Linear Algebra Signal Processing And Wavelets A Unified Approach

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Linear Algebra, Signal Processing, and Wavelets - A Unified Approach

Øyvind Ryan
Linear Algebra Signal Processing and Wavelets A Unified Approach Book PDF

Author : Øyvind Ryan
Publisher : Springer
Page : 360 pages
File Size : 45,8 Mb
Release : 2019-03-05
Category : Mathematics
ISBN : 9783030018122

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Linear Algebra, Signal Processing, and Wavelets - A Unified Approach by Øyvind Ryan Pdf

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.

Linear Algebra, Signal Processing, and Wavelets - A Unified Approach

Øyvind Ryan
Linear Algebra Signal Processing and Wavelets A Unified Approach Book PDF

Author : Øyvind Ryan
Publisher : Springer
Page : 364 pages
File Size : 48,7 Mb
Release : 2019-02-26
Category : Mathematics
ISBN : 9783030029401

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Linear Algebra, Signal Processing, and Wavelets - A Unified Approach by Øyvind Ryan Pdf

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 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.

Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision (Version: 2013-09-26)

Michael D. Adams
Multiresolution Signal and Geometry Processing Filter Banks Wavelets and Subdivision Version 2013 09 26 Book PDF

Author : Michael D. Adams
Publisher : Michael Adams
Page : 580 pages
File Size : 45,5 Mb
Release : 2013-09-26
Category : Electric filters
ISBN : 9781550585087

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Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision (Version: 2013-09-26) by Michael D. Adams Pdf

This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.

Foundations of Signal Processing

Martin Vetterli,Jelena Kovačević,Vivek K Goyal
Foundations of Signal Processing Book PDF

Author : Martin Vetterli,Jelena Kovačević,Vivek K Goyal
Publisher : Cambridge University Press
Page : 745 pages
File Size : 40,7 Mb
Release : 2014-09-04
Category : Computers
ISBN : 9781107038608

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Foundations of Signal Processing by Martin Vetterli,Jelena Kovačević,Vivek K Goyal Pdf

This comprehensive and accessible textbook introduces students to the basics of modern signal processing techniques.

Wavelets

Amir-Homayoon Najmi
Wavelets Book PDF

Author : Amir-Homayoon Najmi
Publisher : JHU Press
Page : 303 pages
File Size : 49,9 Mb
Release : 2012-04-15
Category : Mathematics
ISBN : 9781421405599

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Wavelets by Amir-Homayoon Najmi Pdf

Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi’s introduction to wavelet theory explains this mathematical concept clearly and succinctly. Wavelets are used in processing digital signals and imagery from myriad sources. They form the backbone of the JPEG2000 compression standard, and the Federal Bureau of Investigation uses biorthogonal wavelets to compress and store its vast database of fingerprints. Najmi provides the mathematics that demonstrate how wavelets work, describes how to construct them, and discusses their importance as a tool to investigate and process signals and imagery. He reviews key concepts such as frames, localizing transforms, orthogonal and biorthogonal bases, and multi-resolution. His examples include the Haar, the Shannon, and the Daubechies families of orthogonal and biorthogonal wavelets. Our capacity and need for collecting and transmitting digital data is increasing at an astonishing rate. So too is the importance of wavelets to anyone working with and analyzing digital data. Najmi’s primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.

A Wavelet Tour of Signal Processing

Stephane Mallat
A Wavelet Tour of Signal Processing Book PDF

Author : Stephane Mallat
Publisher : Elsevier
Page : 620 pages
File Size : 41,9 Mb
Release : 1999-09-14
Category : Mathematics
ISBN : 0080520839

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A Wavelet Tour of Signal Processing by Stephane Mallat Pdf

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

An Introduction to Wavelets Through Linear Algebra

M.W. Frazier
An Introduction to Wavelets Through Linear Algebra Book PDF

Author : M.W. Frazier
Publisher : Springer
Page : 517 pages
File Size : 42,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783642855702

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An Introduction to Wavelets Through Linear Algebra by M.W. Frazier Pdf

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.

Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing

Roe W Goodman
Discrete Fourier And Wavelet Transforms An Introduction Through Linear Algebra With Applications To Signal Processing Book PDF

Author : Roe W Goodman
Publisher : World Scientific Publishing Company
Page : 300 pages
File Size : 45,7 Mb
Release : 2016-01-21
Category : Mathematics
ISBN : 9789814725798

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Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing by Roe W Goodman Pdf

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.

Signal Processing with Fractals

Gregory W. Wornell,Gregory Wornell
Signal Processing with Fractals Book PDF

Author : Gregory W. Wornell,Gregory Wornell
Publisher : Prentice Hall
Page : 200 pages
File Size : 42,5 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015034528383

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Signal Processing with Fractals by Gregory W. Wornell,Gregory Wornell Pdf

Fractal geometry and recent developments in wavelet theory are having an important impact on the field of signal processing. Efficient representations for fractal signals based on wavelets are opening up new applications for signal processing, and providing better solutions to problems in existing applications. Signal Processing with Fractals provides a valuable introduction to this new and exciting area, and develops a powerful conceptual foundation for understanding the topic. Practical techniques for synthesizing, analyzing, and processing fractal signals for a wide range of applications are developed in detail, and novel applications in communications are explored.

An Introduction to Wavelet Theory in Finance

Francis In,Sangbae Kim
An Introduction to Wavelet Theory in Finance Book PDF

Author : Francis In,Sangbae Kim
Publisher : World Scientific
Page : 213 pages
File Size : 51,6 Mb
Release : 2013
Category : Business & Economics
ISBN : 9789814397834

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An Introduction to Wavelet Theory in Finance by Francis In,Sangbae Kim Pdf

This book offers an introduction to wavelet theory and provides the essence of wavelet analysis including Fourier analysis and spectral analysis; the maximum overlap discrete wavelet transform; wavelet variance, covariance, and correlation in a unified and friendly manner. It aims to bridge the gap between theory and practice by presenting substantial applications of wavelets in economics and finance. This book is the first to provide a comprehensive application of wavelet analysis to financial markets, covering new frontier issues in empirical finance and economics. The first chapter of this unique text starts with a description of the key features and applications of wavelets. After an overview of wavelet analysis, successive chapters rigorously examine the various economic and financial topics and issues that stimulate academic and professional research, including equity, interest swaps, hedges and futures, foreign exchanges, financial asset pricing, and mutual fund markets. This detail-oriented text is descriptive and designed purely for academic researchers and financial practitioners. It assumes no prior knowledge of econometrics and covers important topics such as portfolio asset allocation, asset pricing, hedging strategies, new risk measures, and mutual fund performance. Its accessible presentation is also suitable for post-graduates in a variety of disciplines applied economics, financial engineering, international finance, financial econometrics, and fund management. To facilitate the subject of wavelets, sophisticated proofs and mathematics are avoided as much as possible when applying the wavelet multiscaling method. To enhance the reader's understanding in practical applications of the wavelet multiscaling method, this book provides sample programming instruction backed by Matlab wavelet code.

Linear Algebra for Signal Processing

Adam Bojanczyk,George Cybenko
Linear Algebra for Signal Processing Book PDF

Author : Adam Bojanczyk,George Cybenko
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461242284

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Linear Algebra for Signal Processing by Adam Bojanczyk,George Cybenko Pdf

Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This trend will continue as many new signal processing applications are opening up in consumer products and communications systems. In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. This volume gives particular emphasis to exposing broader contexts of the signal processing problems so that the impact of algorithms and hardware can be better understood; it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques. This volume will be of interest to both applied mathematicians and engineers.

Wavelets and Subband Coding

Jelena Kovacevic,Martin Vetterli
Wavelets and Subband Coding Book PDF

Author : Jelena Kovacevic,Martin Vetterli
Publisher : Prentice Hall
Page : 488 pages
File Size : 42,6 Mb
Release : 1995
Category : Technology & Engineering
ISBN : 0130970808

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Wavelets and Subband Coding by Jelena Kovacevic,Martin Vetterli Pdf

A central goal of signal processing is to describe real-time signals, be it for computation, compression, or understanding. This book presents a unified view of wavelets and subband coding with a signal processing perspective. Covers the discrete-time case, or filter banks; development of wavelets; continuous wavelet and local Fourier transforms; efficient algorithms for filter banks and wavelet computations; and signal compression. *provides broad coverage of theory and applications and a different perspective based on signal processing. *gives framework for applications in speech, audio, image and video compression as used in multimedia. *includes sufficient background material so that people without signal processing knowledge will find it useful.

Computational Signal Processing with Wavelets

Anthony Teolis
Computational Signal Processing with Wavelets Book PDF

Author : Anthony Teolis
Publisher : Birkhäuser
Page : 324 pages
File Size : 43,5 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9783319657479

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Computational Signal Processing with Wavelets by Anthony Teolis Pdf

This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web. Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient "overcomplete" wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools. The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic...is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology

An Introduction to Wavelets

Charles K. Chui
An Introduction to Wavelets Book PDF

Author : Charles K. Chui
Publisher : Elsevier
Page : 278 pages
File Size : 46,8 Mb
Release : 2016-06-03
Category : Science
ISBN : 9781483282862

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An Introduction to Wavelets by Charles K. Chui Pdf

Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on “wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students.

Introduction to Linear and Matrix Algebra

Nathaniel Johnston
Introduction to Linear and Matrix Algebra Book PDF

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 43,5 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119

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Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf

This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.