Fourier Transforms Principles and Applications [Hardcover]

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.

• Class-tested at Dartmouth
• Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing
• Modular coverage of material allows for topics to be covered by preference
• MATLAB files and Solutions Manual available to instructors
• Over 300 figures, 200 worked examples, and 432 homework problems

PREFACE xi

CHAPTER 1 REVIEW OF PREREQUISITE MATHEMATICS 1

1.1 Common Notation 1

1.2 Vectors in Space 3

1.3 Complex Numbers 8

1.4 Matrix Algebra 11

1.5 Mappings and Functions 15

1.6 Sinusoidal Functions 20

1.7 Complex Exponentials 22

1.8 Geometric Series 24

1.9 Results from Calculus 25

1.10 Top 10 Ways to Avoid Errors in Calculations 33

Problems 33

CHAPTER 2 VECTOR SPACES 36

2.1 Signals and Vector Spaces 37

2.2 Finite-dimensional Vector Spaces 39

2.3 Infinite-dimensional Vector Spaces 64

2.4 ⋆ Operators 8lCš