Continued Fractions And Signal Processing
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Continued Fractions And Signal Processing
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Author : Tomas Sauer
language : en
Publisher: Springer Nature
Release Date : 2021-09-06
Continued Fractions And Signal Processing written by Tomas Sauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-06 with Mathematics categories.
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 Pad Approximants
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Author : Claude Brezinski
language : en
Publisher: North Holland
Release Date : 1990
Continued Fractions And Pad Approximants written by Claude Brezinski and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Padeacute; approximants and continued fractions are typical examples of old areas of mathematics (continued fractions can be traced back to Euclid's g.c.d. algorithm more than 2000 years ago) which are again very much alive. This is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital filtering, signal processing, fractals, fluid mechanics, theoretical physics, chemistry, engineering etc. This renewal of interest is also due to their intimate connection with other important topics such as orthogonal polynomials (another old subject now again in full vitality), rational approximation, Gaussian quadratures, extrapolation and convergence acceleration methods, differential equations etc.
Continued Fractions And Orthogonal Functions
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Author : S. Clement Cooper
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Continued Fractions And Orthogonal Functions written by S. Clement Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
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.
Continued Fractions
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Author : Lisa Lorentzen
language : en
Publisher: atlantis press
Release Date : 2008
Continued Fractions written by Lisa Lorentzen and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Continued Fractions consists of two volumes -- Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given.This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.
Signal Processing In Magnetic Resonance Spectroscopy With Biomedical Applications
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Author : Dzevad Belkic
language : en
Publisher: CRC Press
Release Date : 2010-01-29
Signal Processing In Magnetic Resonance Spectroscopy With Biomedical Applications written by Dzevad Belkic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-29 with Science categories.
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-
Mathematical Analysis Wavelets And Signal Processing
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Author : Mourad Ismail
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-01-01
Mathematical Analysis Wavelets And Signal Processing written by Mourad Ismail and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Computers categories.
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.
Continued Fractions With Applications
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Author : L. Lorentzen
language : en
Publisher: North Holland
Release Date : 1992-11-08
Continued Fractions With Applications written by L. Lorentzen and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Computers categories.
This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.
Photonic Signal Processing Second Edition
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Author : Le Nguyen Binh
language : en
Publisher: CRC Press
Release Date : 2019-01-15
Photonic Signal Processing Second Edition written by Le Nguyen Binh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-15 with Technology & Engineering categories.
This Second Edition of "Photonic Signal Processing" updates most recent R&D on processing techniques of signals in photonic domain from the fundamentals given in its first edition. Several modern techniques in Photonic Signal Processing (PSP) are described: Graphical signal flow technique to simplify the analysis of the photonic transfer functions, plus its insights into the physical phenomena of such processors. The resonance and interference of optical fields are presented by the poles and zeros of the optical circuits, respectively. Detailed design procedures for fixed and tunable optical filters. These filters, "brick-wall-like", now play a highly important role in ultra-broadband (100GBaud) to spectral shaping of sinc temporal response so as to generate truly Nyquist sampler of the received eye diagrams 3-D PSP allows multi-dimensional processing for highly complex optical signals Photonic differentiators and integrators for dark soliton generations. Optical dispersion compensating processors for ultra-long haul optical transmission systems. Some optical devices essentials for PSP. Many detailed PSP techniques are given in the chapters of this Second Edition.
Quantum Mechanical Signal Processing And Spectral Analysis
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Author : Dzevad Belkic
language : en
Publisher: CRC Press
Release Date : 2019-08-22
Quantum Mechanical Signal Processing And Spectral Analysis written by Dzevad Belkic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.
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.
Analytic Theory Of Continued Fractions
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Author : W. B. Jones
language : en
Publisher: Springer
Release Date : 2006-11-17
Analytic Theory Of Continued Fractions written by W. B. Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-17 with Mathematics categories.