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© 2019

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

MATLAB Version

Textbook
  • 18k Downloads

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. Øyvind Ryan
    Pages 1-46
  3. Øyvind Ryan
    Pages 93-139
  4. Øyvind Ryan
    Pages 187-224
  5. Øyvind Ryan
    Pages 225-253
  6. Øyvind Ryan
    Pages 283-312
  7. Back Matter
    Pages 339-360

About this book

Introduction

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.


Keywords

Linear Algebra Wavelets Discrete Wavelet Transforms Signal processing Fast Fourier Transforms Sampling Fourier Analysis Image Compression Tensor Products

Authors and affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

About the authors

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.

Bibliographic information

Reviews

“A beginning student who is unfamiliar with the mathematics behind signal processing will find much here that explains the techniques and the issues associated with their use. Altogether the book presents a beautiful introduction to the uses of linear algebra in signal processing.” (MAA Reviews, July 18, 2020)

“This book is a very useful textbook for undergraduate students in applied mathematics and engineering disciplines, but it is also suitable for graduate level courses.” (Manfred Tasche, zbMATH 1420.65001, 2019)