An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93
Author: Robert M. Young
Publisher: Academic Press
Total Pages: 254
Release: 2001-05-16
Genre: Mathematics
ISBN: 9780127729558

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook. Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Harmonic Analysis and Applications

Harmonic Analysis and Applications
Author: Christopher Heil
Publisher: Springer Science & Business Media
Total Pages: 390
Release: 2007-08-02
Genre: Mathematics
ISBN: 0817645047

This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.

Fourier Series in Control Theory

Fourier Series in Control Theory
Author: Vilmos Komornik
Publisher: Springer Science & Business Media
Total Pages: 230
Release: 2005-01-27
Genre: Computers
ISBN: 0387223835

This book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published results with new results by the authors.

Wavelet Structure and Design

Wavelet Structure and Design
Author: Daniel J. Greenhoe
Publisher: Abstract Space Publishing
Total Pages: 451
Release: 2013-08-21
Genre: Mathematics
ISBN: 0983801134

This book presents the structure of wavelets, principles of wavelet design, and mathematical structure that supports wavelet theory.

Finite Frame Theory: A Complete Introduction to Overcompleteness

Finite Frame Theory: A Complete Introduction to Overcompleteness
Author: Kasso A. Okoudjou
Publisher: American Mathematical Soc.
Total Pages: 266
Release: 2016-07-13
Genre: Mathematics
ISBN: 1470420198

Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics. This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX. Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.

Signal Analysis

Signal Analysis
Author: Ronald L. Allen
Publisher: John Wiley & Sons
Total Pages: 961
Release: 2004-06-07
Genre: Technology & Engineering
ISBN: 0471660361

Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more

Industrial Mathematics and Complex Systems

Industrial Mathematics and Complex Systems
Author: Pammy Manchanda
Publisher: Springer
Total Pages: 358
Release: 2017-10-18
Genre: Mathematics
ISBN: 9811037582

The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business transactions, and brain-like computers are also highlighted. These contributions – all prepared by respected academicians, scientists and researchers from across the globe – are based on papers presented at the international conference organized on the occasion of the Silver Jubilee of the Indian Society of Industrial and Applied Mathematics (ISIAM) held from 29 to 31 January 2016 at Sharda University, Greater Noida, India. The book will help young scientists and engineers grasp systematic developments in those areas of mathematics that are essential to properly understand challenging contemporary problems.

New Perspectives on Approximation and Sampling Theory

New Perspectives on Approximation and Sampling Theory
Author: Ahmed I. Zayed
Publisher: Springer
Total Pages: 487
Release: 2014-11-03
Genre: Mathematics
ISBN: 3319088017

Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing.

Wavelets

Wavelets
Author: Amir-Homayoon Najmi
Publisher: JHU Press
Total Pages: 303
Release: 2012-04-15
Genre: Mathematics
ISBN: 1421405598

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.

Signal Processing and Machine Learning Theory

Signal Processing and Machine Learning Theory
Author: Paulo S.R. Diniz
Publisher: Elsevier
Total Pages: 1236
Release: 2023-07-10
Genre: Technology & Engineering
ISBN: 032397225X

Signal Processing and Machine Learning Theory, authored by world-leading experts, reviews the principles, methods and techniques of essential and advanced signal processing theory. These theories and tools are the driving engines of many current and emerging research topics and technologies, such as machine learning, autonomous vehicles, the internet of things, future wireless communications, medical imaging, etc. - Provides quick tutorial reviews of important and emerging topics of research in signal processing-based tools - Presents core principles in signal processing theory and shows their applications - Discusses some emerging signal processing tools applied in machine learning methods - References content on core principles, technologies, algorithms and applications - Includes references to journal articles and other literature on which to build further, more specific, and detailed knowledge