Prolate Spheroidal Wave Functions of Order Zero

Author: Andrei Osipov
Publisher: Springer Science & Business Media
ISBN: 1461482593
Format: PDF, Kindle
Download Now
Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.

The Bispectral Problem

Author: John P. Harnad
Publisher: American Mathematical Soc.
ISBN: 0821809490
Format: PDF, ePub, Mobi
Download Now
Although originally posed in the context of mathematical problems related to medical imaging, the bispectral problem is now closely related to other topics and has connections to many areas of pure and applied mathematics. The central theme of this book is the search for solutions to eigenvalue problems that satisfy additional equations in the spectral parameter, for example, pairs of eigenvalue equations. This problem, which looks very simple at first, has turned out to be both deep and difficult. Moreover, this concept of bispectrality has been shown to be useful in many active areas of current research in mathematics and physics. Following several years of exciting new results on the subject, in March 1997 the Centre de Recherches Mathematiques held the first scientific meeting devoted exclusively to the bispectral problem. Collected in this volume are contributions from the speakers at this meeting. The participants at this workshop included a majority of those researchers who have made significant contributions to the subject and many others working on related problems.

A Course in Commutative Algebra

Author: Gregor Kemper
Publisher: Springer Science & Business Media
ISBN: 9783642035456
Format: PDF, Kindle
Download Now
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.

Mathematical and Statistical Methods for Multistatic Imaging

Author: Habib Ammari
Publisher: Springer
ISBN: 3319025856
Format: PDF, ePub, Mobi
Download Now
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.

Ultra Wideband Signals and Systems in Communication Engineering

Author: M. Ghavami
Publisher: John Wiley & Sons
ISBN: 0470060506
Format: PDF, ePub, Mobi
Download Now
The thoroughly revised and updated second edition of Ultra Wideband Signals and Systems in Communication Engineering features new standards, developments and applications. It addresses not only recent developments in UWB communication systems, but also related IEEE standards such as IEEE 802.15 wireless personal area network (WPAN). Examples and problems are included in each chapter to aid understanding. Enhanced with new chapters and several sections including Standardization, advanced topics in UWB Communications and more applications, this book is essential reading for senior undergraduates and postgraduate students interested in studying UWB. The emphasis on UWB development for commercial consumer communications products means that any communication engineer or manager cannot afford to be without it! New material included in the second edition: Two new chapters covering new regulatory issues for UWB systems and new systems such as ad-hoc and sensor networks, MAC protocols and space-time coding for UWB systems IEEE proposals for channel models and their specifications Interference and coexistence of UWB with other systems UWB antennas and arrays, and new types of antennas for UWB systems such as printed bow-tie antennas Coverage of new companies working on UWB such as Artimi and UBISense UWB potential for use in medicine, including cardiology, respiratory medicine, obstetrics and gynaecology, emergency room and acute care, assistance for disabled people, and throat and vocals Companion website features a solutions manual, Matlab programs and electronic versions of all figures.

Recent Advances in Fourier Analysis and Its Applications

Author: J.S. Byrnes
Publisher: Springer Science & Business Media
ISBN: 940090665X
Format: PDF, Mobi
Download Now
This volume contains papers presented at the July, 1989 NATO Advanced Study Institute on Fourier Analysis and its Applications. The conference, held at the beautiful II Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy, created a dynamic in teraction between world-renowned scientists working in the usually disparate communities of pure and applied Fourier analysts. The papers to be found herein include important new results in x-ray crystallography by Nobel Laureate Herbert Hauptman, the application of the new concept of bispectrum to system identification by renowned probabilist Athanasios Papoulis, fascinating appli cations of number theory in Fourier analysis by eminent electrical engineer Manfred R. Schroeder, and exciting concepts regarding polynomials with restricted coefficients by foremost mathematical problem solver Donald J. Newman. The remaining papers further illustrate the inherent power and beauty of classical Fourier analysis, whether the results presented were sought as an end in themselves, or whether these classical methods were employed as a tool in illustrating and solving a particular applied problem. From antenna design to concert hall acoustics to image and speech processing to unimodular polynomi als, each conference participant benefited significantly from his or her exposure, in many cases for the first time, to those scientists on the other end of the spectrum from them selves. The purpose of this volume is to pass those benefits on to the reader.

Excursions in Harmonic Analysis Volume 3

Author: Radu Balan
Publisher: Birkhäuser
ISBN: 331913230X
Format: PDF, ePub, Docs
Download Now
This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include · spectral analysis and correlation; · radar and communications: design, theory, and applications; · sparsity · special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Duration and Bandwidth Limiting

Author: Jeffrey A. Hogan
Publisher: Springer Science & Business Media
ISBN: 0817683070
Format: PDF, Kindle
Download Now
Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive monograph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications engineering, but also to optical engineering, geosciences, planetary sciences, and biomedicine. With broad coverage and a careful balance between rigor and readability, Duration and Bandwidth Limiting is a particularly original and valuable resource both for mathematicians interested in the field and for professional engineers with an interest in theory. While its main target audience is practicing scientists, the book may also serve as useful supplemental reading material for mathematically-based graduate courses in communications and signal processing.

Stochastic Finite Elements A Spectral Approach

Author: Roger G. Ghanem
Publisher: Springer Science & Business Media
ISBN: 1461230942
Format: PDF, Docs
Download Now
This monograph considers engineering systems with random parame ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.