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E-raamat: Fourier Transforms: Principles and Applications

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(Stanford University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 01-Oct-2014
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118901694
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Fourier Transforms: Principles and ApplicationsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 01-Oct-2014
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118901694
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From the preface: "This book is more mathematically detailed and general in scope than a sophomore or junior level signals and systems text, more focused than a survey of mathematical methods, and less rigorous than would be appropriate for students of advanced mathematics." Material is arranged in 10 chapters beginning with a review of prerequisite mathematics. The aim is presentation of the subject for seniors and graduate students in engineering and physics in order to "deepen their grasp of how and why the methods work, enable greater understanding of the application areas, and perhaps motivate further pursuit of the mathematics in its own right." Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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.

Arvustused

It is convenient that every chapter ends up with a summary of the results considered and a bunch of exercises. I hope the author's experience and expertise are what had inspired him to write this book of the present form, size and choice of matter. I also hope that it will find additional readers beyond the author's students.  (Zentralblatt MATH, 1 May 2015)

Preface xi
Chapter 1 Review of Prerequisite Mathematics
1(35)
1.1 Common Notation
1(2)
1.2 Vectors in Space
3(5)
1.3 Complex Numbers
8(3)
1.4 Matrix Algebra
11(4)
1.5 Mappings and Functions
15(5)
1.6 Sinusoidal Functions
20(2)
1.7 Complex Exponentials
22(2)
1.8 Geometric Series
24(1)
1.9 Results from Calculus
25(8)
1.10 Top 10 Ways to Avoid Errors in Calculations
33(3)
Problems
33(3)
Chapter 2 Vector Spaces
36(73)
2.1 Signals and Vector Spaces
37(2)
2.2 Finite-dimensional Vector Spaces
39(25)
2.3 Infinite-dimensional Vector Spaces
64(22)
2.4 * Operators
86(8)
2.5 * Creating Orthonormal Bases-the Gram-Schmidt Process
94(5)
2.6 Summary
99(10)
Problems
101(8)
Chapter 3 The Discrete Fourier Transform
109(68)
3.1 Sinusoidal Sequences
109(5)
3.2 The Discrete Fourier Transform
114(3)
3.3 Interpreting the DFT
117(9)
3.4 DFT Properties and Theorems
126(26)
3.5 Fast Fourier Transform
152(4)
3.6 * Discrete Cosine Transform
156(8)
3.7 Summary
164(13)
Problems
165(12)
Chapter 4 The Fourier Series
177(96)
4.1 Sinusoids and Physical Systems
178(1)
4.2 Definitions and Interpretation
178(9)
4.3 Convergence of the Fourier Series
187(12)
4.4 Fourier Series Properties and Theorems
199(16)
4.5 The Heat Equation
215(8)
4.6 The Vibrating String
223(4)
4.7 Antenna Arrays
227(6)
4.8 Computing the Fourier Series
233(5)
4.9 Discrete Time Fourier Transform
238(18)
4.10 Summary
256(17)
Problems
259(14)
Chapter 5 The Fourier Transform
273(94)
5.1 From Fourier Series to Fourier Transform
274(2)
5.2 Basic Properties and Some Examples
276(5)
5.3 Fourier Transform Theorems
281(18)
5.4 Interpreting the Fourier Transform
299(1)
5.5 Convolution
300(10)
5.6 More about the Fourier Transform
310(8)
5.7 Time-bandwidth Relationships
318(4)
5.8 Computing the Fourier Transform
322(14)
5.9 *Time-frequency Transforms
336(13)
5.10 Summary
349(18)
Problems
351(16)
Chapter 6 Generalized Functions
367(87)
6.1 Impulsive Signals and Spectra
367(4)
6.2 The Delta Function in a Nutshell
371(11)
6.3 Generalized Functions
382(22)
6.4 Generalized Fourier Transform
404(10)
6.5 Sampling Theory and Fourier Series
414(15)
6.6 Unifying the Fourier Family
429(4)
6.7 Summary
433(21)
Problems
436(18)
Chapter 7 Complex Function Theory
454(40)
7.1 Complex Functions and Their Visualization
455(5)
7.2 Differentiation
460(6)
7.3 Analytic Functions
466(4)
7.4 Exp z and Functions Derived from It
470(2)
7.5 Log z and Functions Derived from It
472(17)
7.6 Summary
489(5)
Problems
490(4)
Chapter 8 Complex Integration
494(69)
8.1 Line Integrals in the Plane
494(3)
8.2 The Basic Complex Integral: ∫Γzn dz
497(5)
8.3 Cauchy's Integral Theorem
502(10)
8.4 Cauchy's Integral Formula
512(8)
8.5 Laurent Series and Residues
520(11)
8.6 Using Contour Integration to Calculate Integrals of Real Functions
531(12)
8.7 Complex Integration and the Fourier Transform
543(13)
8.8 Summary
556(7)
Problems
557(6)
Chapter 9 Laplace, Z, And Hilbert Transforms
563(106)
9.1 The Laplace Transform
563(44)
9.2 The Z Transform
607(22)
9.3 The Hilbert Transform
629(23)
9.4 Summary
652(17)
Problems
654(15)
Chapter 10 Fourier Transforms in Two and Three Dimensions
669(74)
10.1 Two-Dimensional Fourier Transform
669(15)
10.2 Fourier Transforms in Polar Coordinates
684(12)
10.3 Wave Propagation
696(13)
10.4 Image Formation and Processing
709(13)
10.5 Fourier Transform of a Lattice
722(9)
10.6 Discrete Multidimensional Fourier Transforms
731(5)
10.7 Summary
736(7)
Problems
737(6)
Bibliography 743(4)
Index 747
Eric W. Hansen, PhD, received his MS and PhD in Electrical Engineering from Stanford University. He is a member of IEEE, OSA, and the ASEE. Dr Hansen has been on the Dartmouth faculty since 1979, and received the Excellence in Teaching Award from the Thayer School of Engineering.
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