Fourier Transforms E-Book

Eric W. Hansen

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1184

Veröffentlichungsjahr: 2014

Beschreibung

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

Leseprobe

FOURIER TRANSFORMS

Principles and Applications

ERIC W. HANSEN

Thayer School of Engineering, Dartmouth College

Cover Image: ©iStockphoto/olgaaltunina

Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data is available.

ISBN: 978-1-118-47914-8

To my family

CONTENTS

Preface

Philosophy and Distinctives

Flow of the Book

Suggested Use

Acknowledgments

Chapter 1: Review of Prerequisite Mathematics

1.1 Common Notation

1.2 Vectors in Space

1.3 Complex Numbers

1.4 Matrix Algebra

1.5 Mappings and Functions

1.6 Sinusoidal Functions

1.7 Complex Exponentials

1.8 Geometric Series

1.9 Results from Calculus

1.10 Top 10 Ways to Avoid Errors in Calculations

Problems

Notes

Chapter 2: Vector Spaces

2.1 Signals and Vector Spaces

2.2 Finite-Dimensional Vector Spaces

2.3 Infinite-Dimensional Vector Spaces

2.4 ∗ Operators

2.5 ∗ Creating Orthonormal Bases—the Gram–Schmidt Process

2.6 Summary

Problems

Notes

Chapter 3: The Discrete Fourier Transform

3.1 Sinusoidal Sequences

3.2 The Discrete Fourier Transform

3.3 Interpreting the DFT

3.4 DFT Properties and Theorems

3.5 Fast Fourier Transform

3.6 ∗ Discrete Cosine Transform

3.7 Summary

Problems

Notes

Chapter 4: The Fourier Series

4.1 Sinusoids and Physical Systems

4.2 Definitions and Interpretation

4.3 Convergence of the Fourier Series

4.4 Fourier Series Properties and Theorems

4.5 The Heat Equation

4.6 The Vibrating String

4.7 Antenna Arrays

4.8 Computing the Fourier Series

4.9 Discrete Time Fourier Transform

4.10 Summary

Problems

Notes

Chapter 5: The Fourier Transform

5.1 From Fourier Series to Fourier Transform

5.2 Basic Properties and Some Examples

5.3 Fourier Transform Theorems

5.4 Interpreting the Fourier Transform

5.5 Convolution

5.6 More About the Fourier Transform

5.7 Time–Bandwidth Relationships

5.8 Computing the Fourier Transform

5.9 ∗ Time–Frequency Transforms

5.10 Summary

Problems

Notes

Chapter 6: Generalized Functions

6.1 Impulsive Signals and Spectra

6.2 The Delta Function in a Nutshell

6.3 Generalized Functions

6.4 Generalized Fourier Transform

6.5 Sampling Theory and Fourier Series

6.6 Unifying the Fourier Family

6.7 Summary

Problems

Notes

Chapter 7: Complex Function Theory

7.1 Complex Functions and Their Visualization

7.2 Differentiation

7.3 Analytic Functions

7.4 exp

z

and Functions Derived From It

7.5 Log

z

and Functions Derived from It

7.6 Summary

Problems

Notes

Chapter 8: Complex Integration

8.1 Line Integrals in the Plane

8.2 The Basic Complex Integral:

8.3 Cauchy's Integral Theorem

8.4 Cauchy's Integral Formula

8.5 Laurent Series and Residues

8.6 Using Contour Integration to Calculate Integrals of Real Functions

8.7 Complex Integration and the Fourier Transform

8.8 Summary

Problems

Notes

Chapter 9: Laplace, Z, and Hilbert Transforms

9.1 The Laplace Transform

9.2 The Z Transform

9.3 The Hilbert Transform

9.4 Summary

Problems

Notes

Chapter 10: Fourier Transforms in Two and Three Dimensions

10.1 Two-Dimensional Fourier Transform

10.2 Fourier Transforms in Polar Coordinates

10.3 Wave Propagation

10.4 Image Formation and Processing

10.5 Fourier Transform of a Lattice

10.6 Discrete Multidimensional Fourier Transforms

10.7 Summary

Problems

Notes

Bibliography

Index

End User License Agreement

List of Tables

Chapter 4

Table 4.1

Table 4.2

Table 4.3

Chapter 5

Table 5.1

Chapter 6

Table 6.1

Table 6.2

Table 6.3

Chapter 9

Table 9.1

Table 9.2