Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

✍ Scribed by Stanković, Radomir S.; Moraga, Claudio; Astola, Jaakko T.

• Publisher: Wiley - IEEE Press
• Year: 2005
• Tongue: English
• Leaves: 216
• Category: Library

✦ Synopsis

This book examines applications of Fourier analysis on finite non-Abelian groups, and discusses different methods to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as a particular example of discrete functions in engineering practice. Consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelain groups. The book demonstrates how transferring a problem from its original form into the spectral domain may provide major advantages, such as simplifying numerical calculation tasks.

✦ Table of Contents

Content:
Front Matter
• Preface
• List of Figures
• List of Tables
• Table of Contents
1. Signals and Their Mathematical Models
2. Fourier Analysis on Non-Abelian Groups
3. Matrix Interpretation of the Fast Fourier Transform
4. Optimization of Decision Diagrams
5. Functional Expressions on Quaternion Groups
6. Gibbs Derivatives on Finite Groups
7. Linear Systems and Gibbs Derivatives on Finite Non-Abelian Groups
8. Hilbert Transform on Finite Groups
Index