The Sparse Fourier Transform
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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.
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.
A Sublinear Algorithm Of Sparse Fourier Transform For Nonequispaced Data
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Author :
language : en
Publisher:
Release Date : 2005
A Sublinear Algorithm Of Sparse Fourier Transform For Nonequispaced Data written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. We address the situation where a signal S is known to consist of N equispaced samples, of which only L
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...
Fast Fourier Transforms
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Author : C. Sidney Burrus
language : en
Publisher: Lulu.com
Release Date :
Fast Fourier Transforms written by C. Sidney Burrus and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on with Computer science categories.
Reconstruction Of Structured Functions From Sparse Fourier Data
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Author : Marius Wischerhoff
language : en
Publisher:
Release Date : 2014
Reconstruction Of Structured Functions From Sparse Fourier Data written by Marius Wischerhoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
In several scientific areas, such as radio astronomy, computed tomography, and magnetic resonance imaging, the reconstruction of structured functions from the knowledge of samples of their Fourier transform is a common problem. For the analysis of the examined object, it is important to reconstruct the underlying original signal as exactly as possible. The dissertation on hand aims to uniquely recover structured functions from a smallest possible set of Fourier data. For this purpose, the Prony method, which is a deterministic method for the recovery of sparse trigonometric functions, is us ...
A Wavelet Tour Of Signal Processing
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Author : Stephane Mallat
language : en
Publisher: Academic Press
Release Date : 2008-12-18
A Wavelet Tour Of Signal Processing written by Stephane Mallat and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Technology & Engineering categories.
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, Third Edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox Balances presentation of the mathematics with applications to signal processing
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.
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.
Inside The Fft Black Box
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Author : Eleanor Chu
language : en
Publisher: CRC Press
Release Date : 1999-11-11
Inside The Fft Black Box written by Eleanor Chu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-11 with Mathematics categories.
Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.