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Fast Polynomial Transforms


Fast Polynomial Transforms
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Fast Polynomial Transforms


Fast Polynomial Transforms
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Author : Jens Keiner
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2011

Fast Polynomial Transforms written by Jens Keiner and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.


Classical orthogonal polynomials and the related associated functions are real classics in approximation theory. They share a rich history of research that has uncovered their many relationships to topics of fundamental importance. This text develops a new aspect of the so-called connection problem. This problem asks how a given expansion in a specific sequence of polynomials or functions may be converted into an equivalent one using a different sequence - often within reason, that is, within the same classical family. A new theory relates this problem to the class of semiseparable matrices. This implies efficient algorithms that have the capacity to cover the connection problem not only numerically efficient, but at the same time, numerically stable. The result has implications for numerical problems whose treatment involves these transformations. One such example, described in more detail, are generalizations of the fast Fourier transform to geometries like the two-sphere or the rotation group SO(3).



Transforms And Fast Algorithms For Signal Analysis And Representations


Transforms And Fast Algorithms For Signal Analysis And Representations
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Author : Guoan Bi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Transforms And Fast Algorithms For Signal Analysis And Representations written by Guoan Bi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.


. . . that is what learning is. You suddenly understand something you've un derstood all your life, but in a new way. Various transforms have been widely used in diverse applications of science, engineering and technology. New transforms are emerging to solve many problems, which may have been left unsolved in the past, or newly created by modern science or technologies. Various meth ods have been continuously reported to improve the implementation of these transforms. Early developments of fast algorithms for discrete transforms have significantly stimulated the advance of digital signal processing technologies. More than 40 years after fast Fourier transform algorithms became known, several discrete transforms, including the discrete Hart ley transform and discrete cosine transform, were proposed and widely used for numerous applications. Although they all are related to the discrete Fourier transform, different fast algorithms and their implementations have to be separately developed to minimize compu tational complexity and implementation costs. In spite of the tremendous increase in the speed of computers or processors, the demands for higher processing throughout seemingly never ends. Fast algorithms have become more important than ever for modern applications to become a reality. Many new algorithms recently reported in the literature have led to important improvements upon a number of issues, which will be addressed in this book. Some discrete transforms are not suitable for signals that have time-varying frequency components. Although several approaches are available for such applications, various inher ent problems still remain unsolved.



Fast Fourier Transform And Convolution Algorithms


Fast Fourier Transform And Convolution Algorithms
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Author : H.J. Nussbaumer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08

Fast Fourier Transform And Convolution Algorithms written by H.J. Nussbaumer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Mathematics categories.


This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm.



Fast Transforms Algorithms Analyses Applications


Fast Transforms Algorithms Analyses Applications
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Author : Douglas F. Elliott
language : en
Publisher: Elsevier
Release Date : 1983-03-09

Fast Transforms Algorithms Analyses Applications written by Douglas F. Elliott and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-03-09 with Mathematics categories.


This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.



Fast Algorithms For Signal Processing


Fast Algorithms For Signal Processing
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Author : Richard E. Blahut
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24

Fast Algorithms For Signal Processing written by Richard E. Blahut and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Technology & Engineering categories.


Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-end applications of signal processing, and extend the reach of high-end applications.



Fast Fourier Transform Algorithms And Applications


Fast Fourier Transform Algorithms And Applications
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Author : K.R. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-21

Fast Fourier Transform Algorithms And Applications written by K.R. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-21 with Mathematics categories.


This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.



Digital Signal Processing Algorithms


Digital Signal Processing Algorithms
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Author : Hari Krishna
language : en
Publisher: CRC Press
Release Date : 1998-03-25

Digital Signal Processing Algorithms written by Hari Krishna and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-25 with Technology & Engineering categories.


Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences. Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples. Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing.



Harmonic Analysis For Engineers And Applied Scientists


Harmonic Analysis For Engineers And Applied Scientists
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Author : Gregory S. Chirikjian
language : en
Publisher: Courier Dover Publications
Release Date : 2016-07-20

Harmonic Analysis For Engineers And Applied Scientists written by Gregory S. Chirikjian and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-20 with Mathematics categories.


Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.



Engineering Applications Of Noncommutative Harmonic Analysis


Engineering Applications Of Noncommutative Harmonic Analysis
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Author : Gregory S. Chirikjian
language : en
Publisher: CRC Press
Release Date : 2021-02-25

Engineering Applications Of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.


First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.



Groups And Computation Ii


Groups And Computation Ii
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Author : Larry Finkelstein, William M. Kantor
language : en
Publisher: American Mathematical Soc.
Release Date :

Groups And Computation Ii written by Larry Finkelstein, William M. Kantor 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 with Algebra categories.


Consists of papers presented at the workshop on Groups and Computation held at DIMACS.