Linear Algebra, Signal Processing, and Wavelets - A Unified Approach: Python Version

✍ Scribed by Øyvind Ryan

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 386
• Series: Springer Undergraduate Texts in Mathematics and Technology
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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 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.

✦ Table of Contents

Front Matter ....Pages I-XXVII
Sound and Fourier Series (Øyvind Ryan)....Pages 1-47
Digital Sound and Discrete Fourier Analysis (Øyvind Ryan)....Pages 49-95
Discrete Time Filters (Øyvind Ryan)....Pages 97-142
Motivation for Wavelets and Some Simple Examples (Øyvind Ryan)....Pages 143-188
The Filter Representation of Wavelets (Øyvind Ryan)....Pages 189-227
Constructing Interesting Wavelets (Øyvind Ryan)....Pages 229-258
The Polyphase Representation of Filter Bank Transforms (Øyvind Ryan)....Pages 259-286
Digital Images (Øyvind Ryan)....Pages 287-316
Using Tensor Products to Apply Wavelets to Images (Øyvind Ryan)....Pages 317-342
Back Matter ....Pages 343-364

✦ Subjects

Mathematics; Linear Algebra; Computational Science and Engineering; Mathematical and Computational Engineering; Signal, Image and Speech Processing; Fourier Analysis