Fourier Transforms

Book description

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

Table of contents

  1. Preface
    1. Philosophy and Distinctives
    2. Flow of the Book
    3. Suggested Use
    4. Acknowledgments
  2. Chapter 1: Review of Prerequisite Mathematics
    1. 1.1 Common Notation
    2. 1.2 Vectors in Space
    3. 1.3 Complex Numbers
    4. 1.4 Matrix Algebra
    5. 1.5 Mappings and Functions
    6. 1.6 Sinusoidal Functions
    7. 1.7 Complex Exponentials
    8. 1.8 Geometric Series
    9. 1.9 Results from Calculus
    10. 1.10 Top 10 Ways to Avoid Errors in Calculations
    11. Problems
    12. Notes
  3. Chapter 2: Vector Spaces
    1. 2.1 Signals and Vector Spaces
    2. 2.2 Finite-Dimensional Vector Spaces
    3. 2.3 Infinite-Dimensional Vector Spaces
    4. 2.4 ∗ Operators
    5. 2.5 ∗ Creating Orthonormal Bases—the Gram–Schmidt Process
    6. 2.6 Summary
    7. Problems
    8. Notes
  4. Chapter 3: The Discrete Fourier Transform
    1. 3.1 Sinusoidal Sequences
    2. 3.2 The Discrete Fourier Transform
    3. 3.3 Interpreting the DFT
    4. 3.4 DFT Properties and Theorems
    5. 3.5 Fast Fourier Transform
    6. 3.6 ∗ Discrete Cosine Transform
    7. 3.7 Summary
    8. Problems
    9. Notes
  5. Chapter 4: The Fourier Series
    1. 4.1 Sinusoids and Physical Systems
    2. 4.2 Definitions and Interpretation
    3. 4.3 Convergence of the Fourier Series
    4. 4.4 Fourier Series Properties and Theorems
    5. 4.5 The Heat Equation
    6. 4.6 The Vibrating String
    7. 4.7 Antenna Arrays
    8. 4.8 Computing the Fourier Series
    9. 4.9 Discrete Time Fourier Transform
    10. 4.10 Summary
    11. Problems
    12. Notes
  6. Chapter 5: The Fourier Transform
    1. 5.1 From Fourier Series to Fourier Transform
    2. 5.2 Basic Properties and Some Examples
    3. 5.3 Fourier Transform Theorems
    4. 5.4 Interpreting the Fourier Transform
    5. 5.5 Convolution
    6. 5.6 More About the Fourier Transform
    7. 5.7 Time–Bandwidth Relationships
    8. 5.8 Computing the Fourier Transform
    9. 5.9 ∗ Time–Frequency Transforms
    10. 5.10 Summary
    11. Problems
    12. Notes
  7. Chapter 6: Generalized Functions
    1. 6.1 Impulsive Signals and Spectra
    2. 6.2 The Delta Function in a Nutshell
    3. 6.3 Generalized Functions
    4. 6.4 Generalized Fourier Transform
    5. 6.5 Sampling Theory and Fourier Series
    6. 6.6 Unifying the Fourier Family
    7. 6.7 Summary
    8. Problems
    9. Notes
  8. Chapter 7: Complex Function Theory
    1. 7.1 Complex Functions and Their Visualization
    2. 7.2 Differentiation
    3. 7.3 Analytic Functions
    4. 7.4 exp z and Functions Derived From It
    5. 7.5 Log z and Functions Derived from It
    6. 7.6 Summary
    7. Problems
    8. Notes
  9. Chapter 8: Complex Integration
    1. 8.1 Line Integrals in the Plane
    2. 8.2 The Basic Complex Integral:
    3. 8.3 Cauchy's Integral Theorem
    4. 8.4 Cauchy's Integral Formula
    5. 8.5 Laurent Series and Residues
    6. 8.6 Using Contour Integration to Calculate Integrals of Real Functions
    7. 8.7 Complex Integration and the Fourier Transform
    8. 8.8 Summary
    9. Problems
    10. Notes
  10. Chapter 9: Laplace, Z, and Hilbert Transforms
    1. 9.1 The Laplace Transform
    2. 9.2 The Z Transform
    3. 9.3 The Hilbert Transform
    4. 9.4 Summary
    5. Problems
    6. Notes
  11. Chapter 10: Fourier Transforms in Two and Three Dimensions
    1. 10.1 Two-Dimensional Fourier Transform
    2. 10.2 Fourier Transforms in Polar Coordinates
    3. 10.3 Wave Propagation
    4. 10.4 Image Formation and Processing
    5. 10.5 Fourier Transform of a Lattice
    6. 10.6 Discrete Multidimensional Fourier Transforms
    7. 10.7 Summary
    8. Problems
    9. Notes
  12. Bibliography
  13. Index
  14. End User License Agreement

Product information

  • Title: Fourier Transforms
  • Author(s): Eric W. Hansen
  • Release date: September 2014
  • Publisher(s): Wiley
  • ISBN: 9781118479148