed Fitouhi ◽  
Néji Bettaibi ◽  
Rym H. Bettaieb ◽  
Wafa Binous
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Uncertainty Principles ◽  
Fourier Cosine ◽  
Quantum Calculus ◽  
Fourier Sine ◽  
Local Uncertainty ◽  
Heisenberg Uncertainty

The aim of this paper is to generalize the -Heisenberg uncertainty principles studied by Bettaibi et al. (2007), to state local uncertainty principles for the -Fourier-cosine, the -Fourier-sine, and the -Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the -Bessel-Fourier transform.

scholarly journals Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yong-Gang Li ◽  
Bing-Zhao Li ◽  
Hua-Fei Sun
Keyword(s):  
Signal Processing ◽  
Harmonic Analysis ◽  
Uncertainty Principle ◽  
Linear Canonical Transform ◽  
The Novel ◽  
Uncertainty Principles ◽  
Research Topics ◽  
Heisenberg Uncertainty Principle ◽  
Physics Community ◽  
Heisenberg Uncertainty

The Heisenberg uncertainty principle of harmonic analysis plays an important role in modern applied mathematical applications, signal processing and physics community. The generalizations and extensions of the classical uncertainty principle to the novel transforms are becoming one of the most hottest research topics recently. In this paper, we firstly obtain the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform, and then then-dimensional cases are investigated in detail based on the proposed Heisenberg uncertainty principle of then-dimensional linear canonical transform.

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