About Book

Fourier transform is a tool that breaks a waveform (a function or signal) into an alternate representation, characterized by sine and cosines. Fourier transform shows that any waveform can be re-written as the sum of sinusoidal functions. It decomposes a function of time (a signal) into the frequencies that make it up, similarly to how a musical chord can be expressed as the amplitude (or loudness) of its constituent notes. Fourier transform of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function and whose complex argument is the phase offset of the basic sinusoid in that frequency. In general, functions to which fourier methods are applicable are complex-valued, and possibly vector-valued. Not only the fourier transform give us a special insight into how the world works, it shows up in real-world applications such as MRI, signal processing, electromagnetics, quantum physics and theoretical mathematics. This book gives details of theory and applications of fourier transform. It deals with ultrafast spectroscopy, fourier transform infrared, analytical tool, spectral line profiles, biological macromolecules, spectroscopy of cotton and methodological aspects. This book is a valuable compilation of topics, ranging from the basic to the most complex theories and principles in the field of fourier transform. It explores all the important aspects in the present-day scenario. Student-friendly language and extensive use of examples make this textbook an invaluable source of knowledge. Such selected concepts that redefine this field have been presented in this book. For all those who are interested in fourier transform, this book can prove to be an essential guide.

Preface............................................................................................................v

Chapter 1 Fourier Transform in Ultrafast Spectroscopy......................................1

Abstract...................................................................................................1

1. Introduction............................................................................................1

2. Fourier transform in the experimental setup..................................2

3. Fourier transform in data processing...............................................9

4. Fourier transform in data analysis..................................................12

5. Conclusion............................................................................................14

Acknowledgements.............................................................................14

Conflict of interest..............................................................................15

Other declarations...............................................................................15

Chapter 2 Fourier Transform Infrared Spectroscopy in the Study of Hydrated Biological Macromolecules.....................................................................18

Abstract.................................................................................................18

1. Introduction..........................................................................................19

2. Infrared spectroscopy of water........................................................20

3. Experimental section..........................................................................22

4. Collagen................................................................................................27

5. Lysozyme..............................................................................................35

6. Concluding remarks...........................................................................42

Chapter 3 Fourier Transform Infrared and Two-Dimensional Correlation Spectroscopy for Substance Analysis..................................................47

Abstract.................................................................................................47

1. Introduction..........................................................................................47

2. Fourier transform infrared spectrum and 2DIR correlation

spectroscopy for pure compound analysis....................................48

3. Fourier transform infrared spectrum and 2DIR correlation

spectroscopy for fractions analysis..................................................52

4. Fourier transform infrared spectrum and 2DIR correlation

spectroscopy for raw material analysis..........................................57

5. Fourier transform infrared spectrum and 2DIR correlation

spectroscopy for natural product analysis.....................................61

6. Fourier transform infrared spectrum and 2DIR correlation

spectroscopy for complex mixture analysis...................................63

7. Limitations of FTIR and 2DIR..........................................................64

8. Conclusion............................................................................................65

Acknowledgements.............................................................................65

Chapter 4 Fourier Transform Spectroscopy of Cotton and Cotton Trash......67

1. Introduction ........................................................................................67

2. Theory of FT-MIR ..............................................................................68

3. Instrumentation for FT-IR ................................................................69

4. Theory of FT-NIR................................................................................69

5. Instrumentation of FT-NIR................................................................70

6. Comparison of the FT-IR and FT-NIR ..........................................70

7. Cotton fibers .......................................................................................70

8. Cotton trash ........................................................................................71

9. Non-fourier transform techniques to analyze cotton trash........72

10. Applications of fourier transform spectroscopy to cotton and

cotton trash .........................................................................................74

11. Summary .............................................................................................85

Chapter 5 Fourier Transform Infrared Spectroscopy for the Measurement of

Spectral Line Profiles...............................................................................90

1. Introduction..........................................................................................90

2. Fourier transform spectroscopy.......................................................92

3. Measurement of line profiles using Fourier transform infrared

spectroscopy ......................................................................................101

4. Conclusion .........................................................................................125

5. Acknowledgments ...........................................................................126

Chapter 6 Fourier Transform Infrared Spectroscopy for Natural Fibres.....133

1. Introduction........................................................................................133

2. Hydrogen bonds analysis of natural celluloses by using

FTIR.....................................................................................................134

3. Structure of natural fibres determined by using FTIR..............138

4. Chemical composition of natural fibres by using FTIR............144

5. Morphologies of natural fibres by using FTIR...........................148

6. Conclusions .......................................................................................152

Chapter 7 Fourier Transform Infrared Spectroscopy – Useful Analytical Tool

for Non-Destructive Analysis .............................................................162

1. Introduction........................................................................................162

2. Applicability of Fourier Transform Infrared technique in the

assessment of archeological samples--- Case study- Amber .163

3. Applicability of Fourier Transform Infrared technique in the

assessment of bio-mimicking systems--- Case study-Human low

density lipoproteins .........................................................................173

4. Conclusions .......................................................................................177

5. Acknowledgment .............................................................................178

Chapter 8 Fourier Transform Spectroscopy with Partially Scanned Interferograms

as a Tool to Retrieve Atmospheric Gases Concentrations

from High Spectral Resolution Satellite Observations –

Methodological Aspects and Application to IASI..........................182

1. Introduction........................................................................................182

2. Background.........................................................................................185

3. Application to CO2 ........................................................................191

4. Application to CO.............................................................................200

5. Application to CH4 ..........................................................................205

6. Application to N2O ..........................................................................208

7. Conclusion..........................................................................................210

8. Acknowledgements...........................................................................211

Citation......................................................................................................215

Index...........................................................................................................217

About Author

Lily Ibsan obtained her Ph.D. in Astrophysics from the Technical University, Liege. She is working as an Independent Researcher, Technical Writer and Editor at Porto, in the fields of Mathematics, Physics, Astronomy and Astrophysics. She has diverse areas of academic interests including speech signal processing, digital image processing and statistical signal processing. She has contributed many articles and journals in the field of Fourier Transform. She has been an invited speaker at numerous international telecommunication conferences across the globe.