| Description |
1 online resource (xviii, 423 pages) : illustrations |
| Series |
Signals and communication technology, 1860-4862 |
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Signals and communication technology.
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| Contents |
Fast Fourier Transform: Algorithms and Applications; Preface; Organization of the Book; Contents; Abbreviations; Chapter 1: Introduction; 1.1 Applications of Discrete Fourier Transform; Chapter 2: Discrete Fourier Transform; 2.1 Definitions; 2.1.1 DFT; 2.1.2 IDFT; 2.1.3 Unitary DFT (Normalized); 2.2 The Z-Transform; 2.3 Properties of the DFT; 2.4 Convolution Theorem; 2.4.1 Multiplication Theorem; 2.5 Correlation Theorem; 2.6 Overlap-Add and Overlap-Save Methods; 2.6.1 The Overlap-Add Method; 2.7 Zero Padding in the Data Domain |
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2.8 Computation of DFTs of Two Real Sequences Using One Complex FFT2.9 A Circulant Matrix Is Diagonalized by the DFT Matrix; 2.9.1 Toeplitz Matrix; 2.9.2 Circulant Matrix; 2.9.3 A Circulant Matrix Is Diagonalized by the DFT Matrix; 2.10 Summary; 2.11 Problems; 2.12 Projects; Chapter 3: Fast Algorithms; 3.1 Radix-2 DIT-FFT Algorithm; 3.1.1 Sparse Matrix Factors for the IFFT N = 8; 3.2 Fast Algorithms by Sparse Matrix Factorization; 3.3 Radix-2 DIF-FFT; 3.3.1 DIF-FFT N=8; 3.3.2 In-Place Computations; 3.4 Radix-3 DIT FFT; 3.5 Radix-3 DIF-FFT; 3.6 FFT for N a Composite Number; 3.7 Radix-4 DIT-FFT |
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3.8 Radix-4 DIF-FFT3.9 Split-Radix FFT Algorithm; 3.10 Fast Fourier and BIFORE Transforms by Matrix Partitioning; 3.10.1 Matrix Partitioning; 3.10.2 DFT Algorithm; 3.10.3 BT (BIFORE Transform); 3.10.4 CBT (Complex BIFORE Transform); 3.10.5 DFT (Sparse Matrix Factorization); 3.11 The Winograd Fourier Transform Algorithm; 3.11.1 Five-Point DFT (Fig. 3.22); 3.11.2 Seven-Point DFT (Fig. 3.23); 3.11.3 Nine-Point DFT (Fig. 3.24); 3.11.4 DFT Algorithms for Real-Valued Input Data; 3.11.5 Winograd Short-N DFT Modules; 3.11.6 Prime Factor Map Indexing; 3.11.7 Winograd Fourier Transform Algorithm (WFTA) |
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3.12 Sparse Factorization of the DFT Matrix3.12.1 Sparse Factorization of the DFT Matrix Using Complex Rotations; 3.12.1.1 Preliminary; 3.12.1.2 Analysis; 3.12.2 Sparse Factorization of the DFT Matrix Using Unitary Matrices; 3.12.2.1 The QR decomposition of the DFT matrix [F]; 3.12.2.2 The unitary matrices in the form of rotations of some kind; 3.13 Unified Discrete Fourier-Hartley Transform; 3.13.1 Fast Structure for UDFHT; 3.14 Bluestein ́s FFT Algorithm; 3.15 Rader Prime Algorithm [A34]; 3.16 Summary; 3.17 Problems; 3.18 Projects; Chapter 4: Integer Fast Fourier Transform; 4.1 Introduction |
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4.2 The Lifting Scheme4.3 Algorithms; 4.3.1 Fixed-Point Arithmetic Implementation; 4.4 Integer Discrete Fourier Transform; 4.4.1 Near-Complete Integer DFT; 4.4.2 Complete Integer DFT; 4.4.3 Energy Conservation; 4.4.4 Circular Shift; 4.5 Summary; 4.6 Problems; 4.7 Projects; Chapter 5: Two-Dimensional Discrete Fourier Transform; 5.1 Definitions; 5.2 Properties; 5.2.1 Periodicity; 5.2.2 Conjugate Symmetry; 5.2.3 Circular Shift in Time/Spatial Domain (Periodic Shift); 5.2.4 Circular Shift in Frequency Domain (Periodic Shift); 5.2.5 Skew Propertyskew property |
| Summary |
Fast Fourier Transform - Algorithms and Applications presents an introduction to the principles of the fast Fourier transform (FFT). It 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 the 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. Fast Fourier Transform - Algorithms and Applications provides a 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 - Algorithms and Applications is designed for senior undergraduate and graduate students, faculty, engineers, and scientists in the field, and self-learners to understand FFTs and directly apply them to their fields, efficiently. It is designed to be both a text and a reference. Thus examples, projects and problems all tied with MATLAB, are provided for grasping the concepts concretely. It also includes references to books and review papers and lists of applications, hardware/software, and useful websites. By including many figures, tables, bock diagrams and graphs, this book helps the reader understand the concepts of fast algorithms readily and intuitively. It provides new MATLAB functions and MATLAB source codes. The material in Fast Fourier Transform - Algorithms and Applications is presented without assuming any prior knowledge of FFT. This book is for any professional who wants to have a basic understanding of the latest developments in and applications of FFT. It provides a good reference for any engineer planning to work in this field, either in basic implementation or in research and development |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| In |
Springer eBooks |
| Subject |
Signal processing -- Digital techniques -- Mathematics.
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Fourier transformations.
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Telecommunication.
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telecommunications.
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Ingénierie.
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Fourier transformations
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Signal processing -- Digital techniques -- Mathematics
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| Form |
Electronic book
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| Author |
Kim, D. N
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Hwang, J. J
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| LC no. |
2010934857 |
| ISBN |
9781402066290 |
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1402066295 |
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