The DFT

An Owners' Manual for the Discrete Fourier Transform

Author: William L. Briggs,Van Emden Henson

Publisher: SIAM

ISBN: 0898713420

Category: Mathematics

Page: 434

View: 8501

This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

The Discrete Fourier Transform

Theory, Algorithms and Applications

Author: D. Sundararajan

Publisher: World Scientific

ISBN: 9789812810298

Category: Mathematics

Page: 392

View: 2939

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."

Multiplicative Complexity, Convolution, and the DFT

Author: Michael T. Heideman

Publisher: Springer Science & Business Media

ISBN: 1461239125

Category: Technology & Engineering

Page: 155

View: 7729

This book is intended to be a comprehensive reference to multiplicative com plexity theory as applied to digital signal processing computations. Although a few algorithms are included to illustrate the theory, I concentrated more on the develop ment of the theory itself. Howie Johnson's infectious enthusiasm for designing efficient DfT algorithms got me interested in this subject. I am grateful to Prof. Sid Burrus for encouraging and supporting me in this effort. I would also like to thank Henrik Sorensen and Doug Jones for many stimulating discussions. lowe a great debt to Shmuel Winograd, who, almost singlehandedly, provided most of the key theoretical results that led to this present work. His monograph, Arithmetic Complexity o/Computations, introduced me to the mechanism behind the proofs of theorems in multiplicative complexity. enabling me to return to his earlier papers and appreciate the elegance of his methods for deriving the theory. The second key work that influenced me was the paper by Louis Auslander and Winograd on multiplicative complexity of semilinear systems defined by polynomials. After reading this paper, it was clear to me that this theory could be applied to many impor tant computational problems. These influences can be easily discerned in the present work.

Mastering the Discrete Fourier Transform in One, Two or Several Dimensions

Pitfalls and Artifacts

Author: Isaac Amidror

Publisher: Springer Science & Business Media

ISBN: 1447151674

Category: Mathematics

Page: 375

View: 9005

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

Digital Signal Processing

An Experimental Approach

Author: Shlomo Engelberg

Publisher: Springer Science & Business Media

ISBN: 1848001193

Category: Technology & Engineering

Page: 212

View: 4311

A mathematically rigorous but accessible treatment of digital signal processing that intertwines basic theoretical techniques with hands-on laboratory instruction is provided by this book. The book covers various aspects of the digital signal processing (DSP) "problem". It begins with the analysis of discrete-time signals and explains sampling and the use of the discrete and fast Fourier transforms. The second part of the book — covering digital to analog and analog to digital conversion — provides a practical interlude in the mathematical content before Part III lays out a careful development of the Z-transform and the design and analysis of digital filters.

Signal Processing Handbook

Author: C.H. Chen

Publisher: CRC Press

ISBN: 9780824779566

Category: Technology & Engineering

Page: 840

View: 3440

Introductory, systematic treatment of the many interrelated aspects. Twenty-three contributions address the fundamentals, spectral estimation algorithms, image processing, land and ocean seismic data, telecommunications, 3-D object reconstructions. Alk. paper. Annotation copyright Book News, Inc. Po

Non-covalent Interactions

Theory and Experiment

Author: Pavel Hobza,Klaus Müller-Dethlefs

Publisher: Royal Society of Chemistry

ISBN: 1847558534

Category: Science

Page: 225

View: 5984

Co-authored by an experimentalist (Klaus M ller-Dethlefs ) and theoretician (Pavel Hobza), the aim of this book is to provide a general introduction into the science behind non-covalent interactions and molecular complexes using some important experimental and theoretical methods and approaches."

Fourier and Laplace Transforms

Author: H. G. ter Morsche,J. C. van den Berg,E. M. van de Vrie

Publisher: Cambridge University Press

ISBN: 9780521534413

Category: Mathematics

Page: 447

View: 758

This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Signals and Systems with MATLAB

Author: Won Young Yang

Publisher: Springer Science & Business Media

ISBN: 3540929541

Category: Technology & Engineering

Page: 474

View: 392

This book is primarily intended for junior-level students who take the courses on ‘signals and systems’. It may be useful as a reference text for practicing engineers and scientists who want to acquire some of the concepts required for signal proce- ing. The readers are assumed to know the basics about linear algebra, calculus (on complex numbers, differentiation, and integration), differential equations, Laplace R transform, and MATLAB . Some knowledge about circuit systems will be helpful. Knowledge in signals and systems is crucial to students majoring in Electrical Engineering. The main objective of this book is to make the readers prepared for studying advanced subjects on signal processing, communication, and control by covering from the basic concepts of signals and systems to manual-like introduc- R R tions of how to use the MATLAB and Simulink tools for signal analysis and lter design. The features of this book can be summarized as follows: 1. It not only introduces the four Fourier analysis tools, CTFS (continuous-time Fourier series), CTFT (continuous-time Fourier transform), DFT (discrete-time Fourier transform), and DTFS (discrete-time Fourier series), but also illuminates the relationship among them so that the readers can realize why only the DFT of the four tools is used for practical spectral analysis and why/how it differs from the other ones, and further, think about how to reduce the difference to get better information about the spectral characteristics of signals from the DFT analysis.

Techniques in Speech Acoustics

Author: J. Harrington,S. Cassidy

Publisher: Springer Science & Business Media

ISBN: 9401146578

Category: Language Arts & Disciplines

Page: 319

View: 5615

Techniques in Speech Acoustics provides an introduction to the acoustic analysis and characteristics of speech sounds. The first part of the book covers aspects of the source-filter decomposition of speech, spectrographic analysis, the acoustic theory of speech production and acoustic phonetic cues. The second part is based on computational techniques for analysing the acoustic speech signal including digital time and frequency analyses, formant synthesis, and the linear predictive coding of speech. There is also an introductory chapter on the classification of acoustic speech signals which is relevant to aspects of automatic speech and talker recognition. The book intended for use as teaching materials on undergraduate and postgraduate speech acoustics and experimental phonetics courses; also aimed at researchers from phonetics, linguistics, computer science, psychology and engineering who wish to gain an understanding of the basis of speech acoustics and its application to fields such as speech synthesis and automatic speech recognition.

Sound Capture for Human / Machine Interfaces

Practical Aspects of Microphone Array Signal Processing

Author: Wolfgang Herbordt

Publisher: Springer Science & Business Media

ISBN: 9783540239543

Category: Technology & Engineering

Page: 276

View: 7358

With a continuously increasing desire for natural and comfortable human/machine interaction, the acoustic interface of any terminal for multimedia or telecommunication services is challenged to allow seamless and hands-free audio communication. Sound Capture for Human-Machine Interfaces introduces the practical aspects of microphone array signal processing and presents various combinations of beamforming and acoustic echo cancellation.

Discrete and Continuous Fourier Transforms

Analysis, Applications and Fast Algorithms

Author: Eleanor Chu

Publisher: CRC Press

ISBN: 9781420063646

Category: Mathematics

Page: 424

View: 8629

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 Transforms: Analysis, Applications and Fast Algorithms presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and FFT algorithms. This accessible, self-contained book provides meaningful interpretations of essential formulas in the context of applications, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. It comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and many FFT algorithms unified under the frameworks of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text. Requiring no prior knowledge of Fourier analysis or signal processing, this book supplies the basis for using FFT algorithms to compute the DFT in a variety of application areas.

Introductory Signal Processing

Author: Roland Priemer

Publisher: World Scientific

ISBN: 9789971509194

Category: Technology & Engineering

Page: 734

View: 2669

A valuable introduction to the fundamentals of continuous and discrete time signal processing, this book is intended for the reader with little or no background in this subject. The emphasis is on development from basic principles. With this book the reader can become knowledgeable about both the theoretical and practical aspects of digital signal processing.Some special features of this book are: (1) gradual and step-by-step development of the mathematics for signal processing, (2) numerous examples and homework problems, (3) evolutionary development of Fourier series, Discrete Fourier Transform, Fourier Transform, Laplace Transform, and Z-Transform, (4) emphasis on the relationship between continuous and discrete time signal processing, (5) many examples of using the computer for applying the theory, (6) computer based assignments to gain practical insight, (7) a set of computer programs to aid the reader in applying the theory.

Mobile Communications Handbook, Third Edition

Author: Jerry D. Gibson

Publisher: CRC Press

ISBN: 1439817235

Category: Technology & Engineering

Page: 813

View: 1700

With 26 entirely new and 5 extensively revised chapters out of the total of 39, the Mobile Communications Handbook, Third Edition presents an in-depth and up-to-date overview of the full range of wireless and mobile technologies that we rely on every day. This includes, but is not limited to, everything from digital cellular mobile radio and evolving personal communication systems to wireless data and wireless networks Illustrating the extraordinary evolution of wireless communications and networks in the last 15 years, this book is divided into five sections: Basic Principles provides the essential underpinnings for the wide-ranging mobile communication technologies currently in use throughout the world. Wireless Standards contains technical details of the standards we use every day, as well as insights into their development. Source Compression and Quality Assessment covers the compression techniques used to represent voice and video for transmission over mobile communications systems as well as how the delivered voice and video quality are assessed. Wireless Networks examines the wide range of current and developing wireless networks and wireless methodologies. Emerging Applications explores newly developed areas of vehicular communications and 60 GHz wireless communications. Written by experts from industry and academia, this book provides a succinct overview of each topic, quickly bringing the reader up to date, but with sufficient detail and references to enable deeper investigations. Providing much more than a "just the facts" presentation, contributors use their experience in the field to provide insights into how each topic has emerged and to point toward forthcoming developments in mobile communications.

Novel Sampling Approaches in Higher Dimensional NMR

Author: Martin Billeter,Vladislav Orekhov

Publisher: Springer Science & Business Media

ISBN: 3642271596

Category: Science

Page: 152

View: 7590

Concepts in Projection-Reconstruction, by Ray Freeman and riks Kupe.- Automated Projection Spectroscopy and Its Applications, by Sebastian Hiller and Gerhard Wider.- Data Sampling in Multidimensional NMR: Fundamentals and Strategies, by Mark W. Maciejewski, Mehdi Mobli, Adam D. Schuyler, Alan S. Stern and Jeffrey C. Hoch.- Generalized Fourier Transform for Non-Uniform Sampled Data, by Krzysztof Kazimierczuk, Maria Misiak, Jan Stanek, Anna Zawadzka-Kazimierczuk and Wiktor Komiski.- Applications of Non-Uniform Sampling and Processing, by Sven G. Hyberts, Haribabu Arthanari and Gerhard Wagner

DSP for MATLAB and LabVIEW: Fundamentals of discrete frequency transforms

Author: Forester W. Isen

Publisher: Morgan & Claypool Publishers

ISBN: 1598298933

Category: Technology & Engineering

Page: 217

View: 939

This book is Volume II of the series DSP for MATLABâ„¢ and LabVIEWâ„¢. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z -Transform (including definition and properties, the inverse z -transform, frequency response via z-transform, and alternate filter realization topologies (including Direct Form, Direct Form Transposed, Cascade Form, Parallel Form, and Lattice Form), and the Discrete Fourier Transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair, DFT of common signals, bin width, sampling duration and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT). The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form (available via the internet at http://www.morganclaypool.com/page/isen) will run on both MATLABâ„¢ and LabVIEWâ„¢. The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEWâ„¢ Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer. Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter 4 of Volume I, in particular, provides an intuitive or "first principle" understanding of how digital filtering and frequency transforms work, preparing the reader for the present volume (Volume II). Volume III of the series covers digital filter design (FIR design using Windowing, Frequency Sampling, and Optimum Equiripple techniques, and Classical IIR design) and Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications.

Algebraic and Stochastic Coding Theory

Author: Dave K. Kythe,Prem K. Kythe

Publisher: CRC Press

ISBN: 1466505621

Category: Computers

Page: 512

View: 623

Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.