Transform Techniques in Chemistry

Spectroscopy.- 6.5. Reflection Spectrometry.- 6.6. Emission Spectrometry.- 6.7. Atomic Spectrometry.- 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.- 8 Pulsed and Fourier Transform NMR Spectroscopy.- 8.1. Introduction.- 8.2. Basic Concepts of FT-NMR.- 8.3. Basic Instrumentation.- 8.4. Recent Instrumental Improvements.- 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.- 9.4. Rapid-Scan (Correlation) NMR.- 9.5. Noise Excitation Methods.- 9.6. Measure of the Spin-Lattice Relaxation Time T1.- 9.7. Techniques for the Suppression of Strong Solvent Peaks.- 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.- 11 Fourier Domain Processing of General Data Arrays.- 11.1. Introduction.- 11.2. Fourier Transformation and a GeneralData Array.- 11.3. Amplitude and Phase Arrays.- 11.4. Transformation as a Reversible Operation.- 11.5. Specific Manipulations of Data in the Fourier Domain.- 11.6. Summary.- 12 Fourier and Hadamard Transforms in Pattern Recognition.- 12.1. Introduction.- 12.2. Binary Pattern Classifiers.- 12.3. Fourier and Hadamard Transforms in Pattern Recognition.- 12.4. Conclusions.- 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.- 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.