Download or read book Multiplicative Complexity Convolution and the DFT written by Michael T. Heideman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a comprehensive reference to multiplicative com plexity theory as applied to digital signal processing computations. Although a few algorithms are included to illustrate the theory, I concentrated more on the develop ment of the theory itself. Howie Johnson's infectious enthusiasm for designing efficient DfT algorithms got me interested in this subject. I am grateful to Prof. Sid Burrus for encouraging and supporting me in this effort. I would also like to thank Henrik Sorensen and Doug Jones for many stimulating discussions. lowe a great debt to Shmuel Winograd, who, almost singlehandedly, provided most of the key theoretical results that led to this present work. His monograph, Arithmetic Complexity o/Computations, introduced me to the mechanism behind the proofs of theorems in multiplicative complexity. enabling me to return to his earlier papers and appreciate the elegance of his methods for deriving the theory. The second key work that influenced me was the paper by Louis Auslander and Winograd on multiplicative complexity of semilinear systems defined by polynomials. After reading this paper, it was clear to me that this theory could be applied to many impor tant computational problems. These influences can be easily discerned in the present work.
Download or read book On the Multiplicative Complexity of the Discrete Fourier Transform written by S. Winograd and published by . This book was released on 1978 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiplicative Complexity Convolution and the DFT written by Michael T Heideman and published by . This book was released on 1988-08-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Digital Signal Processing Algorithms written by Hari Krishna and published by Routledge. This book was released on 2017-11-22 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Academic Press. This book was released on 2014-05-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.
Download or read book Algorithms for Discrete Fourier Transform and Convolution written by Richard Tolimieri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Next Generation Arithmetic written by John Gustafson and published by Springer Nature. This book was released on 2023-05-11 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Next Generation Arithmetic, CoNGA 2023, held in Singapore, during March 1-2, 2023. The 11 full papers in this book were carefully reviewed and selected from 16 submissions. They were organized in topical sections as follows: Lossless FFTs Using Posit Arithmetic, PLAUs: Posit Logarithmic Approximate Units to Implement Low-Cost Operations with Real Numbers.
Download or read book Computer Science Theory and Applications written by Alexander Kulikov and published by Springer Science & Business Media. This book was released on 2011-06-03 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.
Download or read book Digital Signal Processing Handbook on CD ROM written by VIJAY MADISETTI and published by CRC Press. This book was released on 1999-02-26 with total page 1725 pages. Available in PDF, EPUB and Kindle. Book excerpt: A best-seller in its print version, this comprehensive CD-ROM reference contains unique, fully searchable coverage of all major topics in digital signal processing (DSP), establishing an invaluable, time-saving resource for the engineering community. Its unique and broad scope includes contributions from all DSP specialties, including: telecommunications, computer engineering, acoustics, seismic data analysis, DSP software and hardware, image and video processing, remote sensing, multimedia applications, medical technology, radar and sonar applications
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Download or read book The Digital Signal Processing Handbook written by VIJAY MADISETTI and published by CRC Press. This book was released on 1997-12-29 with total page 1792 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of digital signal processing (DSP) has spurred developments from basic theory of discrete-time signals and processing tools to diverse applications in telecommunications, speech and acoustics, radar, and video. This volume provides an accessible reference, offering theoretical and practical information to the audience of DSP users. This immense compilation outlines both introductory and specialized aspects of information-bearing signals in digital form, creating a resource relevant to the expanding needs of the engineering community. It also explores the use of computers and special-purpose digital hardware in extracting information or transforming signals in advantageous ways. Impacted areas presented include: Telecommunications Computer engineering Acoustics Seismic data analysis DSP software and hardware Image and video processing Remote sensing Multimedia applications Medical technology Radar and sonar applications This authoritative collaboration, written by the foremost researchers and practitioners in their fields, comprehensively presents the range of DSP: from theory to application, from algorithms to hardware.
Download or read book Communications Information and Network Security written by Vijay K. Bhargava and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Communications, Information and Network Security is an excellent reference for both professional and academic researchers in the field of communication. Those working in space-time coding, multiuser detection, and wireless networks will find the book to be of particular use. New and highly original results by leading experts in communication, information theory, and data security are presented. Communications, Information and Network Security is a tribute to the broad and profound work of Ian Blake in the field of communication. All of the contributors have individually and collectively dedicated their work to Professor Blake.
Download or read book Multidimensional Discrete Unitary Transforms written by Artyom M. Grigoryan and published by CRC Press. This book was released on 2003-07-31 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm sele
Download or read book Arithmetic Complexity of Computations written by Shmuel Winograd and published by SIAM. This book was released on 1980-01-01 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms. Results that lead to applications in the area of signal processing are emphasized, since (1) even a modest reduction in the execution time of signal processing problems could have practical significance; (2) results in this area are relatively new and are scattered in journal articles; and (3) this emphasis indicates the flavor of complexity of computation.
