Fast Fourier Transforms

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Fast Fourier Transform and Convolution Algorithms

H.J. Nussbaumer
Fast Fourier Transform and Convolution Algorithms Book PDF

Author : H.J. Nussbaumer
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,7 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9783662005514

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Fast Fourier Transform and Convolution Algorithms by H.J. Nussbaumer Pdf

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.

Fast Fourier Transform - Algorithms and Applications

K.R. Rao,Do Nyeon Kim,Jae Jeong Hwang
Fast Fourier Transform Algorithms and Applications Book PDF

Author : K.R. Rao,Do Nyeon Kim,Jae Jeong Hwang
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 53,7 Mb
Release : 2011-02-21
Category : Mathematics
ISBN : 9781402066290

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Fast Fourier Transform - Algorithms and Applications by K.R. Rao,Do Nyeon Kim,Jae Jeong Hwang Pdf

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.

The Fast Fourier Transform and Its Applications

E. Oran Brigham
The Fast Fourier Transform and Its Applications Book PDF

Author : E. Oran Brigham
Publisher : Pearson
Page : 474 pages
File Size : 45,9 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015047815561

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The Fast Fourier Transform and Its Applications by E. Oran Brigham Pdf

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.

Computational Frameworks for the Fast Fourier Transform

Charles Van Loan
Computational Frameworks for the Fast Fourier Transform Book PDF

Author : Charles Van Loan
Publisher : SIAM
Page : 285 pages
File Size : 41,9 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 9780898712858

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Computational Frameworks for the Fast Fourier Transform by Charles Van Loan Pdf

The author captures the interplay between mathematics and the design of effective numerical algorithms.

The Fast Fourier Transform

E. Oran Brigham
The Fast Fourier Transform Book PDF

Author : E. Oran Brigham
Publisher : Prentice Hall
Page : 272 pages
File Size : 46,8 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015000492960

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The Fast Fourier Transform by E. Oran Brigham Pdf

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.

Fast Fourier Transforms

C. Sidney Burrus
Fast Fourier Transforms Book PDF

Author : C. Sidney Burrus
Publisher : Lulu.com
Page : 256 pages
File Size : 46,6 Mb
Release : 2012-11-30
Category : Technology & Engineering
ISBN : 9781300461647

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Fast Fourier Transforms by C. Sidney Burrus Pdf

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.

Inside the FFT Black Box

Eleanor Chu,Alan George
Inside the FFT Black Box Book PDF

Author : Eleanor Chu,Alan George
Publisher : CRC Press
Page : 346 pages
File Size : 50,8 Mb
Release : 1999-11-11
Category : Mathematics
ISBN : 1420049968

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Inside the FFT Black Box by Eleanor Chu,Alan George Pdf

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

Daisuke Takahashi
Fast Fourier Transform Algorithms for Parallel Computers Book PDF

Author : Daisuke Takahashi
Publisher : Springer Nature
Page : 120 pages
File Size : 41,5 Mb
Release : 2019-10-05
Category : Computers
ISBN : 9789811399657

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Fast Fourier Transform Algorithms for Parallel Computers by Daisuke Takahashi Pdf

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.

Mathematics of the Discrete Fourier Transform (DFT)

Julius O. Smith
Mathematics of the Discrete Fourier Transform DFT Book PDF

Author : Julius O. Smith
Publisher : Julius Smith
Page : 323 pages
File Size : 43,7 Mb
Release : 2008
Category : Fourier transformations
ISBN : 9780974560748

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Mathematics of the Discrete Fourier Transform (DFT) by Julius O. Smith Pdf

"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

Fast Fourier Transforms

James S. Walker
Fast Fourier Transforms Book PDF

Author : James S. Walker
Publisher : CRC Press
Page : 242 pages
File Size : 47,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351448871

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Fast Fourier Transforms by James S. Walker Pdf

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 :

Discrete and Continuous Fourier Transforms

Eleanor Chu
Discrete and Continuous Fourier Transforms Book PDF

Author : Eleanor Chu
Publisher : CRC Press
Page : 423 pages
File Size : 48,5 Mb
Release : 2008-03-19
Category : Mathematics
ISBN : 9781420063646

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Discrete and Continuous Fourier Transforms by Eleanor Chu Pdf

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

Fast Transforms Algorithms, Analyses, Applications

Douglas F. Elliott,K. Ramamohan Rao
Fast Transforms Algorithms Analyses Applications Book PDF

Author : Douglas F. Elliott,K. Ramamohan Rao
Publisher : Elsevier
Page : 448 pages
File Size : 44,5 Mb
Release : 1983-03-09
Category : Mathematics
ISBN : 9780080918068

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Fast Transforms Algorithms, Analyses, Applications by Douglas F. Elliott,K. Ramamohan Rao Pdf

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.

Data-Driven Science and Engineering

Steven L. Brunton,J. Nathan Kutz
Data Driven Science and Engineering Book PDF

Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Page : 615 pages
File Size : 43,6 Mb
Release : 2022-05-05
Category : Computers
ISBN : 9781009098489

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Data-Driven Science and Engineering by Steven L. Brunton,J. Nathan Kutz Pdf

A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing

Sonali Bagchi,Sanjit K. Mitra
The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing Book PDF

Author : Sonali Bagchi,Sanjit K. Mitra
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461549253

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The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing by Sonali Bagchi,Sanjit K. Mitra Pdf

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.

Mathematics of Multidimensional Fourier Transform Algorithms

Richard Tolimieri,Myoung An,Chao Lu
Mathematics of Multidimensional Fourier Transform Algorithms Book PDF

Author : Richard Tolimieri,Myoung An,Chao Lu
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781468402056

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Mathematics of Multidimensional Fourier Transform Algorithms by Richard Tolimieri,Myoung An,Chao Lu Pdf

The main emphasis of this book is the development of algorithms for processing multi-dimensional digital signals, and particularly algorithms for multi-dimensional Fourier transforms, in a form that is convenient for writing highly efficient code on a variety of vector and parallel computers.