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An Introduction to Wavelets Through Linear Algebra

2013-12-11 Mathematics
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Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 709/5 ( reviews)

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Book Synopsis An Introduction to Wavelets Through Linear Algebra by : M.W. Frazier

Download or read book An Introduction to Wavelets Through Linear Algebra written by M.W. Frazier. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Wavelets Through Linear Algebra

2014-01-15
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Release : 2014-01-15
Genre :
Kind : eBook
Book Rating : 982/5 ( reviews)

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Book Synopsis An Introduction to Wavelets Through Linear Algebra by : Michael W Frazier

Download or read book An Introduction to Wavelets Through Linear Algebra written by Michael W Frazier. This book was released on 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:

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

2019-03-05 Mathematics
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Release : 2019-03-05
Genre : Mathematics
Kind : eBook
Book Rating : 121/5 ( reviews)

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Book Synopsis Linear Algebra, Signal Processing, and Wavelets - A Unified Approach by : Øyvind Ryan

Download or read book Linear Algebra, Signal Processing, and Wavelets - A Unified Approach written by Øyvind Ryan. This book was released on 2019-03-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Wavelet Analysis

2013-12-11 Computers
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Release : 2013-12-11
Genre : Computers
Kind : eBook
Book Rating : 016/5 ( reviews)

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Book Synopsis An Introduction to Wavelet Analysis by : David F. Walnut

Download or read book An Introduction to Wavelet Analysis written by David F. Walnut. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

Wavelet Theory

2011-09-15 Mathematics
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Release : 2011-09-15
Genre : Mathematics
Kind : eBook
Book Rating : 667/5 ( reviews)

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Book Synopsis Wavelet Theory by : David K. Ruch

Download or read book Wavelet Theory written by David K. Ruch. This book was released on 2011-09-15. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, elementary introduction to wavelet theory and applications Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications. The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets, and biorthogonal wavelets. In addition, the authors include two chapters that carefully detail the transition from wavelet theory to the discrete wavelet transformations. To illustrate the relevance of wavelet theory in the digital age, the book includes two in-depth sections on current applications: the FBI Wavelet Scalar Quantization Standard and image segmentation. In order to facilitate mastery of the content, the book features more than 400 exercises that range from theoretical to computational in nature and are structured in a multi-part format in order to assist readers with the correct proof or solution. These problems provide an opportunity for readers to further investigate various applications of wavelets. All problems are compatible with software packages and computer labs that are available on the book's related Web site, allowing readers to perform various imaging/audio tasks, explore computer wavelet transformations and their inverses, and visualize the applications discussed throughout the book. Requiring only a prerequisite knowledge of linear algebra and calculus, Wavelet Theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.

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