Fast Polynomial Transforms

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Fast Polynomial Transforms

Author : Jens Keiner
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832528504
Total Pages : 231 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Fast Polynomial Transforms by : Jens Keiner

Download or read book Fast Polynomial Transforms written by Jens Keiner and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Fast Fourier Transform and Convolution Algorithms

Author : H.J. Nussbaumer
Publisher : Springer Science & Business Media
ISBN 13 : 3662005514
Total Pages : 260 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Fast Fourier Transform and Convolution Algorithms by : H.J. Nussbaumer

Download or read book Fast Fourier Transform and Convolution Algorithms written by H.J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Transforms and Fast Algorithms for Signal Analysis and Representations

Author : Guoan Bi
Publisher : Springer Science & Business Media
ISBN 13 : 0817682201
Total Pages : 439 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Transforms and Fast Algorithms for Signal Analysis and Representations by : Guoan Bi

Download or read book Transforms and Fast Algorithms for Signal Analysis and Representations written by Guoan Bi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive presentation of recent results and developments on several widely used transforms and their fast algorithms. In many cases, new options are provided for improved or new fast algorithms, some of which are not well known in the digital signal processing community. The book is suitable as a textbook for senior undergraduate and graduate courses in digital signal processing. It may also serve as an excellent self-study reference for electrical engineers and applied mathematicians whose work is related to the fields of electronics, signal processing, image and speech processing, or digital design and communication.

Fast Fourier Transform and Convolution Algorithms

Author : Henri J Nussbaumer
Publisher :
ISBN 13 : 9783642818981
Total Pages : 292 pages
Book Rating : 4.8/5 (189 download)

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Book Synopsis Fast Fourier Transform and Convolution Algorithms by : Henri J Nussbaumer

Download or read book Fast Fourier Transform and Convolution Algorithms written by Henri J Nussbaumer and published by . This book was released on 1982-09-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fast Fourier Transform and Convolution Algorithms

Author : Henri J. Nussbaumer
Publisher : Springer Science & Business Media
ISBN 13 : 3642818978
Total Pages : 286 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Fast Fourier Transform and Convolution Algorithms by : Henri J. Nussbaumer

Download or read book Fast Fourier Transform and Convolution Algorithms written by Henri J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first edition of this book, we covered in Chapter 6 and 7 the applications to multidimensional convolutions and DFT's of the transforms which we have introduced, back in 1977, and called polynomial transforms. Since the publication of the first edition of this book, several important new developments concerning the polynomial transforms have taken place, and we have included, in this edition, a discussion of the relationship between DFT and convolution polynomial transform algorithms. This material is covered in Appendix A, along with a presentation of new convolution polynomial transform algorithms and with the application of polynomial transforms to the computation of multidimensional cosine transforms. We have found that the short convolution and polynomial product algorithms of Chap. 3 have been used extensively. This prompted us to include, in this edition, several new one-dimensional and two-dimensional polynomial product algorithms which are listed in Appendix B. Since our book is being used as part of several graduate-level courses taught at various universities, we have added, to this edition, a set of problems which cover Chaps. 2 to 8. Some of these problems serve also to illustrate some research work on DFT and convolution algorithms. I am indebted to Mrs A. Schlageter who prepared the manuscript of this second edition. Lausanne HENRI J. NUSSBAUMER April 1982 Preface to the First Edition 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.

Fast Transforms Algorithms, Analyses, Applications

Author : Douglas F. Elliott
Publisher : Elsevier
ISBN 13 : 0080918069
Total Pages : 448 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Fast Transforms Algorithms, Analyses, Applications by : Douglas F. Elliott

Download or read book Fast Transforms Algorithms, Analyses, Applications written by Douglas F. Elliott and published by Elsevier. This book was released on 1983-03-09 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Binary Polynomial Transforms and Non-Linear Digital Filters

Author : S. Agaian
Publisher : CRC Press
ISBN 13 : 9780824796426
Total Pages : 332 pages
Book Rating : 4.7/5 (964 download)

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Book Synopsis Binary Polynomial Transforms and Non-Linear Digital Filters by : S. Agaian

Download or read book Binary Polynomial Transforms and Non-Linear Digital Filters written by S. Agaian and published by CRC Press. This book was released on 1995-04-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. The book also: introduces the Rademacher logical functions; considers fast algorithms for computing Rademacher and polynomial logical functions; focuses attention on general auto- and cross-correlation functions; and more.;The work is intended for applied mathematicians; electrical, electronics and other engineers; computer scientists; and upper-level undergraduate and graduate students in these disciplines.

Fast Fourier Transforms

Author : C. Sidney Burrus
Publisher : Lulu.com
ISBN 13 : 1300461640
Total Pages : 256 pages
Book Rating : 4.3/5 (4 download)

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Book Synopsis Fast Fourier Transforms by : C. Sidney Burrus

Download or read book Fast Fourier Transforms written by C. Sidney Burrus and published by Lulu.com. This book was released on 2012-11-30 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.

The Fast Fourier Transform

Author : E. Oran Brigham
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Fast Fourier Transform by : E. Oran Brigham

Download or read book The Fast Fourier Transform written by E. Oran Brigham and published by Prentice Hall. This book was released on 1974 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourier transform; Fourier transform properties; Convolution and correlation; Fourier series and sampled waveforms; The discrete fourier transform; Discrete convolutiion and correlation; Applying the discrete fourier transform.

Fast Fourier Transform - Algorithms and Applications

Author : K.R. Rao
Publisher : Springer Science & Business Media
ISBN 13 : 1402066295
Total Pages : 437 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Fast Fourier Transform - Algorithms and Applications by : K.R. Rao

Download or read book Fast Fourier Transform - Algorithms and Applications written by K.R. Rao and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Engineering Applications of Noncommutative Harmonic Analysis

Author : Gregory S. Chirikjian
Publisher : CRC Press
ISBN 13 : 1000694259
Total Pages : 697 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian

Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2021-02-25 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fast Algorithms for Signal Processing

Author : Richard E. Blahut
Publisher : Cambridge University Press
ISBN 13 : 1139487957
Total Pages : 469 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Fast Algorithms for Signal Processing by : Richard E. Blahut

Download or read book Fast Algorithms for Signal Processing written by Richard E. Blahut and published by Cambridge University Press. This book was released on 2010-06-24 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Digital Image Processing Algorithms and Applications

Author : Ioannis Pitas
Publisher : John Wiley & Sons
ISBN 13 : 9780471377399
Total Pages : 436 pages
Book Rating : 4.3/5 (773 download)

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Book Synopsis Digital Image Processing Algorithms and Applications by : Ioannis Pitas

Download or read book Digital Image Processing Algorithms and Applications written by Ioannis Pitas and published by John Wiley & Sons. This book was released on 2000-02-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique collection of algorithms and lab experiments for practitioners and researchers of digital image processing technology With the field of digital image processing rapidly expanding, there is a growing need for a book that would go beyond theory and techniques to address the underlying algorithms. Digital Image Processing Algorithms and Applications fills the gap in the field, providing scientists and engineers with a complete library of algorithms for digital image processing, coding, and analysis. Digital image transform algorithms, edge detection algorithms, and image segmentation algorithms are carefully gleaned from the literature for compatibility and a track record of acceptance in the scientific community. The author guides readers through all facets of the technology, supplementing the discussion with detailed lab exercises in EIKONA, his own digital image processing software, as well as useful PDF transparencies. He covers in depth filtering and enhancement, transforms, compression, edge detection, region segmentation, and shape analysis, explaining at every step the relevant theory, algorithm structure, and its use for problem solving in various applications. The availability of the lab exercises and the source code (all algorithms are presented in C-code) over the Internet makes the book an invaluable self-study guide. It also lets interested readers develop digital image processing applications on ordinary desktop computers as well as on Unix machines.

Inside the FFT Black Box

Author : Eleanor Chu
Publisher : CRC Press
ISBN 13 : 9781420049961
Total Pages : 346 pages
Book Rating : 4.0/5 (499 download)

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Book Synopsis Inside the FFT Black Box by : Eleanor Chu

Download or read book Inside the FFT Black Box written by Eleanor Chu and published by CRC Press. This book was released on 1999-11-11 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.

Computational Frameworks for the Fast Fourier Transform

Author : Charles Van Loan
Publisher : SIAM
ISBN 13 : 9781611970999
Total Pages : 286 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Computational Frameworks for the Fast Fourier Transform by : Charles Van Loan

Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.

Discrete Cosine Transform

Author : K. Ramamohan Rao
Publisher : Academic Press
ISBN 13 : 0080925340
Total Pages : 517 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Discrete Cosine Transform by : K. Ramamohan Rao

Download or read book Discrete Cosine Transform written by K. Ramamohan Rao and published by Academic Press. This book was released on 2014-06-28 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive treatment of the theoretical aspects of the discrete cosine transform (DCT), which is being recommended by various standards organizations, such as the CCITT, ISO etc., as the primary compression tool in digital image coding. The main purpose of the book is to provide a complete source for the user of this signal processing tool, where both the basics and the applications are detailed. An extensive bibliography covers both the theory and applications of the DCT. The novice will find the book useful in its self-contained treatment of the theory of the DCT, the detailed description of various algorithms supported by computer programs and the range of possible applications, including codecs used for teleconferencing, videophone, progressive image transmission, and broadcast TV. The more advanced user will appreciate the extensive references. Tables describing ASIC VLSI chips for implementing DCT, and motion estimation and details on image compression boards are also provided.

Digital Signal Processing Fundamentals

Author : Vijay Madisetti
Publisher : CRC Press
ISBN 13 : 1351835726
Total Pages : 995 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Digital Signal Processing Fundamentals by : Vijay Madisetti

Download or read book Digital Signal Processing Fundamentals written by Vijay Madisetti and published by CRC Press. This book was released on 2017-12-19 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in a three-volume set, this updated and expanded edition of the bestselling The Digital Signal Processing Handbook continues to provide the engineering community with authoritative coverage of the fundamental and specialized aspects of information-bearing signals in digital form. Encompassing essential background material, technical details, standards, and software, the second edition reflects cutting-edge information on signal processing algorithms and protocols related to speech, audio, multimedia, and video processing technology associated with standards ranging from WiMax to MP3 audio, low-power/high-performance DSPs, color image processing, and chips on video. Drawing on the experience of leading engineers, researchers, and scholars, the three-volume set contains 29 new chapters that address multimedia and Internet technologies, tomography, radar systems, architecture, standards, and future applications in speech, acoustics, video, radar, and telecommunications. Emphasizing theoretical concepts, Digital Signal Processing Fundamentals provides comprehensive coverage of the basic foundations of DSP and includes the following parts: Signals and Systems; Signal Representation and Quantization; Fourier Transforms; Digital Filtering; Statistical Signal Processing; Adaptive Filtering; Inverse Problems and Signal Reconstruction; and Time–Frequency and Multirate Signal Processing.