Transform Techniques in Chemistry

Edited by Griffiths, P.


  • 1 Transform Techniques in Chemistry: Past, Present, and Future.- 1.1. The Past.- 1.1.1. Optical Spectroscopy.- 1.1.2. NMR Spectroscopy.- 1.1.3. Data Processing.- 1.2. The Present.- 1.3. The Future.- References.- 2 The Fourier Transform and Related Concepts: A First Look.- 2.1. Introduction: Guitar Tuning.- 2.2. Differences in Space and Time: Phase.- 2.3. Sums, Integrals, and Orthogonality.- 2.4. Various Expressions of Fourier Transform Relationships.- 2.5. Concepts and Corollaries for Fourier Transforms.- 2.6. More on Phase and Phase Correction.- 2.7. Apodization and Resolution Enhancement.- 2.8. The Discrete Fourier Transform.- 2.9. Walsh and Hadamard Transforms.- 2.10. Summary.- References.- 3 Multichannel Methods in Spectroscopy.- 3.1. Introduction.- 3.2. Spectrometer Sources and Detectors.- 3.2.1. Terminology.- 3.2.2. Single-Channel (Scanning-Type) Spectrometer.- 3.2.3. Multidetector Spectrometer.- 3.3. Weights on a Balance: The Multichannel Advantage. Multiplex Methods.- 3.3.1. One-at-a-Time Weighing: The Scanning Spectrometer.- 3.3.2. Many Balances: The Multidetector Spectrometer.- 3.3.3. Half the Weights on the Balance at Once: Hadamard Multiplexing.- 3.3.4. All the Weights on the Balance at Once: The Fourier Advantage.- 3.4. Hadamard Multiplexing of Spatially Dispersed Spectra.- 3.5. Advantages of Coherent Radiation in Spectrometer Detection.- 3.6. Fourier Methods.- 3.6.1. Fourier Multiplexing: The Multichannel Advantage.- 3.6.2. Fourier Analysis of Detector Response: Spectral Line Shape.- 3.6.3. Pulsed Monochromatic Coherent Radiation as a Broad-Band Radiation Source.- 3.7. Summary: Relations Between Different Spectrometers.- 3.8. Appendix. Noise Considerations for Multichannel Spectrometers.- 3.8.1. NB ? (signal)1/2: "Source-Limited" Noise.- 3.8.2. NA = constant: "Detector-Limited" Noise.- 3.8.3. NC ? signal: "Fluctuation" Noise.- References and Notes.- 4 Data Handling in Fourier Transform Spectroscopy.- 4.1. The Computer System.- 4.1.1. Introduction to Computers.- 4.1.2. Data Acquisition.- 4.1.3. Timing in Data Acquisition.- 4.1.4. The Sampling Theorem.- 4.1.5. Digital Phase Correction.- 4.1.6. Signal Averaging.- 4.1.7. Signals Having High Dynamic Range.- 4.1.8. Other Computer Requirements.- 4.1.9. Disk-Based Data Acquisition.- 4.1.10. Comparison of Data System Requirements in NMR and IR.- 4.2. The Fourier Transform.- 4.2.1. Introduction.- 4.2.2. The Cooley-Tukey Algorithm.- 4.2.3. The Signal Flow Graph.- 4.2.4. In-Place Transforms.- 4.3. Writing a Fourier Transform for a Minicomputer.- 4.3.1. Introduction.- 4.3.2. The Form of W.- 4.3.3. The Fundamental Operations.- 4.3.4. The Sine Look-Up Table.- 4.3.5. Binary Fractions.- 4.3.6. The Sine Look-Up Routine.- 4.3.7. Scaling during the Transform.- 4.3.8. Forward and Inverse Transforms.- 4.3.9. Forward Transforms of Real Data.- 4.3.10. Inverse Real Transforms.- 4.3.11. Baseline Correction.- 4.3.12. A Fourier Transform Routine.- 4.3.13. Correlation.- 4.3.14. Disk-Based Fourier Transforms.- 4.3.15. Hardware Fourier Processors.- 4.4. Noise in the Fourier Transform Process.- 4.4.1. Round-Off Errors.- 4.4.2. Block Averaging.- 4.4.3. Double-Precision Fourier Transforms.- 4.5. Summary.- References.- 5 Fourier Transform Infrared Spectrometry: Theory and Instrumentation.- 5.1. Introduction.- 5.2. The Michelson Interferometer.- 5.3. Resolution and Apodization.- 5.4. Effect of Beam Divergence.- 5.5. Mirror Drive Tolerance.- 5.6. Dynamic Range.- 5.7. Scan Speed and Spectral Modulation.- 5.8. Data Acquisition.- 5.9. Beamsplitters.- 5.10. Lamellar Grating Interferometers.- 5.11. Detectors for FT-IR.- 5.11.1. Far-Infrared Detectors.- 5.11.2. Mid- and Near-Infrared Detectors.- 5.11.3. Ultraviolet-Visible Spectroscopy.- 5.12. Auxiliary Optics.- 5.12.1. Source Optics.- 5.12.2. Absorption Spectroscopy.- 5.12.3. Reflection Spectroscopy.- 5.13. Data Systems.- 5.13.1. Far-Infrared Spectroscopy.- 5.13.2. Mid-Infrared Spectroscopy.- 5.13.3. Ultra-High-Resolution Spectroscopy.- 5.14. Dual-Beam Fourier Transform Spectroscopy.- References.- 6 Infrared Fourier Transform Spectrometry: Applications to Analytical Chemistry.- 6.1. FT-IR versus Grating Spectrophotometers.- 6.1.1. Fellgett's Advantage.- 6.1.2. Jacquinot's Advantage.- 6.1.3. Effect of Detector Performance.- 6.1.4. Other Differences.- 6.1.5. Implications.- 6.2. Spectra of Transient Species.- 6.2.1. GC-IR.- 6.2.2. LC-IR.- 6.2.3. Reaction Kinetics.- 6.3. Low-Energy Absorption Spectrometry.- 6.3.1. Far-Infrared Spectrometry.- 6.3.2. Mid-Infrared Absorption Spectrometry.- 6.4. Difference Spectroscopy.- 6.5. Reflection Spectrometry.- 6.6. Emission Spectrometry.- 6.7. Atomic Spectrometry.- References.- 7 Hadamard Transform Analytical Systems.- 7.1. Introduction.- 7.2. Weighing Designs and Optical Multiplexing.- 7.3. Historical Background of Multiplexing by Means of Masks.- 7.4. Mathematical Development.- 7.5. Varieties of Encoded Spectrometers.- 7.6. Limitations: HTS Instruments and Interferometers.- 7.7. Imagers and Spectrometric Imagers.- 7.8. Signal and Noise Limitations.- 7.9. Special Optical Systems.- 7.10. Some Future Applications.- References.- 8 Pulsed and Fourier Transform NMR Spectroscopy.- 8.1. Introduction.- 8.2. Basic Concepts of FT-NMR.- 8.3. Basic Instrumentation.- 8.3.1. The Spectrometer.- 8.3.2. The Sample Probe.- 8.4. Recent Instrumental Improvements.- 8.4.1. Coherent Broad-Band Decoupling.- 8.4.2. Gated Decoupling Methods and Quantitative Measurements.- 8.4.3. Microsample Techniques.- 8.4.4. Selective Population Transfer.- 8.4.5. Studies of Chemical Dynamics.- 8.4.6. High-Resolution 13C NMR in Solid Materials.- 8.4.7. FT-NMR at High Fields.- References.- 9 Advanced Techniques in Fourier Transform NMR.- 9.1. Introduction.- 9.2. Systematic Noise Reduction.- 9.2.1. Noise Reduction Methods.- 9.2.2. Relaxation Times and Spin Echoes.- 9.3. Sideband Filters and Quadrature Detection NMR.- 9.3.1. The Crystal Sideband Filter.- 9.3.2. Quadrature Detection Spectroscopy.- 9.3.3. Operational Details in Quadrature NMR.- 9.3.4. Comparison between Crystal Sideband Filter and Quadrature Detection.- 9.4. Rapid-Scan (Correlation) NMR.- 9.4.1. General Description.- 9.4.2. Data Processing Methods.- 9.5. Noise Excitation Methods.- 9.5.1. Stochastic Resonance Spectroscopy.- 9.5.2. Hadamard Transform NMR.- 9.5.3. Tailored Excitation.- 9.6. Measure of the Spin-Lattice Relaxation Time T1.- 9.6.1. General Description.- 9.6.2. Reasons for Measuring T1.- 9.6.3. Methods of Measuring T1.- 9.6.4. Progressive Saturation.- 9.6.5. Homospoil-T1 Methods.- 9.6.6. Experimental Techniques in the Measurement of T1.- 9.7. Techniques for the Suppression of Strong Solvent Peaks.- 9.7.1. Introduction.- 9.7.2. Block Averaging.- References.- 10 Fourier Transform Ion Cyclotron Resonance Spectroscopy.- 10.1. Introduction.- 10.2. Fundamental Equations for ICR Linewidth and Resolution.- 10.3. Fourier Transform Ion Cyclotron Resonance (FT-ICR) Spectroscopy.- 10.4. Analytical FT-ICR Linewidth and Mass Resolution.- 10.5. FT-ICR Mass Range, Computer Data Size, and Sampling Rate.- 10.6. Discussion.- References.- 11 Fourier Domain Processing of General Data Arrays.- 11.1. Introduction.- 11.2. Fourier Transformation and a General Data Array.- 11.3. Amplitude and Phase Arrays.- 11.4. Transformation as a Reversible Operation.- 11.5. Specific Manipulations of Data in the Fourier Domain.- 11.5.1. Fourier Domain Manipulations without Using Weighting Functions.- Zero Filling.- Contrast Enhancement.- 11.5.2. Fourier Domain Manipulations Using Weighting Functions.- Smoothing.- Elimination of Low-Frequency Interferences.- Differentiation and Integration.- Resolution Enhancement and Functional Isolation.- 11.6. Summary.- References.- 12 Fourier and Hadamard Transforms in Pattern Recognition.- 12.1. Introduction.- 12.1.1. Basic Pattern Recognition System.- 12.1.2. Preprocessor-Feature Extractor.- 12.1.3. Classifier.- 12.2. Binary Pattern Classifiers.- 12.2.1. Pattern Vectors.- 12.2.2. Similarity and Clustering.- 12.2.3. K-Nearest-Neighbor Classification.- 12.2.4. Decision Surfaces.- 12.2.5. TLUs as Binary Pattern Classifiers.- Training of TLUs Using Error Correction Feedback.- Properties of TLUs.- 12.2.6. Preprocessing and Transformations.- 12.3. Fourier and Hadamard Transforms in Pattern Recognition.- 12.3.1. Feature Reduction.- 12.3.2. Pattern Recognition Analysis of NMR Data.- Simulated Free-Induction Decay Analysis.- Hadamard-Transformed Data Analysis.- Autocorrelation Transforms.- 12.4. Conclusions.- References.- 13 Spectral Representations for Quantized Chemical Signals.- 13.1. Introduction.- 13.2. 13C FID Signals and Their Spectra.- 13.3. Orthogonal Expansions and Spectral Representations.- 13.4. Clipped Signals and Their Spectral Representations.- 13.5. Random Real-Zero Signals.- 13.6. Zero-Based Product Representations for Band-Limited Signals.- 13.7. Spectra of Clipped FID Signals.- 13.8. Summary, Implications, and Open Questions.- Notation.- Appendix. Intermodulation Distortion in the CFID.- References.- 14 Applications of the FFT in Electrochemistry.- 14.1. Introduction.- 14.2. Faradaic Admittance Measurements-Basic Principles.- 14.3. Instrumentation.- 14.4. Kinetics of Electrode Processes.- 14.5. Relevant Properties of the FFT for Electrochemical Relaxation Measurements.- 14.6. Published and Future Applications of the FFT in Electrochemistry.- References.

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書名 Transform Techniques in Chemistry
著作者等 Griffiths, P.
シリーズ名 Modern Analytical Chemistry
出版元 Springer-Verlag New York Inc.
刊行年月 2012.12.12
版表示 Softcover reprint of the original 1st ed. 1978
ページ数 404p
大きさ H229 x W152
ISBN 9781468424058
言語 英語
出版国 アメリカ合衆国