Fourier transforms in spectroscopy:
"This handbook covers all topics about Fourier transforms and their use in spectral applications. All important aspects are included with respect to their use with optical spectroscopic data. Some aspects of Fourier self-deconvolution and linear prediction are explained thoroughly for the first...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Wiley-VCH
2001
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This handbook covers all topics about Fourier transforms and their use in spectral applications. All important aspects are included with respect to their use with optical spectroscopic data. Some aspects of Fourier self-deconvolution and linear prediction are explained thoroughly for the first time, e. g. Linear Prediction which allows resolution enhancement and gives much more useful spectra." "Starting from the mathematical fundamentals, this book is suitable for graduate students as well as scientists and engineers working in this field. The main part of this book is dedicated to applications of FT in signal processing and spectroscopy. IR and NIR, NMR and mass spectroscopy are dealt with both in a theoretical and practical point of view."--BOOK JACKET. |
| Beschreibung: | Literaturverzeichnis Seite [265] - 267 |
| Beschreibung: | 271 S. Ill. 24 cm |
| ISBN: | 3527402896 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128313083428865 |
|---|---|
| adam_text | Contents
1 Basic definitions 11
1.1 Fourier series................................. 11
1.2 Fourier transform............................... 14
1.3 Dirac s delta function............................. 17
2 General properties of Fourier transforms 23
2.1 Shift theorem................................. 24
2.2 Similarity theorem .............................. 25
2.3 Modulation theorem.............................. 26
2.4 Convolution theorem............................. 26
2.5 Power theorem ................................ 28
2.6 Parseval s theorem .............................. 29
2.7 Derivative theorem.............................. 29
2.8 Correlation theorem.............................. 30
2.9 Autocorrelation theorem ........................... 31
3 Discrete Fourier transform 35
3.1 Effect of truncation.............................. 36
3.2 Effect of sampling............................... 39
3.3 Discrete spectrum............................... 43
4 Fast Fourier transform (FFT) 49
4.1 Basis of FFT.................................. 49
4.2 Cooley-Tukey algorithm........................... 54
4.3 Computation time............................... 56
5 Other integral transforms 61
5.1 Laplace transform............................... 61
5.2 Transfer function of a linear system ..................... 66
5.3 ; transform .................................. 73
6 Fourier transform spectroscopy (FTS) 77
6.1 Interference of light.............................. 77
6.2 Michelson interferometer........................... 78
6.3 Sampling and truncation in FTS ....................... 83
8 0 Contents
6.4 Collimated beam and extended light source ................. 89
6.5 Apodization.................................. 99
6.6 Applications of FTS.............................. 100
7 Nuclear magnetic resonance (NMR) spectroscopy 109
7.1 Nuclear magnetic moment in a magnetic field................ 109
7.2 Principles of NMR spectroscopy....................... 112
7.3 Applications of NMR spectroscopy...................... 115
8 Ion cyclotron resonance (ICR) mass spectrometry 119
8.1 Conventional mass spectrometry....................... 119
8.2 ICR mass spectrometry............................ 121
8.3 Fourier transforms in ICR mass spectrometry................ 124
9 Diffraction and Fourier transform 127
9.1 Fraunhofer and Fresnel diffraction...................... 127
9.2 Diffraction through a narrow slit....................... 128
9.3 Diffraction through two slits......................... 130
9.4 Transmission grating............................. 132
9.5 Grating with only three orders ........................ 137
9.6 Diffraction through a rectangular aperture.................. 138
9.7 Diffraction through a circular aperture.................... 143
9.8 Diffraction through a lattice.......................... 144
9.9 Lens and Fourier transform.......................... 145
10 Uncertainty principle 155
10.1 Equivalent width ............................... 155
10.2 Moments of a function............................ 158
10.3 Second moment................................ 160
11 Processing of signal and spectrum 165
11.1 Interpolation.................................. 165
11.2 Mathematical filtering............................. 170
11.3 Mathematical smoothing........................... 180
11.4 Distortion and (S/N) enhancement in smoothing.............. 184
11.5 Comparison of smoothing functions..................... 190
11.6 Elimination of a background......................... 193
11.7 Elimination of an interference pattern .................... 194
11.8 Deconvolution................................. 196
12 Fourier self-deconvolution (FSD) 205
12.1 Principle of FSD ............................... 205
12.2 Signal-to-noise ratio in FSD ......................... 212
12.3 Underdeconvolution and overdeconvolution................. 217
12.4 Band separation................................ 218
12.5 Fourier complex self-deconvolution ..................... 219
12.6 Even-order derivatives and FSD ....................... 221
13 Linear prediction 229
13.1 Linear prediction and extrapolation...................... 229
13.2 Extrapolation of linear combinations of waves................ 230
13.3 Extrapolation of decaying waves....................... 232
13.4 Predictability condition in the spectral domain................ 233
13.5 Theoretical impulse response......................... 234
13.6 Matrix method impulse responses ...................... 236
13.7 Burg s impulse response ........................... 239
13.8 The^-curve.................................. 240
13.9 Spectral line narrowing by signal extrapolation ............... 242
13.10 Imperfect impulse response.......................... 243
13.11 The LOMEP line narrowing method..................... 248
13.12 Frequency tuning method........................... 250
13.13 Other applications............................... 255
13.14 Summary ................................... 258
Answers to problems 261
Bibliography 265
Index 269
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:47:15Z |
| institution | BVB |
| isbn | 3527402896 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009228822 |
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| spelling | Kauppinen, Jyrki Verfasser aut Fourier transforms in spectroscopy Jyrki Kauppinen ; Jari Partanen 1. ed. Berlin [u.a.] Wiley-VCH 2001 271 S. Ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite [265] - 267 "This handbook covers all topics about Fourier transforms and their use in spectral applications. All important aspects are included with respect to their use with optical spectroscopic data. Some aspects of Fourier self-deconvolution and linear prediction are explained thoroughly for the first time, e. g. Linear Prediction which allows resolution enhancement and gives much more useful spectra." "Starting from the mathematical fundamentals, this book is suitable for graduate students as well as scientists and engineers working in this field. The main part of this book is dedicated to applications of FT in signal processing and spectroscopy. IR and NIR, NMR and mass spectroscopy are dealt with both in a theoretical and practical point of view."--BOOK JACKET. Fourier, Spectroscopie par transformée de Fourier, Spectroscopie par transformée de ram Fourier transform spectroscopy Fourier-Spektroskopie (DE-588)4135413-8 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Spektroskopie (DE-588)4056138-0 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s Spektroskopie (DE-588)4056138-0 s DE-604 Fourier-Spektroskopie (DE-588)4135413-8 s Partanen, Jari Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009228822&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kauppinen, Jyrki Partanen, Jari Fourier transforms in spectroscopy Fourier, Spectroscopie par transformée de Fourier, Spectroscopie par transformée de ram Fourier transform spectroscopy Fourier-Spektroskopie (DE-588)4135413-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd Spektroskopie (DE-588)4056138-0 gnd |
| subject_GND | (DE-588)4135413-8 (DE-588)4018014-1 (DE-588)4056138-0 |
| title | Fourier transforms in spectroscopy |
| title_auth | Fourier transforms in spectroscopy |
| title_exact_search | Fourier transforms in spectroscopy |
| title_full | Fourier transforms in spectroscopy Jyrki Kauppinen ; Jari Partanen |
| title_fullStr | Fourier transforms in spectroscopy Jyrki Kauppinen ; Jari Partanen |
| title_full_unstemmed | Fourier transforms in spectroscopy Jyrki Kauppinen ; Jari Partanen |
| title_short | Fourier transforms in spectroscopy |
| title_sort | fourier transforms in spectroscopy |
| topic | Fourier, Spectroscopie par transformée de Fourier, Spectroscopie par transformée de ram Fourier transform spectroscopy Fourier-Spektroskopie (DE-588)4135413-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd Spektroskopie (DE-588)4056138-0 gnd |
| topic_facet | Fourier, Spectroscopie par transformée de Fourier transform spectroscopy Fourier-Spektroskopie Fourier-Transformation Spektroskopie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009228822&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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