Описание: Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicate that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing Вї sampling, filtering, digital signal processing. Fourier analysis in Hilbert spaces is the focus of the third part, and the last part provides an introduction to wavelet analysis, time-frequency issues, and multiresolution analysis. An appendix provides the necessary background on Lebesgue integrals.
Описание: The Laplace transform is a useful tool for solving practical mathematical problems. It has a wealth of applications (for example, engineers use it to solve engineering problems). This book takes introduces the basics of Laplace Transforms.
Описание: Wavelet analysis and its applications have been one of the fastest-growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the state of the art in wavelet analysis and its applications and active media technology. At the Congress, invited talks were delivered by distinguished researchers, namely Prof John Daugman of Cambridge University, UK; Prof Bruno Torresani of INRIA, France; Prof Victor Wickerhauser of Washington University, USA, Prof Ning Zhong of the Maebashi Institute of Technology, Japan; Prof John Yen of Pennsylvania State University, USA; and Prof Sankar K Pal of the Indian Statistical Institute, India.
Описание: This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a вЂ“ reasonably self-contained вЂ“ exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.
Автор: Kutyniok Gitta Название: Affine Density in Wavelet Analysis ISBN: 354072916X ISBN-13(EAN): 9783540729167 Издательство: Springer Цена: 5190 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems.This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Описание: Discrete wavelet transforms (DWTs) have led the revolutions in image and video coding systems over the past decade. In this book, the DWT is presented
from the VLSI design perspective, and the related theories, algorithms, and architectures are discussed for 1D, 2D, and 3D DWT. The book provides a comprehensive analysis and
discussion of DWTs and their applications including important materials and the newest developments in wavelet processing.
For example, the architecture designs of 2D
DWT in JPEG 2000 and the development of motion-compensated temporal filtering (MCTF) are explored.
Описание: The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour.
Название: Harmonic, wavelet and p-adic analysis ISBN: 981270549X ISBN-13(EAN): 9789812705495 Издательство: World Scientific Publishing Рейтинг: Цена: 29466 р. Наличие на складе: Поставка под заказ.
Описание: The mutual influence between mathematics and science and technology is becoming widespread with profound connections among them being discovered. Important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found. This work reports these findings and guides the reader towards the areas for further research.
Автор: Marks II, Robert J Название: Handbook of Fourier Analysis & Its Applications ISBN: 0195335929 ISBN-13(EAN): 9780195335927 Издательство: Oxford Academ Рейтинг: Цена: 27116 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.
Описание: In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schr?dinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Автор: Ramakrishnan Название: Fourier Analysis on Number Fields ISBN: 0387984364 ISBN-13(EAN): 9780387984360 Издательство: Springer Рейтинг: Цена: 12621 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. This book covers John Tate`s visionary thesis, giving virtually the necessary analytic details and topological preliminaries - technical prerequisites.
Автор: Bracewell Ronald Название: Fourier Analysis and Imaging ISBN: 0306481871 ISBN-13(EAN): 9780306481871 Издательство: Springer Рейтинг: Цена: 30532 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
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