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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.

Author : James S. Walker
ISBN : 9781351448871
Genre : Mathematics
File Size : 56.68 MB
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This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :

Author : H.J. Nussbaumer
ISBN : 9783662005514
Genre : Mathematics
File Size : 85.8 MB
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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.

Author : Eleanor Chu
ISBN : 9781420063646
Genre : Mathematics
File Size : 55.65 MB
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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

Author : Ameen Baig Mirza
ISBN : OCLC:489476806
Genre : Computer science
File Size : 73.3 MB
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"Fourier Transforms have wide range of applications ranging from signal processing to astronomy. The advent of digital computers led to the development of the FFT (Fast Fourier Transform) in 1965. The Fourier Transform algorithm involves many add/multiply computations involving trigonometric functions, and FFT significantly increased the speed at which the Fourier transform could be computed. A great deal of research has been done to optimize the FFT computation to provide much better computational speed. The modern advent of parallel computation offers a new opportunity to significantly increase the speed of computing the Fourier transform. This project provides a C code implementation of a new parallel method of computing this important transform. This implementation assigns computational tasks to different processors using the Message Passing Interface (MPI) library. This method involves parallel computation of the Discrete Cosine Transform (DCT) as one of the parts. Computation on two different computer clusters using up to six processors have been performed, results and comparisons with other implementations are presented."--Abstract.

Author : Jyrki Kauppinen
ISBN : 3527402896
Genre : Science
File Size : 36.94 MB
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This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical point of view. Some aspects, linear prediction for example, are explained here thoroughly for the first time.

Author : Winthrop W. Smith
ISBN : UOM:39015040732474
Genre : Technology & Engineering
File Size : 50.22 MB
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"This useful, logical, unbiased, FFT compendium allows the user to quickly and accurately obtain practical information to implement a solution or simply acquire a general overview without spending months gathering this information elsewhere." —Jay Perry, Executive Vice President, Technology, Catalina Research, Inc. "This is a practical guide for understanding and using FFTs. Win’s (Winthrop Smith, author) years of experience using FFTs to solve real-world problems comes through on page after page. If you’re building an FFT processor, you’ll find this book indispensable." —Tony Agnello, President, Ariel Corp. FFTs are at the heart of ADSL, the new telecom standard (T1.413), which allows phones to transfer digital data 200 times faster and simultaneously transmit speech. Fast Fourier Transforms (FFTs) synthesize, recognize, enhance, compress, modify, or analyze signals in products such as Doppler weather radar, CT and MRI scans, AWACS radar, and satellite imaging radar. In this book, you will get the foundation and facts you need to implement FFT algorithms for many diverse applications. Key features you will put to immediate use include: Comparison matrices and performance measures for objective selection of weighting functions, algorithm building blocks, algorithms, algorithm mappings, arithmetic formats, and DSP chips Extensive algorithm examples with instructions for memory mapping and conversion to code An unbiased listing of the FFT features of 51 fixed-point DSP chips, including ASIC and multiprocessor chips, 13 floating-point DSP chips, and six dedicated FFT chips Test signals with instructions and examples on how to detect and isolate errors during: FFT algorithm/code development and debugging, and end-product operation Design examples for products that use frequency analysis, power spectrum estimation, linear filtering, and two-dimensional processing Questions and answers for selecting commercial-off-the-shelf DSP boards An all-in-one-source for implementing real-time FFT algorithms of any length, this book will be essential to engineers and other technical innovators who want to stay on the cutting edge of FFT technology.

Author : D. Sundararajan
ISBN : 9812810293
Genre : Mathematics
File Size : 54.98 MB
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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."

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.

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Discrete Fourier transform, Unitary matrix, Shift operator, Rotation, Relations between Fourier transforms and Fourier series, Unitary operator, Dilation, Russo-Dye theorem, Fourier operator. Excerpt: The Fourier transform is a mathematical operation that decomposes a signal into its constituent frequencies. Thus the Fourier transform of a musical chord is a mathematical representation of the amplitudes of the individual notes that make it up. The original signal depends on time, and therefore is called the time domain representation of the signal, whereas the Fourier transform depends on frequency and is called the frequency domain representation of the signal. The term Fourier transform refers both to the frequency domain representation of the signal and the process that transforms the signal to its frequency domain representation. In mathematical terms, the Fourier transform 'transforms' one complex-valued function of a real variable into another. In effect, the Fourier transform decomposes a function into oscillatory functions. The Fourier transform and its generalizations are the subject of Fourier analysis. In this specific case, both the time and frequency domains are unbounded linear continua. It is possible to define the Fourier transform of a function of several variables, which is important for instance in the physical study of wave motion and optics. It is also possible to generalize the Fourier transform on discrete structures such as finite groups. The efficient computation of such structures, by fast Fourier transform, is essential for high-speed computing. There are several common conventions for defining the Fourier transform of an integrable function (Kaiser 1994). This article will use the definition: for every real number .When the independent variable x represents time (with SI unit of seconds)...