Fourier transforms and their physical applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Acad. Press
1975
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | Techniques of physics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 256 S. graph. Darst. |
| ISBN: | 0121674509 |
Internformat
MARC
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| 245 | 1 | 0 | |a Fourier transforms and their physical applications |c D. C. Champeney |
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| 264 | 1 | |a London |b Acad. Press |c 1975 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PREFACE v
Part I. Mathematical Foundations
Chapter 1. FOURIER SERIES 1
1.1 Introduction 1
1.2 Basic formulae for Fourier series expansion 2
1.3 Useful information relating to the basic equations 3
1.4 Table of Fourier series for a few illustrative functions .. .. 6
Chapter 2. FOURIER TRANSFORMS 8
2.1 Introduction 8
2.2 The basic formulae for Fourier transforms 8
2.3 Useful information relating to Fourier integrals 10
2.4 Relations between Fourier pairs 15
2.5 Table of Fourier transforms 20
Chapter 3. FOURIER INTEGRALS IN SEVERAL DIMENSIONS .. 40
3.1 The basic result in n dimensions 40
3.2 Use of vectors 41
3.3 Simple operational results 42
3.4 Delta functions in three dimensions 42
3.5 Delta functions in two dimensions 44
3.6 Relations between Fourier pairs in several dimensions .. .. 44
3.7 Table of two dimensional transforms 47
3.8 Table of three dimensional transforms 51
Chapter 4. ENERGY SPECTRA AND POWER SPECTRA .. .. 56
4.1 Introduction 56
4.2 Energy spectrum 58
4.3 Power spectrum 59
4.4 Physical quantities as the real parts of complex quantities .. .. 61
4.5 Spectra in several dimensions 63
4.6 Relations between functions and their spectra 64
vii
viii CONTENTS
Chapter 5. CONVOLUTION AND CORRELATION 66
5.1 Convolution (faltung or folding). Definition and meaning .. 66
5.2 Cross correlation function. Definition and meaning .. .. 68
5.3 Autocorrelation function. Definition and meaning .. .. 71
5.4 The convolution and Wiener Khintchine theorems 73
5.5 Summary of relationships .. .. .. .. .. .. 74
Chapter 6. RANDOM FUNCTIONS 77
6.1 Introduction .. .. .. .. .. .. •. ¦ • 77 f
6.2 Stationary random functions 78
6.3 Signals with non zero mean .. .. .. .. .. .. 81
6.4 Sum of signals .. .. .. .. .. .. .. •• 81
6.5 Shot noise 82
6.6 Random amplitude modulation of a carrier wave .. .. .. 83
6.7 Random phase modulation .. .. .. .. .. .. 85
6.8 Random telegraph signal first type 87
6.9 Random telegraph signal second type .. .. .. .. 88
i
Part II. Applications
Chapter 7. LINEAR SYSTEMS 91 t
7.1 Introduction 91
7.2 Impulse response function and transfer function .. .. .. 92
7.3 Harmonic input. Step input and step response .. .. • • 94
7.4 Energy transfer function .. .. .. .. .. .. 96
7.5 Power transfer. Random or periodic input .. .. .. .. 98
Chapter 8. RESPONSE OF A DAMPED HARMONIC OSCILLATOR
TO A DRIVING FORCE 100
8.1 Introduction 100 1
8.2 Response to harmonic and impulse inputs .. .. .. .. 101
8.3 Damped harmonic driving force .. .. .. .. •• 103
Chapter 9. PASSIVE ELECTRIC CIRCUITS TREATED AS !
LINEAR SYSTEMS 107
9.1 Introduction 107
9.2 Two terminal L,R,C circuits 107
9.3 Ladder network filters 109
9.4 Transmission lines .. .. .. .. .. .. .. 113
9.5 Ideal distortionless filter 115
9.6 Low pass filters 116 ,
9.7 Band pass filters 119
Chapter 10. THE RETRIEVAL OF INFORMATION FROM NOISE ..121
10.1 Introduction 121
10.2 The integrator 122
10.3 The phase sensitive detector 125
10.4 The boxcar detector 126 ;
10.5 The correlator 127 j
10.6 The Wiener Hopf condition 131
10.7 The matched filter 135
f
CONTENTS ix
Chapter 11. COHERENT DIFFRACTION AT PLANE APERTURES
AND LENSES 138
11.1 Introduction 138
11.2 Co ordinate system 139
11.3 Treatment based on the Huygens, Fresnel, Kirchhoff approach .. 140
11.4 Treatment based on the angular spectrum 142
11.5 Evanescent waves .. 143
11.6 Summary of results using the two methods 145
11.7 Power flow and intensity .. .. 147
11.8 Diffraction by one dimensional apertures 148
11.9 Examples of one dimensional systems. Babinet s principle.. .. 149
11.10 Examples of two dimensional systems 154
11.11 The optical transfer and point spread functions 157
11.12 Diffraction at a lens 158
Chapter 12. OPTICAL COHERENCE AND HOLOGRAPHY .. .. 163
12.1 Introduction 163
12.2 The characterisation of coherence 165
12.3 Visibility of interference fringes 166
12.4 Effect of partially coherent illumination on diffraction patterns .. 168
12.5 The Hanbury Brown and Twiss experiment 169
12.6 The propagation of coherence 170
12.7 Holography basic principle 172
12.8 Fourier versus Fresnel holography 176
12.9 Optical processing using holographic techniques 177
Chapter 13. X RAY, NEUTRON AND ELECTRON DIFFRACTION
FROM STATIONARY SCATTERERS 181
13.1 Introduction 181
13.2 Diffraction by an assembly of point scatterers 182
13.3 Scattering by a continuum 184
13.4 Cross section. Scattering function 185
13.5 Density autocorrelation function 186
13.6 The pair correlation function 187
13.7 General comments 188
13.8 The atomic scattering factor 189
13.9 Diffraction by a crystal 190
13.10 Diffraction by liquids and amorphous materials 192
13.11 Density perturbations in a continuous medium 194
13.12 Harmonic distortion of an assembly of point scatterers. Debye
Waller factor 197
13.13 Random displacements of an assembly of point scatterers. Debye
Waller factor 198
Chapter 14. X RAY, NEUTRON AND ELECTRON DIFFRACTION
FROM TIME VARYING SYSTEMS 200
14.1 Basic equations 200
14.2 Other modifications for time dependent systems 202
x CONTENTS
14.3 The time dependent correlation function. Van Hove s formula .. 203
14.4 Density perturbations in a continuum. Brillouin scattering .. 206
14.5 Harmonic distortion of an assembly of point scatterers.
Debye Waller factor 209
14.6 Independent vibrations of an assembly of point scatterers .. .. 210
14.7 The self correlation function for a bound motion 211
14.8 Unbound motion. Diffusion .. .. .. .. .. .. 212
APPENDICES 215
Appendix A Evaluation of Fourier series coefficients .. .. 215
Appendix B Delta functions .. .. .. .. .. .. 216
Appendix C The Fourier integral inversion theorem .. .. 218
Appendix D Expressions for FT+ FT+ {/(*)} and FT~ FT~ {/(*)} 220
Appendix E ParsevaFs theorem 221
Appendix F The Schwartz inequality and the bandwidth theorem 222
Appendix G The product and convolution theorems .. . • 224
Appendix H Bessel functions 225
Appendix I Transforms of symmetrical functions in two and
three dimensions 227
Appendix J The Wiener Khintchine theorem 228
Appendix K The autocorrelation function of a stationary ran¬
dom function 230
Appendix L Spectrum and autocorrelation function for shot noise 230
Appendix M Random phase modulation 232
Appendix N Random telegraph signals 233
Appendix O The response of a linear system expressed in terms of
impulse response 234
Appendix P Use of KirchhofFs formula for diffraction at a
plane aperture 235
Appendix Q Fresnel and Fraunhofer diffraction treated by the
angular spectrum method .. .. .. • ¦ 236
Appendix R Ghosts in diffraction from a distorted array of point
scatterers 239
Appendix S The pair distribution function for randomly dis¬
placed scatterers.. 241
Appendix T Scattering by a time dependent system 242
Appendix U Implications of Causality 244
BIBLIOGRAPHY 247
INDEX 249
|
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| author | Champeney, D. C. |
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| discipline | Physik Mathematik |
| edition | 3. print. |
| format | Book |
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| indexdate | 2024-07-09T15:43:22Z |
| institution | BVB |
| isbn | 0121674509 |
| language | English |
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| physical | X, 256 S. graph. Darst. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
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| publisher | Acad. Press |
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| series | Techniques of physics |
| series2 | Techniques of physics |
| spelling | Champeney, D. C. Verfasser (DE-588)172018021 aut Fourier transforms and their physical applications D. C. Champeney 3. print. London Acad. Press 1975 X, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Techniques of physics 1 Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s Mathematische Physik (DE-588)4037952-8 s DE-604 Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 Techniques of physics 1 (DE-604)BV001890126 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001501443&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Champeney, D. C. Fourier transforms and their physical applications Techniques of physics Harmonische Analyse (DE-588)4023453-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4037952-8 (DE-588)4018014-1 |
| title | Fourier transforms and their physical applications |
| title_auth | Fourier transforms and their physical applications |
| title_exact_search | Fourier transforms and their physical applications |
| title_full | Fourier transforms and their physical applications D. C. Champeney |
| title_fullStr | Fourier transforms and their physical applications D. C. Champeney |
| title_full_unstemmed | Fourier transforms and their physical applications D. C. Champeney |
| title_short | Fourier transforms and their physical applications |
| title_sort | fourier transforms and their physical applications |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Harmonische Analyse Mathematische Physik Fourier-Transformation |
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