Fourier transforms in spectroscopy / Jyrki Kauppinen, Jari Partanen.

Format:

Book

Author/Creator:

Kauppinen, Jyrki.

Contributor:

Partanen, Jari.

Language:

English

Subjects (All):

Fourier transform spectroscopy.

Genre:

Handbooks and manuals.

Physical Description:

271 pages : illustrations ; 25 cm

Edition:

First edition.

Place of Publication:

Weinheim ; New York : Wiley-VCH, 2001.

Summary:

This modern 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.

Contents:

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 z 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

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 q-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.

Notes:

Includes bibliographical references (pages [265]-267) and index.

ISBN:

3527402896

OCLC:

48892559