Dft Fft And Convolution Algorithms And Implementation
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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.
Dft Fft And Convolution Algorithms
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Author : T. W. Parks
language : en
Publisher:
Release Date : 1985
Dft Fft And Convolution Algorithms written by T. W. Parks and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Convolutions (Mathematics) categories.
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 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 : 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.
Inside The Fft Black Box
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Author : Eleanor Chu
language : en
Publisher: CRC Press
Release Date : 1999-11-11
Inside The Fft Black Box 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 1999-11-11 with Mathematics categories.
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.
Fast Fourier Transform Algorithms For Parallel Computers
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Author : Daisuke Takahashi
language : en
Publisher: Springer Nature
Release Date : 2019-10-05
Fast Fourier Transform Algorithms For Parallel Computers written by Daisuke Takahashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-05 with Computers categories.
Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity analysis, this book offers a valuable reference guide for graduate students, engineers, and scientists in the field who wish to apply FFT to large-scale problems. Parallel computation is becoming indispensable in solving the large-scale problems increasingly arising in a wide range of applications. The performance of parallel supercomputers is steadily improving, and it is expected that a massively parallel system with hundreds of thousands of compute nodes equipped with multi-core processors and accelerators will be available in the near future. Accordingly, the book also provides up-to-date computational techniques relevant to the FFT in state-of-the-art parallel computers. Following the introductory chapter, Chapter 2 introduces readers to the DFT and the basic idea of the FFT. Chapter 3 explains mixed-radix FFT algorithms, while Chapter 4 describes split-radix FFT algorithms. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms, and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers. In closing, Chapter 8 describes parallel FFT algorithms for distributed-memory parallel computers.
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.
Partitioned Convolution Algorithms For Real Time Auralization
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Author : Frank Wefers
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2015-05-11
Partitioned Convolution Algorithms For Real Time Auralization written by Frank Wefers 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 2015-05-11 with Computers categories.
This work discusses methods for efficient audio processing with finite impulse response (FIR) filters. Such filters are widely used for high-quality acoustic signal processing, e.g. for headphone or loudspeaker equalization, in binaural synthesis, in spatial sound reproduction techniques and for the auralization of reverberant environments. This work focuses on real-time applications, where the audio processing is subject to minimal delays (latencies). Different fast convolution concepts (transform-based, interpolation-based and number-theoretic), which are used to implement FIR filters efficiently, are examined regarding their applicability in real-time. These fast, elementary techniques can be further improved by the concept of partitioned convolution. This work introduces a classification and a general framework for partitioned convolution algorithms and analyzes the algorithmic classes which are relevant for real-time filtering: Elementary concepts which do not partition the filter impulse response (e.g. regular Overlap-Add and Overlap-Save convolution) and advanced techniques, which partition filters uniformly and non-uniformly. The algorithms are thereby regarded in their analytic complexity, their performance on target hardware, the optimal choice of parameters, assemblies of multiple filters, multi-channel processing and the exchange of filter impulse responses without audible artifacts. Suitable convolution techniques are identified for different types of audio applications, ranging from resource-aware auralizations on mobile devices to extensive room acoustics audio rendering using dedicated multi-processor systems.