Deterministic Sparse Fft Algorithms
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Deterministic Sparse Fft Algorithms
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Author : Katrin Ulrike Wannenwetsch
language : en
Publisher:
Release Date : 2016
Deterministic Sparse Fft Algorithms written by Katrin Ulrike Wannenwetsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
The discrete Fourier transform (DFT) is a well-known transform with many applications in various fields. By fast Fourier transform (FFT) algorithms, the DFT of a vector can be efficiently computed. Using these algorithms, one can reconstruct a complex vector x of length N from its discrete Fourier transform applying O(N log N) arithmetical operations. In order to improve the complexity of FFT algorithms, one needs additional a priori assumptions on the vector x. In this thesis, the focus is on vectors with small support or sparse vectors for which several new deterministic algorithms are pr...
The Sparse Fourier Transform
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Author : Haitham Hassanieh
language : en
Publisher: Morgan & Claypool
Release Date : 2018-02-27
The Sparse Fourier Transform written by Haitham Hassanieh and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-27 with Computers categories.
The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications. The fastest algorithm for computing the Fourier transform is the Fast Fourier Transform (FFT), which runs in near-linear time making it an indispensable tool for many applications. However, today, the runtime of the FFT algorithm is no longer fast enough especially for big data problems where each dataset can be few terabytes. Hence, faster algorithms that run in sublinear time, i.e., do not even sample all the data points, have become necessary. This book addresses the above problem by developing the Sparse Fourier Transform algorithms and building practical systems that use these algorithms to solve key problems in six different applications: wireless networks; mobile systems; computer graphics; medical imaging; biochemistry; and digital circuits. This is a revised version of the thesis that won the 2016 ACM Doctoral Dissertation Award.
Numerical Fourier Analysis
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Author : Gerlind Plonka
language : en
Publisher: Springer Nature
Release Date : 2023-11-08
Numerical Fourier Analysis written by Gerlind Plonka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Numerical Fourier Analysis
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Author : Gerlind Plonka
language : en
Publisher: Springer
Release Date : 2019-02-05
Numerical Fourier Analysis written by Gerlind Plonka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-05 with Mathematics categories.
This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Fast Fourier Transform Algorithms And Applications
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Author : K.R. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-21
Fast Fourier Transform Algorithms And Applications written by K.R. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-21 with Mathematics categories.
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.
Sparse Sensing And Sparsity Sensed In Multi Sensor Array Applications
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Author : Xiangrong Wang
language : en
Publisher: Springer Nature
Release Date :
Sparse Sensing And Sparsity Sensed In Multi Sensor Array Applications written by Xiangrong Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Algorithms And Theory Of Computation Handbook
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Author : Mikhail J. Atallah
language : en
Publisher: CRC Press
Release Date : 1998-11-23
Algorithms And Theory Of Computation Handbook written by Mikhail J. Atallah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-23 with Computers categories.
Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
A Wavelet Tour Of Signal Processing
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Author : Stephane Mallat
language : en
Publisher: Elsevier
Release Date : 1999-09-14
A Wavelet Tour Of Signal Processing written by Stephane Mallat and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-14 with Mathematics categories.
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
A Mathematical Introduction To Compressive Sensing
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Author : Simon Foucart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
A Mathematical Introduction To Compressive Sensing written by Simon Foucart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Computers categories.
At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Computing In Engineering And Technology
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Author : Brijesh Iyer
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Computing In Engineering And Technology written by Brijesh Iyer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Technology & Engineering categories.
The book is a collection of selected high quality research papers presented at the International Conference on Computing in Engineering and Technology (ICCET 2019), held on January 10–11, 2019 at Deogiri Institute of Engineering and Management Studies, Aurangabad, India. Focusing on frontier topics and next-generation technologies, it presents original and innovative research from academics, scientists, students, and engineers alike.