Continued Fractions And Signal Processing

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Continued Fractions and Signal Processing

Author : Tomas Sauer
Publisher : Springer Nature
ISBN 13 : 3030843602
Total Pages : 275 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Continued Fractions and Signal Processing by : Tomas Sauer

Download or read book Continued Fractions and Signal Processing written by Tomas Sauer and published by Springer Nature. This book was released on 2021-09-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Continued Fractions and Signal Processing

Author : Tomas Sauer
Publisher :
ISBN 13 : 9783030843618
Total Pages : 0 pages
Book Rating : 4.8/5 (436 download)

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Book Synopsis Continued Fractions and Signal Processing by : Tomas Sauer

Download or read book Continued Fractions and Signal Processing written by Tomas Sauer and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony's problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Continued Fractions and Orthogonal Functions

Author : S. Clement Cooper
Publisher : CRC Press
ISBN 13 : 1000111059
Total Pages : 400 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Continued Fractions and Orthogonal Functions by : S. Clement Cooper

Download or read book Continued Fractions and Orthogonal Functions written by S. Clement Cooper and published by CRC Press. This book was released on 2020-12-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.

Quantum-Mechanical Signal Processing and Spectral Analysis

Author : Dzevad Belkic
Publisher : CRC Press
ISBN 13 : 9781420033601
Total Pages : 486 pages
Book Rating : 4.0/5 (336 download)

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Book Synopsis Quantum-Mechanical Signal Processing and Spectral Analysis by : Dzevad Belkic

Download or read book Quantum-Mechanical Signal Processing and Spectral Analysis written by Dzevad Belkic and published by CRC Press. This book was released on 2019-08-22 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum-Mechanical Signal Processing and Spectral Analysis describes the novel application of quantum mechanical methods to signal processing across a range of interdisciplinary research fields. Conventionally, signal processing is viewed as an engineering discipline with its own specific scope, methods, concerns and priorities, not usually encompassing quantum mechanics. However, the dynamics of systems that generate time signals can be successfully described by the general principles and methods of quantum physics, especially within the Schroedinger framework. Most time signals that are measured experimentally are mathematically equivalent to quantum-mechanical auto-correlation functions built from the evolution operator and wavefunctions. This fact allows us to apply the rich conceptual strategies and mathematical apparatus of quantum mechanics to signal processing. Among the leading quantum-mechanical signal processing methods, this book emphasizes the role of Pade approximant and the Lanczos algorithm, highlighting the major benefits of their combination. These two methods are carefully incorporated within a unified framework of scattering and spectroscopy, developing an algorithmic power that can be exported to other disciplines. The novelty of the author's approach to key signal processing problems, the harmonic inversion and the moment problem, is in establishing the Pade approximant and Lanczos algorithm as entirely algerbraic spectral estimators. This is of paramount theoretical and practical importance, as now spectral analysis can be carried out from closed analytical expressions. This overrides the notorious mathematical ill-conditioning problems with round-off errors that plague inverse reconstructions in those fields that rely upon signal processing. Quantum-Mechanical Signal Processing and Spectral Analysis will be an invaluable resource for researchers involved in signal processing across a wide range of disciplines.

Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications

Author : Dzevad Belkic
Publisher : CRC Press
ISBN 13 : 1000687341
Total Pages : 349 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications by : Dzevad Belkic

Download or read book Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications written by Dzevad Belkic and published by CRC Press. This book was released on 2010-01-29 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses the FPT to Solve the Quantification Problem in MRSAn invaluable tool in non-invasive clinical oncology diagnosticsAddressing the critical need in clinical oncology for robust and stable signal processing in magnetic resonance spectroscopy (MRS), Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications explores cutting-

Analytic Theory of Continued Fractions

Author : W. B. Jones
Publisher : Springer
ISBN 13 : 3540392769
Total Pages : 250 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Analytic Theory of Continued Fractions by : W. B. Jones

Download or read book Analytic Theory of Continued Fractions written by W. B. Jones and published by Springer. This book was released on 2006-11-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extrapolation and Rational Approximation

Author : Claude Brezinski
Publisher : Springer Nature
ISBN 13 : 3030584186
Total Pages : 410 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Extrapolation and Rational Approximation by : Claude Brezinski

Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.

Advances in Quantum Chemistry

Author :
Publisher : Academic Press
ISBN 13 : 0080887856
Total Pages : 347 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Advances in Quantum Chemistry by :

Download or read book Advances in Quantum Chemistry written by and published by Academic Press. This book was released on 2009-03-14 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field. With invited reviews written by leading international researchers, each presenting new results, it provides a single vehicle for following progress in this interdisciplinary area. - Publishes articles, invited reviews and proceedings of major international conferences and workshops - Written by leading international researchers in quantum and theoretical chemistry - Highlights important interdisciplinary developments

Continued Fractions: From Analytic Number Theory to Constructive Approximation

Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 0821812009
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Continued Fractions: From Analytic Number Theory to Constructive Approximation by : Bruce C. Berndt

Download or read book Continued Fractions: From Analytic Number Theory to Constructive Approximation written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 1999 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Analytic Theory of Continued Fractions II

Author : Wolfgang J. Thron
Publisher : Springer
ISBN 13 : 3540388176
Total Pages : 305 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Analytic Theory of Continued Fractions II by : Wolfgang J. Thron

Download or read book Analytic Theory of Continued Fractions II written by Wolfgang J. Thron and published by Springer. This book was released on 2006-11-14 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Developments in Mathematical and Conceptual Physics

Author : Harish Parthasarathy
Publisher : Springer Nature
ISBN 13 : 9811550581
Total Pages : 454 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Developments in Mathematical and Conceptual Physics by : Harish Parthasarathy

Download or read book Developments in Mathematical and Conceptual Physics written by Harish Parthasarathy and published by Springer Nature. This book was released on 2020-06-22 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infinite-dimensional operator theory, perturbation theory, stochastic differential equations, and Riemannian geometry. These mathematical tools have been applied to study problems in mechanics, fluid dynamics, quantum mechanics and quantum field theory, nonlinear dynamical systems, general relativity, cosmology, and electrodynamics. A particularly interesting topic of research interest developed in this book is the design of quantum unitary gates of large size using the Feynman diagrammatic approach to quantum field theory. Through this book, the reader will be able to observe how basic physics can revolutionize technology and also how diverse branches of mathematical physics like large deviation theory, quantum field theory, general relativity, and electrodynamics have many common issues that provide the starting point for unifying the whole of physics, namely in the formulation of Grand Unified Theories (GUTS).

Orthogonal Polynomials on the Unit Circle: Spectral theory

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836750
Total Pages : 608 pages
Book Rating : 4.8/5 (367 download)

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Book Synopsis Orthogonal Polynomials on the Unit Circle: Spectral theory by : Barry Simon

Download or read book Orthogonal Polynomials on the Unit Circle: Spectral theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.

Orthogonal Polynomials on the Unit Circle

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 082184864X
Total Pages : 610 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials on the Unit Circle by : Barry Simon

Download or read book Orthogonal Polynomials on the Unit Circle written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.

Signals, Systems, Transforms, and Digital Signal Processing with MATLAB

Author : Michael Corinthios
Publisher : CRC Press
ISBN 13 : 1420090496
Total Pages : 1337 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Signals, Systems, Transforms, and Digital Signal Processing with MATLAB by : Michael Corinthios

Download or read book Signals, Systems, Transforms, and Digital Signal Processing with MATLAB written by Michael Corinthios and published by CRC Press. This book was released on 2018-09-03 with total page 1337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signals, Systems, Transforms, and Digital Signal Processing with MATLAB® has as its principal objective simplification without compromise of rigor. Graphics, called by the author, "the language of scientists and engineers", physical interpretation of subtle mathematical concepts, and a gradual transition from basic to more advanced topics are meant to be among the important contributions of this book. After illustrating the analysis of a function through a step-by-step addition of harmonics, the book deals with Fourier and Laplace transforms. It then covers discrete time signals and systems, the z-transform, continuous- and discrete-time filters, active and passive filters, lattice filters, and continuous- and discrete-time state space models. The author goes on to discuss the Fourier transform of sequences, the discrete Fourier transform, and the fast Fourier transform, followed by Fourier-, Laplace, and z-related transforms, including Walsh–Hadamard, generalized Walsh, Hilbert, discrete cosine, Hartley, Hankel, Mellin, fractional Fourier, and wavelet. He also surveys the architecture and design of digital signal processors, computer architecture, logic design of sequential circuits, and random signals. He concludes with simplifying and demystifying the vital subject of distribution theory. Drawing on much of the author’s own research work, this book expands the domains of existence of the most important transforms and thus opens the door to a new world of applications using novel, powerful mathematical tools.

Applications in Control

Author : Ivo Petráš
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110570939
Total Pages : 563 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Applications in Control by : Ivo Petráš

Download or read book Applications in Control written by Ivo Petráš and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This sixth volume collects authoritative chapters covering several applications of fractional calculus in control theory, including fractional controllers, design methods and toolboxes, and a large number of engineering applications of control.

Mathematical Analysis, Wavelets, and Signal Processing

Author : Mourad Ismail
Publisher : American Mathematical Soc.
ISBN 13 : 0821803840
Total Pages : 366 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Analysis, Wavelets, and Signal Processing by : Mourad Ismail

Download or read book Mathematical Analysis, Wavelets, and Signal Processing written by Mourad Ismail and published by American Mathematical Soc.. This book was released on 1995 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of an international conference held in Cairo, Egypt (January 1994). Mathematics and engineering discoveries, such as wavelets, multiresolution analysis, and subband coding schemes, caused rapid advancements in signal processing, necessitating an interdisciplinary approach. Contributors to this conference demonstrated that some traditional areas of mathematical analysis - sampling theory, approximation theory, and orthogonal polynomials - have proven extremely useful in solving various signal processing problems.

Gröbner Bases in Control Theory and Signal Processing

Author : Hyungju Park
Publisher : Walter de Gruyter
ISBN 13 : 311090974X
Total Pages : 261 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Gröbner Bases in Control Theory and Signal Processing by : Hyungju Park

Download or read book Gröbner Bases in Control Theory and Signal Processing written by Hyungju Park and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey and original articles presenting the state of the art on the application of Gröbner bases in control theory and signal processing. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods at the Johann Radon Institute of Computational and Applied Mathematics (RICAM), Linz, Austria, in May 2006.