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Fast Fourier Transform Algorithms And Applications
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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.
Book Synopsis Fast Fourier Transform Algorithms for Parallel Computers by : Daisuke Takahashi
Download or read book Fast Fourier Transform Algorithms for Parallel Computers written by Daisuke Takahashi and published by Springer Nature. This book was released on 2019-10-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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 511 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.
Book Synopsis The Fast Fourier Transform and Its Applications by : E. Oran Brigham
Download or read book The Fast Fourier Transform and Its Applications written by E. Oran Brigham and published by Pearson. This book was released on 1988 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
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.
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 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author captures the interplay between mathematics and the design of effective numerical algorithms.
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.
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.
Book Synopsis Discrete and Continuous Fourier Transforms by : Eleanor Chu
Download or read book Discrete and Continuous Fourier Transforms written by Eleanor Chu and published by CRC Press. This book was released on 2008-03-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing by : Sonali Bagchi
Download or read book The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing written by Sonali Bagchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.
Book Synopsis Algorithms for Discrete Fourier Transform and Convolution by : Richard Tolimieri
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 2013-06-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easily accessible book provides a broad view of the latest developments in the field of fast digital signal processing algorithms. It bridges the gap between DSP algorithms and their implementation on a variety of serial and super computers.
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.
Book Synopsis Digital Signal Processing Algorithms by : Hari Krishna
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 676 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.
Book Synopsis Mathematics of the Discrete Fourier Transform (DFT) by : Julius O. Smith
Download or read book Mathematics of the Discrete Fourier Transform (DFT) written by Julius O. Smith and published by Julius Smith. This book was released on 2008 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover
Book Synopsis The Sparse Fourier Transform by : Haitham Hassanieh
Download or read book The Sparse Fourier Transform written by Haitham Hassanieh and published by Morgan & Claypool. This book was released on 2018-02-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary. This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits. This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.
Book Synopsis DFT/FFT and Convolution Algorithms and Implementation by : C. S. Burrus
Download or read book DFT/FFT and Convolution Algorithms and Implementation written by C. S. Burrus and published by Wiley-Interscience. This book was released on 1985-01-18 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
