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

Python Version
1. Auflage 2019
ISBN: 978-3-030-02939-5
Verlag: Springer International Publishing

Buch, Englisch, 364 Seiten, Book w. online files / update, Format (B × H): 183 mm x 260 mm, Gewicht: 932 g

Reihe: Springer Undergraduate Texts in Mathematics and Technology

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 feasibilityand applications of both approaches. Most of the 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Ryan, Øyvind

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

1. Sound and Fourier series.- 2. Digital Sound and Discrete Fourier Analysis.- 3. Discrete Time Filters.- 4. Motivation for Wavelets and Some Simple Examples.- 5. The Filter Representation of Wavelets.- 6. Constructing Interesting Wavelets.- 7. The Polyphase Representation of Filter Bank Transforms.- 8. Digital Images.- 9. Using Tensor Products to Apply Wavelets to Images.- A Basic Linear Algebra.

Über Autor(innen)

Øyvind Ryan holds a position as an associate professor at the Department of Mathematics at the University of Oslo. Over several years he has been teaching and writing course material for courses in undergraduate mathematics and signal processing. His research interests are information theory, wavelets, and compressive sensing.