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On The Butterfly Sparse Fourier Transform
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Book Synopsis The Sparse Fourier Transform by : Haitham Hassanieh
Download or read book The Sparse Fourier Transform written by Haitham Hassanieh and published by Morgan & Claypool. This book was released on 2018-02-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fast and approximate computation of Laplace and Fourier transforms by : Ines Melzer
Download or read book Fast and approximate computation of Laplace and Fourier transforms written by Ines Melzer and published by Logos Verlag Berlin GmbH. This book was released on 2016-03-20 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments.
Book Synopsis Fast Fourier Transform - Algorithms and Applications by : K.R. Rao
Download or read book Fast Fourier Transform - Algorithms and Applications written by K.R. Rao and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Issues in Mathematical Theory and Modeling: 2013 Edition by :
Download or read book Issues in Mathematical Theory and Modeling: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Mathematical Theory and Modeling / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Lie Theory. The editors have built Issues in Mathematical Theory and Modeling: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Lie Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Mathematical Theory and Modeling: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Book Synopsis Computational Frameworks for the Fast Fourier Transform by : Charles Van Loan
Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author captures the interplay between mathematics and the design of effective numerical algorithms.
Book Synopsis Numerical Fourier Analysis by : Gerlind Plonka
Download or read book Numerical Fourier Analysis written by Gerlind Plonka and published by Springer. This book was released on 2019-02-05 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Extraction of Quantifiable Information from Complex Systems by : Stephan Dahlke
Download or read book Extraction of Quantifiable Information from Complex Systems written by Stephan Dahlke and published by Springer. This book was released on 2014-11-13 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Download or read book Fourier Transform written by Salih Salih and published by BoD – Books on Demand. This book was released on 2015-06-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of Fourier transform (FT) in signal processing and physical sciences has increased in the past decades. Almost all the textbooks on signal processing or physics have a section devoted to the FT theory. For this reason, this book focuses on signal processing and physical sciences. The book chapters are related to fast hybrid recursive FT based on Jacket matrix, acquisition algorithm for global navigation satellite system, determining the sensitivity of output parameters based on FFT, convergence of integrals of products based on Riemann-Lebesgue Lemma function, extending the real and complex number fields for treating the FT, nonmaterial structure, Gabor transform, and chalcopyrite bioleaching. The book provides applications oriented to signal processing and physics written primarily for engineers, mathematicians, physicians and graduate students, will also find it useful as a reference for their research activities.
Book Synopsis Numerical Methods for Least Squares Problems, Second Edition by : Åke Björck
Download or read book Numerical Methods for Least Squares Problems, Second Edition written by Åke Björck and published by SIAM. This book was released on 2024-07-05 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to-date treatment of direct and iterative methods for solving different types of least squares problems and for computing the singular value decomposition. It also is unique because it covers generalized, constrained, and nonlinear least squares problems as well as partial least squares and regularization methods for discrete ill-posed problems. The bibliography of over 1,100 historical and recent references provides a comprehensive survey of past and present research in the field. This book will be of interest to graduate students and researchers in applied mathematics and to researchers working with numerical linear algebra applications.
Book Synopsis The Fast Fourier Transform by : E. Oran Brigham
Download or read book The Fast Fourier Transform written by E. Oran Brigham and published by Prentice Hall. This book was released on 1974 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing by :
Download or read book 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing written by and published by . This book was released on 1997 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partitioned convolution algorithms for real-time auralization by : Frank Wefers
Download or read book Partitioned convolution algorithms for real-time auralization written by Frank Wefers and published by Logos Verlag Berlin GmbH. This book was released on 2015-05-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work discusses methods for efficient audio processing with finite impulse response (FIR) filters. Such filters are widely used for high-quality acoustic signal processing, e.g. for headphone or loudspeaker equalization, in binaural synthesis, in spatial sound reproduction techniques and for the auralization of reverberant environments. This work focuses on real-time applications, where the audio processing is subject to minimal delays (latencies). Different fast convolution concepts (transform-based, interpolation-based and number-theoretic), which are used to implement FIR filters efficiently, are examined regarding their applicability in real-time. These fast, elementary techniques can be further improved by the concept of partitioned convolution. This work introduces a classification and a general framework for partitioned convolution algorithms and analyzes the algorithmic classes which are relevant for real-time filtering: Elementary concepts which do not partition the filter impulse response (e.g. regular Overlap-Add and Overlap-Save convolution) and advanced techniques, which partition filters uniformly and non-uniformly. The algorithms are thereby regarded in their analytic complexity, their performance on target hardware, the optimal choice of parameters, assemblies of multiple filters, multi-channel processing and the exchange of filter impulse responses without audible artifacts. Suitable convolution techniques are identified for different types of audio applications, ranging from resource-aware auralizations on mobile devices to extensive room acoustics audio rendering using dedicated multi-processor systems.
Book Synopsis Official Gazette of the United States Patent and Trademark Office by :
Download or read book Official Gazette of the United States Patent and Trademark Office written by and published by . This book was released on 1986 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Transforms by : Goran Nikolic
Download or read book Fourier Transforms written by Goran Nikolic and published by BoD – Books on Demand. This book was released on 2011-04-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide information about Fourier transform to those needing to use infrared spectroscopy, by explaining the fundamental aspects of the Fourier transform, and techniques for analyzing infrared data obtained for a wide number of materials. It summarizes the theory, instrumentation, methodology, techniques and application of FTIR spectroscopy, and improves the performance and quality of FTIR spectrophotometers.
Book Synopsis Introduction to Wavelets and Wavelet Transforms by : C. S. Burrus
Download or read book Introduction to Wavelets and Wavelet Transforms written by C. S. Burrus and published by Pearson. This book was released on 1998 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.
Book Synopsis Multitarget Tracking Using Orientation Estimation for Optical Belt Sorting by : Pfaff, Florian
Download or read book Multitarget Tracking Using Orientation Estimation for Optical Belt Sorting written by Pfaff, Florian and published by KIT Scientific Publishing. This book was released on 2019-10-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
