Download or read book The Linear Canonical Transform and Its Broadened Scope written by Aamir Hamid Dar and published by Mohammed Abdul Sattar. This book was released on 2024-03-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Linear Canonical Transform (LCT) is a mathematical operation that generalizes the Fourier transform, fractional Fourier transform, and other similar transforms. It describes the transformation of signals or functions in time and frequency domains in a linear, continuous, and reversible manner. The LCT can be expressed using a 4x4 matrix, which allows for efficient computation and manipulation. The broadened scope of the LCT encompasses various applications in signal processing, optics, image processing, and quantum mechanics. Its versatility lies in its ability to handle a wide range of signal types, including non-stationary, chirp-like, and spatially varying signals. Additionally, the LCT provides a unified framework for analyzing and processing signals with different degrees of chirpiness or time-frequency characteristics. Applications of the LCT include signal modulation, filtering, feature extraction, pattern recognition, and image reconstruction. It has found particular utility in optical systems for beam shaping, propagation, and manipulation. Furthermore, the LCT has been applied in quantum mechanics to study wave-particle duality and quantum information processing.
Download or read book Discrete Linear Canonical Transform and Its Applications written by 賴韻曲 and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Canonical Transforms written by John J. Healy and published by Springer. This book was released on 2015-11-26 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Download or read book Numerical Approximation of the Linear Canonical Transform written by J. Healy and published by . This book was released on 2010 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unitary and Additive Discrete Linear Canonical Transform written by Liang Zhao and published by . This book was released on 2015 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Phase Space Picture Of Quantum Mechanics Group Theoretical Approach written by Young Suh Kim and published by World Scientific. This book was released on 1991-03-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Canonical Equational Proofs written by Bachmair and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations occur in many computer applications, such as symbolic compu tation, functional programming, abstract data type specifications, program verification, program synthesis, and automated theorem proving. Rewrite systems are directed equations used to compute by replacing subterms in a given formula by equal terms until a simplest form possible, called a normal form, is obtained. The theory of rewriting is concerned with the compu tation of normal forms. We shall study the use of rewrite techniques for reasoning about equations. Reasoning about equations may, for instance, involve deciding whether an equation is a logical consequence of a given set of equational axioms. Convergent rewrite systems are those for which the rewriting process de fines unique normal forms. They can be thought of as non-deterministic functional programs and provide reasonably efficient decision procedures for the underlying equational theories. The Knuth-Bendix completion method provides a means of testing for convergence and can often be used to con struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite based proof procedures. We shall view theorem provers as proof transformation procedures, so as to express their essential properties as proof normalization theorems.
Download or read book An Introduction to Laplace Transforms and Fourier Series written by P.P.G. Dyke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Download or read book Automated Technology for Verification and Analysis written by Franck Cassez and published by Springer. This book was released on 2014-10-24 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 12th International Symposium on Automated Technology for Verification and Analysis, ATVA 2014, held in Sydney, Australia, in November 2014. The 29 revised papers presented in this volume were carefully reviewed and selected from 76 submissions. They show current research on theoretical and practical aspects of automated analysis, verification and synthesis by providing an international forum for interaction among the researchers in academia and industry.
Download or read book Foundations of Time Frequency Analysis written by Karlheinz Gröchenig and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Download or read book Investigation of Nonlinear Control Systems Continuously acting control systems written by Nicolai Minorsky and published by . This book was released on 1960 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Processes written by Anthony Ephremides and published by . This book was released on 1973 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Download or read book An Introduction to Wavelets Through Linear Algebra written by M.W. Frazier and published by Springer. This book was released on 2013-12-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.
Download or read book Linear State Space Control Systems written by Robert L. Williams, II and published by John Wiley & Sons. This book was released on 2007-02-09 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book blends readability and accessibility common to undergraduate control systems texts with the mathematical rigor necessary to form a solid theoretical foundation. Appendices cover linear algebra and provide a Matlab overivew and files. The reviewers pointed out that this is an ambitious project but one that will pay off because of the lack of good up-to-date textbooks in the area.
Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.
