Algorithms For Discrete Fourier Transform And Convolution
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Algorithms For Discrete Fourier Transform And Convolution
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Author : Richard Tolimieri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Algorithms For Discrete Fourier Transform And Convolution written by Richard Tolimieri 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 2013-06-29 with Technology & Engineering categories.
This book is based on several courses taught during the last five years at the City College of the City University of New York and at Fudan University, Shanghai, China in the Summer, 1986. It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level, a collection of algorithms which would serve to represent the vast array of algorithms designed over the last twenty years for com puting the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical con cepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools which can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural lan guage and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algorithms. This belief is reenforced by the complex and time-consumming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and precedures which reduce and at times automate this task. In Chapter 1, a survey is given of basic algebra.
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.
Algorithms For Discrete Fourier Transform And Convolution
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Author : Richard Tolimieri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algorithms For Discrete Fourier Transform And Convolution written by Richard Tolimieri 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 2013-03-09 with Technology & Engineering categories.
This book is based on several courses taught during the years 1985-1989 at the City College of the City University of New York and at Fudan Univer sity, Shanghai, China, in the summer of 1986. It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level a collection of algorithms that would serve to represent the vast array of algorithms designed over the last twenty years for computing the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical concepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools that can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural language and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algo rithms. This belief is reinforced by the complex and time-consuming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and procedures that reduce and at times automate this task.
Dft Fft And Convolution Algorithms And Implementation
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Author : C. S. Burrus
language : en
Publisher: Wiley-Interscience
Release Date : 1985-01-18
Dft Fft And Convolution Algorithms And Implementation written by C. S. Burrus and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-18 with Technology & Engineering categories.
This readable handbook provides complete coverage of both the theory and implementation of modern signal processing algorithms for computing the Discrete Fourier transform. Reviews continuous and discrete-time transform analysis of signals and properties of DFT, several ways to compute the DFT at a few frequencies, and the three main approaches to an FFT. Practical, tested FORTRAN and assembly language programs are included with enough theory to adapt them to particular applications. Compares and evaluates various algorithms.
Digital Signal Processing Algorithms
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Author : Hari Krishna
language : en
Publisher:
Release Date : 2017
Digital Signal Processing Algorithms written by Hari Krishna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with 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."--Provided by publisher.
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.
Fast Fourier Transform And Convolution Algorithms
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Author : Henri J Nussbaumer
language : en
Publisher:
Release Date : 1982-09-01
Fast Fourier Transform And Convolution Algorithms written by Henri J Nussbaumer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-09-01 with categories.
The Discrete Fourier Transform
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Author : D. Sundararajan
language : en
Publisher: World Scientific
Release Date : 2001
The Discrete Fourier Transform written by D. Sundararajan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."
Discrete And Continuous Fourier Transforms
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Author : Eleanor Chu
language : en
Publisher: CRC Press
Release Date : 2008-03-19
Discrete And Continuous Fourier Transforms written by Eleanor Chu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-19 with Mathematics categories.
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform