Fourier transforms: principles and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken
Wiley
[2014]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xv, 755 Seiten Diagramme |
| ISBN: | 9781118479148 |
Internformat
MARC
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|---|---|---|---|
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| 005 | 20171018 | ||
| 007 | t | ||
| 008 | 140901s2014 |||| |||| 00||| eng d | ||
| 010 | |a 2014003068 | ||
| 020 | |a 9781118479148 |c hbk. |9 978-1-118-47914-8 | ||
| 035 | |a (OCoLC)895287159 | ||
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| 040 | |a DE-604 |b ger |e rda | ||
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| 100 | 1 | |a Hansen, Eric W. |e Verfasser |0 (DE-588)1141814803 |4 aut | |
| 245 | 1 | 0 | |a Fourier transforms |b principles and applications |c Eric W. Hansen |
| 264 | 1 | |a Hoboken |b Wiley |c [2014] | |
| 264 | 4 | |c © 2014 | |
| 300 | |a xv, 755 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Fourier-Transformation |0 (DE-588)4018014-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fourier-Transformation |0 (DE-588)4018014-1 |D s |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027494488&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027494488&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027494488 | ||
Datensatz im Suchindex
| _version_ | 1804152487614087168 |
|---|---|
| adam_text | CONTENTS
Я
PREFACE
xi
CHAPTER
1
REVIEW OF PREREQUISITE MATHEMATICS
1
1.1
Common Notation
1
1.2
Vectors in Space
з
1.3
Complex Numbers
8
1.4
Matrix Algebra
її
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
86
2.5 •
Creating Orthonormal Bases-the Gram-Schmidt Process
94
2.6
Summary
99
Problems
101
chapter
з
THE DISCRETE FOURIER TRANSFORM
______________________________109
3.1
Sinusoidal Sequences
109
3.2
The Discrete Fourier Transform
114
3.3
Interpreting the DFT
117
3.4
DFT Properties and Theorems
126
3.5
Fast Fourier Transform
152
3.6 •
Discrete Cosine Transform
156
3.7
Summary
164
Problems
165
CHAPTER
4
THE FOURIER SERIES
177
4.1
Sinusoids and Physical Systems
178
4.2
Definitions and Interpretation
178
4.3
Convergence of the Fourier Series
187
vii
VIII CONTENTS
4.4
Fourier
Series
Properties and Theorems
199
4.5
The Heat Equation
215
4.6
The Vibrating String
223
4.7
Antenna Arrays
227
4.8
Computing the Fourier Series
233
4.9
Discrete Time Fourier Transform
238
4.10
Summary
256
Problems
259
CHAPTER
5
THE FOURIER TRANSFORM
273
5.1
From Fourier Series to Fourier Transform
274
5.2
Basic Properties and Some Examples
276
5.3
Fourier Transform Theorems
281
5.4
Interpreting the Fourier Transform
299
5.5
Convolution
300
5.6
More about the Fourier Transform
зі
о
5.7
Time—bandwidth Relationships
318
5.8
Computing the Fourier Transform
322
5.9
~k Time—frequency Transforms
336
5.10
Summary
349
Problems
351
CHAPTER
6
GENERALIZED FUNCTIONS
_______________________________________367
6.1
Impulsive Signals and Spectra
367
6.2
The Delta Function in a Nutshell
371
6.3
Generalized Functions
382
6.4
Generalized Fourier Transform
404
6.5
Sampling Theory and Fourier Series
414
6.6
Unifying the Fourier Family
429
6.7
Summary
433
Problems
436
CHAPTER
7
COMPLEX FUNCTION THEORY
454
7.1
Complex Functions and Their Visualization
455
7.2
Differentiation
460
7.3
Analytic Functions
466
7.4
exp z
and Functions Derived from It
470
7.5
Log
z
and Functions Derived from It
472
7.6
Summary
489
Problems
490
CHAPTER
8
COMPLEX INTEGRATION
494
8.1
Line Integrals in the Plane
494
8.2
The Basic Complex Integral:
φ
zfdz
497
8.3
Cauchy s Integral Theorem
502
CONTENTS
IX
8.4 Cauchy s Integral
Formula
512
8.5 Laurent
Series and Residues
520
8.6
Using Contour Integration to Calculate Integrals of Real Functions
531
8.7
Complex Integration and the Fourier Transform
543
8.8
Summary
556
Problems
557
CHAPTER
9
LAPLACE, Z, AND HILBERT TRANSFORMS
563
9.1
The Laplace Transform
563
9.2
The
Z
Transform
607
9.3
The Hubert Transform
629
9.4
Summary
652
Problems
654
CHAPTER
10
FOURIER TRANSFORMS IN TWO AND THREE DIMENSIONS
669
10.
1 Two-Dimensional Fourier Transform
669
10.2
Fourier Transforms in Polar Coordinates
684
10.3
Wave Propagation
696
10.4
Image Formation and Processing
709
10.5
Fourier Transform of a Lattice
722
10.6
Discrete Multidimensional Fourier Transforms
731
10.7
Summary
736
Problems
737
BIBLIOGRAPHY
743
INDEX
747
FOURIER
TRANSFO
Principles and Applications
Explains the theory and practical applications of various transform
methods to electrical systems, from circuits and antennas to
signal processors
Fourier and related transforms are ¡nvaiuable mathematical tools with a wide
variety of applications in branches of engineering and science. Fourier Transforms:
Principles and Applications explains the theoretical underpinnings of vanous
transform methods and describes their practical applications to
electrica!
systems,
from circuits and antennas to Signal processors.
Following a review of prerequu
mathematica!
topics and some fundamentals of
vector spaces, topic coverage includes:
»
The Discrete Fourier
Transé: DFT]
the Fourier series, the Discrete Time
Fourier Transform (DTFT), the (continuous-time) Fourier transform, and
generalized functions
•
Complex functions ana integral tr
e
Laplace, Z, and Hubert transforms
*
The Fourier transform in two and three dimensions, with applications to wave
propagation and imaging
Throughout the
-: ■
computai
- -
lustrations and end-of-chapter problems serve
enhance the clarity of topics for readers. Designed primarily for practicing
engineers and students in engineering and physics, Feu
ne r
Trans
f
orms
is an essential
resource in gasntng an dersta of the methodology and development of
Fc. era 3ted trans- >a
tei
pp
:зїюп
areas.
Eric W. Hansen
is Associate Professor of Engineering, Thayer School of Engineering
at Dartmouth, Hanover, NH, where he teaches courses tn systems, signal processing,
and diqital design. Heisamembe :f the IEEE and the
ASEE.
|
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| institution | BVB |
| isbn | 9781118479148 |
| language | English |
| lccn | 2014003068 |
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| physical | xv, 755 Seiten Diagramme |
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| spelling | Hansen, Eric W. Verfasser (DE-588)1141814803 aut Fourier transforms principles and applications Eric W. Hansen Hoboken Wiley [2014] © 2014 xv, 755 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027494488&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027494488&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hansen, Eric W. Fourier transforms principles and applications Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4018014-1 |
| title | Fourier transforms principles and applications |
| title_auth | Fourier transforms principles and applications |
| title_exact_search | Fourier transforms principles and applications |
| title_full | Fourier transforms principles and applications Eric W. Hansen |
| title_fullStr | Fourier transforms principles and applications Eric W. Hansen |
| title_full_unstemmed | Fourier transforms principles and applications Eric W. Hansen |
| title_short | Fourier transforms |
| title_sort | fourier transforms principles and applications |
| title_sub | principles and applications |
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| topic_facet | Fourier-Transformation |
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