Discrete Fourier Analysis

Author : M. W. Wong
Publisher : Springer Science & Business Media
ISBN 13 : 3034801165
Total Pages : 175 pages
Book Rating : 4.64/5 ( download)

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Download or read book Discrete Fourier Analysis written by M. W. Wong and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Author : Julius O. Smith
Publisher : Julius Smith
ISBN 13 : 097456074X
Total Pages : 323 pages
Book Rating : 4.48/5 ( download)

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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

Author : Sonali Bagchi
Publisher : Springer Science & Business Media
ISBN 13 : 1461549256
Total Pages : 216 pages
Book Rating : 4.53/5 ( download)

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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.

Author : S. Allen Broughton
Publisher : John Wiley & Sons
ISBN 13 : 1119258243
Total Pages : 464 pages
Book Rating : 4.47/5 ( download)

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Download or read book Discrete Fourier Analysis and Wavelets written by S. Allen Broughton and published by John Wiley & Sons. This book was released on 2018-04-03 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets. Discrete Fourier Analysis and Wavelets introduces a new chapter on frames—a new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sophisticated signal analysis. The new coverage also expands upon the discussion on spectrograms using a frames approach. In addition, the book includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets. These new chapters also include appropriate exercises and MATLAB® projects for further experimentation and practice. • Features updated and revised content throughout, continues to emphasize discreteand digital methods, and utilizes MATLAB® to illustrate these concepts • Contains two new chapters on frames and lifting schemes, which take into account crucial new advances in the field of signal and image processing • Expands the discussion on spectrograms using a frames approach, which is an ideal method for reconstructing signals after information has been lost or corrupted (packet erasure) • Maintains a comprehensive treatment of linear signal processing for audio and image signals with a well-balanced and accessible selection of topics that appeal to a diverse audience within mathematics and engineering • Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods • Supplemented with a companion website containing solution sets and software exploration support for MATLAB and SciPy (Scientific Python) Thoroughly class-tested over the past fifteen years, Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing is an appropriately self-contained book ideal for a one-semester course on the subject. S. Allen Broughton, PhD, is Professor Emeritus of Mathematics at Rose-Hulman Institute of Technology. Dr. Broughton is a member of the American Mathematical Society (AMS) and the Society for the Industrial Applications of Mathematics (SIAM), and his research interests include the mathematics of image and signal processing, and wavelets. Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles. div id="_mcePaste" style="position: absolute; left: -10000px; top: 0px; width: 1px; height: 1px; overflow: hidden;"Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles.Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and r

Author : William L. Briggs
Publisher : SIAM
ISBN 13 : 0898713420
Total Pages : 446 pages
Book Rating : 4.28/5 ( download)

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Download or read book The DFT written by William L. Briggs and published by SIAM. This book was released on 1995-01-01 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : D. Sundararajan
Publisher : World Scientific
ISBN 13 : 9789812810298
Total Pages : 400 pages
Book Rating : 4.93/5 ( download)

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Download or read book The Discrete Fourier Transform written by D. Sundararajan and published by World Scientific. This book was released on 2001 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Author : Eleanor Chu
Publisher : CRC Press
ISBN 13 : 1420063642
Total Pages : 423 pages
Book Rating : 4.46/5 ( download)

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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

Author : H. Joseph Weaver
Publisher :
ISBN 13 : 9780894647352
Total Pages : 375 pages
Book Rating : 4.50/5 ( download)

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Download or read book Applications of Discrete and Continuous Fourier Analysis written by H. Joseph Weaver and published by . This book was released on 1992 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven L. Brunton
Publisher : Cambridge University Press
ISBN 13 : 1009098489
Total Pages : 615 pages
Book Rating : 4.89/5 ( download)

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Download or read book Data-Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Author : Richard Tolimieri
Publisher : Springer Science & Business Media
ISBN 13 : 1475738544
Total Pages : 363 pages
Book Rating : 4.44/5 ( download)

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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.