The Wigner Distribution PDF Download

Author: W. Mecklenbräuker
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 492

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Book Description
Seven contributions discuss in depth several aspects of one of the methods for representing both the frequency domain and the temporal localization of signals, which has tremendous importance in signal analysis and processing. Among them are properties like positivity, spread, and interference-term geometry; signal synthesis methods and their application to signal design, time- frequency filtering, and signal separation; the analysis of non- stationary random processes; singular value decompositions and their application to detection and classification; and optical applications of the Wigner Distribution. Also includes a bibliography of published works on the subject from 1985 to 1992. Annotation copyrighted by Book News, Inc., Portland, OR

Author: Lokenath Debnath
Publisher: Springer Science & Business Media
ISBN: 1461200970
Category : Technology & Engineering
Languages : en
Pages : 575

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Book Description
Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.

Author: Cosmas Zachos
Publisher: World Scientific
ISBN: 9812383840
Category : Science
Languages : en
Pages : 560

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Book Description
Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics.

Author: Young Suh Kim
Publisher: World Scientific
ISBN: 9814506672
Category : Science
Languages : en
Pages : 352

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Book Description
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

Author: David K. Ferry
Publisher:
ISBN: 9780750316712
Category : Mathematical physics
Languages : en
Pages : 0

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Book Description
"This book is designed to give a background on the origins and development of Wigner functions, as well as its mathematical underpinnings. Along the way the authors emphasise the connections, and differences, from the more popular non-equilibrium Green's function approaches. But, the importance of the text lies in the discussions of the applications of the Wigner function in various fields of science, including quantum information, coherent optics, and superconducting qubits. These disciplines approach it differently, and the goal here is to give a unified background and highlight how it is utilized in the different disciplines." -- Prové de l'editor.

Author: Maurice A De Gosson
Publisher: World Scientific Publishing Company
ISBN: 1786343118
Category : Science
Languages : en
Pages : 250

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Book Description
This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.

Author: Amalia Torre
Publisher: Elsevier
ISBN: 0444636080
Category : Science
Languages : en
Pages : 662

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Book Description
Linear Ray and Wave Optics in Phase Space, Second Edition, is a comprehensive introduction to Wigner optics. The book connects ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics. Analogies with other branches of classical and quantum physics—such as classical and quantum mechanics, quantum optics, signal theory and magnetic optics—are evidenced by pertinent comments and/or rigorous mathematics. Lie algebra and group methods are introduced and explained through the elementary optical systems within the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a similar manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space. This second edition contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics. All chapters are fully revised and updated. All topics have been developed to a deeper level than in the previous edition and are now supported with Mathematica and Mathcad codes. Provides powerful tools to solve problems in quantum mechanics, quantum optics and signal theory Includes numerous examples supporting a gradual and comprehensive introduction to Wigner optics Treats both ray and wave optics, resorting to Lie-algebra based methods Connects the subject with other fields, such as quantum optics, quantum mechanics, signal theory and optics of charged particles Introduces abstract concepts through concrete examples Includes logical diagrams to introduce mathematics in an intuitive way Contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics Supported with Mathematica and Mathcad codes

Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 3642559255
Category : Mathematics
Languages : en
Pages : 687

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Book Description
Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Author:
Publisher:
ISBN:
Category : Statistical mechanics
Languages : en
Pages :

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Book Description

Author: Antonia Papandreou-Suppappola
Publisher: CRC Press
ISBN: 1420042467
Category : Technology & Engineering
Languages : en
Pages : 432

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Book Description
Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency. Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems. Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.