Uncertainty Principle and Wavelet Transforms

2019 ◽  
pp. 57-90
Author(s):  
Wojbor A. Woyczyński
Keyword(s):  
Uncertainty Principle ◽  
Wavelet Transforms

scholarly journals A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Wavelet Transforms ◽  
Quaternion Algebra ◽  
Uncertainty Principles ◽  
Quaternion Fourier Transform ◽  
Coordinate Form ◽  
Quaternion Wavelet Transform ◽  
Polar Coordinate ◽  
Extended Uncertainty

The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform.

Wavelet Transforms with a Compact Carrier on the Basis of Spline Wavelets

2007 ◽  
Vol 66 (6) ◽  
pp. 505-512
Author(s):  
A. D. Kukharev ◽  
Yu. S. Evstifeev ◽  
V. G. Yakovlev
Keyword(s):  
Wavelet Transforms ◽  
Spline Wavelets

The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

2014 ◽  
Vol 3 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
Uncertainty Principle ◽  
Large Scale ◽  
Uncertainty Relations ◽  
Speed Of Light ◽  
Energy Fluctuation ◽  
Hydrodynamic Analogy ◽  
Non Local ◽  
Minimum Uncertainty ◽  
Quantum Hydrodynamic ◽  
Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

The inner bound of quantum spacetime

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Wigner Function ◽  
Uncertainty Principle ◽  
Quantum Spacetime

This article addresses the connection of the UNCERTAINTY PRINCIPLE with the WIGNER FUNCTION.

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