Discrete Fourier And Wavelet Transforms An Introduction Through Linear Algebra With Applications To Signal Processing
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Discrete Fourier And Wavelet Transforms An Introduction Through Linear Algebra With Applications To Signal Processing
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Author : Roe W Goodman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-01-21
Discrete Fourier And Wavelet Transforms An Introduction Through Linear Algebra With Applications To Signal Processing written by Roe W Goodman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-21 with Mathematics categories.
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Linear Algebra Signal Processing And Wavelets A Unified Approach
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Author : Øyvind Ryan
language : en
Publisher: Springer
Release Date : 2019-03-05
Linear Algebra Signal Processing And Wavelets A Unified Approach written by Øyvind Ryan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-05 with Mathematics categories.
This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications. The approach is novel, and the book can be used in undergraduate courses, for example, following a first course in linear algebra, but is also suitable for use in graduate level courses. The book will benefit anyone with a basic background in linear algebra. It defines fundamental concepts in signal processing and wavelet theory, assuming only a familiarity with elementary linear algebra. No background in signal processing is needed. Additionally, the book demonstrates in detail why linear algebra is often the best way to go. Those with only a signal processing background are also introduced to the world of linear algebra, although a full course is recommended. The book comes in two versions: one based on MATLAB, and one on Python, demonstrating the feasibility and applications of both approaches. Most of the MATLAB code is available interactively. The applications mainly involve sound and images. The book also includes a rich set of exercises, many of which are of a computational nature.
An Introduction To Wavelets Through Linear Algebra
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Author : M.W. Frazier
language : en
Publisher: Springer
Release Date : 2013-12-11
An Introduction To Wavelets Through Linear Algebra written by M.W. Frazier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.
The Xft Quadrature In Discrete Fourier Analysis
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Author : Rafael G. Campos
language : en
Publisher: Springer
Release Date : 2019-05-24
The Xft Quadrature In Discrete Fourier Analysis written by Rafael G. Campos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-24 with Mathematics categories.
This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.
Eeg Signal Processing A Machine Learning Based Framework
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Author : R. John Martin
language : en
Publisher: Ashok Yakkaldevi
Release Date : 2022-01-31
Eeg Signal Processing A Machine Learning Based Framework written by R. John Martin and has been published by Ashok Yakkaldevi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Art categories.
1.1 Motivation Analysis of non-stationary and non-linear nature of signal data is the prime talk in signal processing domain today. On employing biomedical equipments huge volume of physiological data is acquired for analysis and diagnostic purposes. Inferring certain decisions from these signals by manual observation is quite tedious due to artefacts and its time series nature. As large volume of data involved in biomedical signal processing, adopting suitable computational methods is important for analysis. Data Science provides space for processing these signals through machine learning approaches. Many more biomedical signal processing implementations are in place using machine learning methods. This is the inspiration in adopting machine learning approach for analysing EEG signal data for epileptic seizure detection.
Discrete Fourier Analysis
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Author : M. W. Wong
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-30
Discrete Fourier Analysis written by M. W. Wong 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 2011-05-30 with Mathematics categories.
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.
Intelligent Systems And Networks
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Author : Duc-Tan Tran
language : en
Publisher: Springer Nature
Release Date : 2021-05-12
Intelligent Systems And Networks written by Duc-Tan Tran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-12 with Technology & Engineering categories.
This book presents Proceedings of the International Conference on Intelligent Systems and Networks (ICISN 2021), held at Hanoi in Vietnam. It includes peer-reviewed high-quality articles on intelligent system and networks. It brings together professionals and researchers in the area and presents a platform for exchange of ideas and to foster future collaboration. The topics covered in this book include—foundations of computer science; computational intelligence language and speech processing; software engineering software development methods; wireless communications signal processing for communications; electronics track IoT and sensor systems embedded systems; etc.
Algorithms From The Book
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Author : Kenneth Lange
language : en
Publisher: SIAM
Release Date : 2020-05-04
Algorithms From The Book written by Kenneth Lange and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-04 with Mathematics categories.
Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.
Multiscale Transforms With Application To Image Processing
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Author : Aparna Vyas
language : en
Publisher: Springer
Release Date : 2017-12-05
Multiscale Transforms With Application To Image Processing written by Aparna Vyas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-05 with Technology & Engineering categories.
This book provides an introduction to image processing, an overview of the transforms which are most widely used in the field of image processing, and an introduction to the application of multiscale transforms in image processing. The book is divided into three parts, with the first part offering the reader a basic introduction to image processing. The second part of the book starts with a chapter on Fourier analysis and Fourier transforms, wavelet analysis, and ends with a chapter on new multiscale transforms. The final part of the book deals with all of the most important applications of multiscale transforms in image processing. The chapters consist of both tutorial and highly advanced material, and as such the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications. The technique of solving problems in the transform domain is common in applied mathematics and widely used in research and industry, but is a somewhat neglected subject within the undergraduate curriculum. It is hoped that faculty can use this book to create a course that can be offered early in the curriculum and fill this void. Also, the book is intended to be used as a reference manual for scientists who are engaged in image processing research, developers of image processing hardware and software systems, and practising engineers and scientists who use image processing as a tool in their applications.
Algorithms From The Book Second Edition
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Author : Kenneth Lange
language : en
Publisher: SIAM
Release Date : 2025-06-12
Algorithms From The Book Second Edition written by Kenneth Lange and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-12 with Science categories.
Most books on algorithms are narrowly focused on a single field of application. This unique book cuts across discipline boundaries, exposing readers to the most successful algorithms from a variety of fields. Algorithm derivation is a legitimate branch of the mathematical sciences driven by hardware advances and the demands of many scientific fields. The best algorithms are undergirded by beautiful mathematics. This book enables readers to look under the hood and understand how some basic algorithms operate and how to assemble complex algorithms from simpler building blocks. Since publication of the first edition of Algorithms from THE BOOK, the number of new algorithms has swelled exponentially, with the fields of neural net modeling and natural language processing leading the way. These developments warranted the addition of a new chapter on automatic differentiation and its applications to neural net modeling. The second edition also corrects previous errors, clarifies explanations, adds worked exercises, and introduces new algorithms in existing chapters. In Algorithms from THE BOOK, Second Edition, the majority of algorithms are accompanied by Julia code for experimentation, the many classroom-tested exercises make the material suitable for use as a textbook, and appendices contain not only background material often missing in undergraduate education but also solutions to selected problems. This book is intended for students and professionals in the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.