Wavelets and Filter Banks


Author: Gilbert Strang,Truong Nguyen

Publisher: SIAM

ISBN: 9780961408879

Category: Technology & Engineering

Page: 490

View: 6416

A comprehensive treatment of wavelets for both engineers and mathematicians.

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


Author: Michael D. Adams

Publisher: Michael Adams

ISBN: 1550585088

Category: Electric filters

Page: 538

View: 2256

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.


Theorie und Anwendungen


Author: Prof. Dr. rer. nat. Alfred Karl Louis,Prof. Dr. rer. nat. Peter Maaß,Dr. rer. nat. Andreas Rieder

Publisher: Springer-Verlag

ISBN: 3322921093

Category: Mathematics

Page: 318

View: 5887

Lineare Algebra


Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 4193

Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Wavelets and multiscale signal processing


Author: Albert Cohen,Robert Dean Ryan

Publisher: Chapman & Hall/CRC

ISBN: 9780412575907

Category: Mathematics

Page: 238

View: 9181

This book is based on Ondelettes et Traitement Numerique du Signal by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing. Throughout, the book concentrates on the fundamentals. It begins with a chapter on the concept of multiresolution analysis, which contains complete proofs of the basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case (Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of the filters, and the importance of regularity for the algorithms are the subjects of Chapter 3. Chapter 5 looks at multiscale decomposition as it applies to stochastic processing, in particular to signal and image processing. Wavelets and Multiscale Signal Processing will be of particular interest to mathematicians working in analysis, academic and industrial electrical engineers, and researchers who need to analyse time series, in areas such as hydrodynamics, aeronautics, meteorology, geophysics, statistics and economics.

Multirate Digital Signal Processing

Multirate Systems - Filter Banks - Wavelets


Author: N. J. Fliege

Publisher: Wiley

ISBN: 9780471492047

Category: Science

Page: 352

View: 1912

Provides a thorough and accessible introduction to the fast-growing area of multirate digital signal processing covering both the fundamental theory and the practical applications. The key characteristic of multirate algorithms is their high computational efficiency, and hence their increasing implementation in a range of applications from digital audio broadcasting to multi-carrier data transmission and subband speech coding. This book gives a comprehensive analysis of the subject and features include: * A summary of the key properties of those filters which employ multirate techniques including cascaded multirate filters, multirate complementary filters, and interpolated FIR filters * An assessment of the properties of various digital filter banks, such as quadratur mirror, parunitary, biorthogonal, modulated, polyphase, and multicomplementary filter banks * Design methodologies for multirate filters and filter banks * An examination of the discrete wavelet transform using filter banks, the construction of wavelets and examples of wavelet systems * A complete overview of current applications and a look ahead towards the future developments in the field This book will be invaluable for advanced students in electronics and computer science. It will also be useful for practising electronics and communications engineers and physicists working in industry.

Signal Analysis

Wavelets, Filter Banks, Time-Frequency Transforms and Applications


Author: Alfred Mertins

Publisher: Wiley

ISBN: 9780471986263

Category: Technology & Engineering

Page: 330

View: 764

Signal analysis gives an insight into the properties of signals and stochastic processes by methodology. Linear transforms are integral to the continuing growth of signal processes as they characterize and classify signals. In particular, those transforms that provide time-frequency signal analysis are attracting greater numbers of researchers and are becoming an area of considerable importance. The key characteristic of these transforms, along with a certain time-frequency localization called the wavelet transform and various types of multirate filter banks, is their high computational efficiency. It is this computational efficiently which accounts for their increased application. This book provides a complete overview and introduction to signal analysis. It presents classical and modern signal analysis methods in a sequential structure starting with the background to signal theory. Progressing through the book the author introduces more advanced topics in an easy to understand style. Including recent and emerging topics such as filter banks with perfect reconstruction, time frequency and wavelets. With great accuracy and technical merit, this book makes a useful and original contribution to the current literature.

Wavelets and Subbands

Fundamentals and Applications : with 234 Figures


Author: Agostino Abbate,Casimer DeCusatis,Pankaj K. Das

Publisher: Springer Science & Business Media

ISBN: 9780817641368

Category: Mathematics

Page: 551

View: 7297

Wavelets and Subbands is designed to present an understanding of wavelets and their development from a continuous-domain transformation to a frame representation and finally to multiresolution analysis tools such as subband decomposition. The book presents a theoretical understanding of the subject that is intertwined with practical examples and applications of wavelets in ultrasonic and biomedical domains. There is special emphasis on applications in communications, compression, and image processing.

Längenmesskopf für den Einsatz am Harvester/Prozessor


Author: Robert Holzer

Publisher: diplom.de

ISBN: 3832454020

Category: Technology & Engineering

Page: 173

View: 5565

Inhaltsangabe:Einleitung: In der modernen Forstwirtschaft wird die Schlägerung und Aufarbeitung von Holz mit Hilfe von Harvestern oder Prozessoren durchgeführt. Es sind dies Baumerntemaschinen, welche die Bäume fällen, entasten und zuschneiden. Das Rohholz soll dabei möglichst genau nach Bestellung des Sägewerkes abgelängt werden. In derzeit eingesetzten Systemen wird die Länge des Stammes über die Umdrehungen eines Zahnrades gemessen, welches während des Vorschubs an die Stammoberfläche gepresst wird. Da dieses System verschiedene Nachteile und Mängel aufweist, besteht der Bedarf an einem bezüglich Genauigkeit und Zuverlässigkeit verbesserten System, welches berührungslos misst und womöglich eichfähig ist. Gang der Untersuchung: Dieses Problem wurde in einem zweigeteilten Projekt bearbeitet, in dessen erstem Teil eine Analyse der denkbaren Messvarianten durchgeführt wurde. Der Abschlussbericht dieses Teils ist die vorliegende Arbeit. Die primär behandelten Messprinzipien sind folgende: optische Verfahren - Bildauswertung, lasergestützte Messsysteme, Mikrowellen-Dopplerradar und Ultraschall-Dopplerverfahren. In Abschnitt 3 der vorliegenden Arbeit wird versucht, die Vor- und Nachteile der behandelten Verfahren gegeneinander abzuwägen und eine Empfehlung für das mit den besten Erfolgsaussichten weiterzuverfolgende Konzept abzugeben. Generell lässt sich feststellen, dass die rauen Umgebungsbedingungen das größte Problem bei der Entwicklung eines derartigen Messgerätes sind. Der Bau eines Sensorprototyps für den Laborbetrieb wäre mit jedem Messprinzip denkbar. Als die erfolgversprechendste Variante für die Realisierung eines kostengünstigen Sensors im forstwirtschaftlichen Dauereinsatz hat sich die Verwendung eines Mikrowellen-Dopplerradars herausgestellt. Inhaltsverzeichnis:Inhaltsverzeichnis: 1.AUFGABENSTELLUNG UND RAHMENBEDINGUNGEN10 1.1Aufgabenstellung10 1.2Pflichtenheft12 1.3Diskussion der Anforderungen aus praktischer Sicht13 1.3.1Prinzipielle Kriterien und Gesichtspunkte zu Vermessungssystemen am Harvester13 Messgenauigkeit13 Eichbarkeit14 1.3.2Projekte zur Rohholzvermessung14 1.3.3Rohholz-Identifizierung und -Verfolgung mittels Chips15 1.3.4Quellen für weitere Informationen16 1.4Eichfähigkeit18 1.4.1Eichvorschriften18 1.4.2Anforderungen an automatisierte Rohholzvermessung18 1.4.3Kontakte für weitere Informationen19 1.5Erschütterungsmessungen20 1.5.1Maximalwerte [...]

Multidimensional Filter Banks and Wavelets

Research Developments and Applications


Author: Sankar Basu,Bernard C. Levy

Publisher: Springer Science & Business Media

ISBN: 1475759223

Category: Science

Page: 238

View: 9635

Multidimensional Filter Banks and Wavelets: Reserach Developments and Applications brings together in one place important contributions and up-to-date research results in this important area. Multidimensional Filter Banks and Wavelets: Research Developments and Applications serves as an excellent reference, providing insight into some of the most important research issues in the field.

Fundamentals of Circuits and Filters


Author: Wai-Kai Chen

Publisher: CRC Press

ISBN: 9781420058888

Category: Technology & Engineering

Page: 925

View: 2815

This volume, drawn from the Circuits and Filters Handbook, focuses on mathematics basics; circuit elements, devices, and their models; and linear circuit analysis. It examines Laplace transformation, Fourier methods for signal analysis and processing, z-transform, and wavelet transforms. It also explores network laws and theorems, terminal and port represetnation, analysis in the frequency domain, and more. For the complete set, see catalog no. 55275.

Wavelets and Subband Coding


Author: Jelena Kovacevic,Martin Vetterli

Publisher: Prentice Hall

ISBN: 9780130970800

Category: Technology & Engineering

Page: 488

View: 9318

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.

Sampling, Wavelets, and Tomography


Author: John J. Benedetto,Ahmed I. Zayed

Publisher: Springer Science & Business Media

ISBN: 0817682120

Category: Mathematics

Page: 344

View: 7179

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field. This state-of-the-art book not only presents new results in these research areas, but it also demonstrates the role of sampling in both wavelet theory and tomography. Specific topics covered include: * Robustness of Regular Sampling in Sobolev Algebras * Irregular and Semi-Irregular Weyl-Heisenberg Frames * Adaptive Irregular Sampling in Meshfree Flow Simulation * Sampling Theorems for Non-Bandlimited Signals * Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets * Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces * Sampling Theory and Parallel-Beam Tomography * Thin-Plate Spline Interpolation in Medical Imaging * Filtered Back-Projection Algorithms for Spiral Cone Computed Tomography Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work. Contributors: J.J. Benedetto, N.K. Bose, P.G. Casazza, Y.C. Eldar, H.G. Feichtinger, A. Faridani, A. Iske, S. Jaffard, A. Katsevich, S. Lertrattanapanich, G. Lauritsch, B. Mair, M. Papadakis, P.P. Vaidyanathan, T. Werther, D.C. Wilson, A.I. Zayed

Introduction to Wavelets and Wavelet Transforms

A Primer


Author: C. S. Burrus,Haitao Guo

Publisher: N.A


Category: Mathematics

Page: 268

View: 2247

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.

Subband and Wavelet Transforms

Design and Applications


Author: Ali N. Akansu,Mark J.T. Smith

Publisher: Springer Science & Business Media

ISBN: 1461304830

Category: Technology & Engineering

Page: 452

View: 8391

The scientists and engineers of today are relentless in their continuing study and analysis of the world about us from the microcosm to the macrocosm. A central purpose of this study is to gain sufficient scientific information and insight to enable the development of both representative and useful models of the superabundance of physical processes that surround us. The engineers need these models and the associated insight in order to build the information processing systems and control systems that comprise these new and emerging technologies. Much of the early modeling work that has been done on these systems has been based on the linear time-invariant system theory and its extensive use of Fourier transform theory for both continuous and discrete systems and signals. However many of the signals arising in nature and real systems are neither stationary nor linear but tend to be concentrated in both time and frequency. Hence a new methodology is needed to take these factors properly into account.

Multiresolution Signal Decomposition

Transforms, Subbands, and Wavelets


Author: Paul A. Haddad,Ali N. Akansu

Publisher: Academic Press

ISBN: 0323138365

Category: Technology & Engineering

Page: 376

View: 4446

This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source. n The first book to give a unified and coherent exposition of multiresolutional signal decomposition techniques n Classroom tested textbook clearly describes the commonalities among three key methods-transform coding, and wavelet transforms n Gives comparative performance evaluations of many proposed techniques

Beyond Wavelets


Author: Grant Welland

Publisher: Elsevier

ISBN: 9780080527802

Category: Mathematics

Page: 320

View: 942

"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago by Morlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering. Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach. However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematical foundations for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes a method for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation. Investigators already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume. *Curvelets, Contourlets, Ridgelets, *Digital Implementation of Ridgelet Packets *Steerable Wavelet Packets *Essentially Non-Oscillatory Wavelets *Medical Imaging *Non-Uniform Filter Banks *Spline-wavelet frames and *Vanishing Moment Recovery Functions