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

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.

Self-contained introduction to signal processing and wavelets assuming only a linear algebra background Hands-on introduction to important concepts using computational and interactive examples and exercises Strong rooting of the developed theory in terms of practical applications to sound and images Request lecturer material: sn.pub/lecturer-material

Autorentext

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.

Inhalt

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.