Signal Treatment and Signal Analysis in NMR (eBook)

Front Cover 1
Signal treatment and signal analysis in NMR 4
Copyright Page 5
Contents 8
Preface 6
Part I: General Theory of Signal Analysis in NMR 20
Chapter 1. Fourier Transform and Signal Manipulation 20
Basics of signal processing 20
The Fourier transform : main features 28
Fourier transform of sampled data 34
References 42
Chapter 2. Maximum Entropy Methods in NMR Data Processing 44
Introduction 44
Approaches to the Maximum Entropy Formalism 45
MEM algorithms 52
Applications of MEM in NMR data processing 58
The definition of Entropy 58
References 60
Chapter 3. Analysis of NMR Relaxation Data 63
Introduction 63
Mathematical description 65
Nonlinear parameter estimation 67
Linear inverse theory 68
Orthogonal function expansions 72
Linear Prediction and Singular Value Decomposition 74
Rational function methods 75
Deconvolution methods 77
Nonuniqueness and resolution 78
Conclusions 80
References 81
Chapter 4. Nonlinear Regression 87
Introduction 87
Numerical methods 94
Further topics 112
Acknowledgments 115
References 115
Chapter 5. The Padé-Laplace Analysis of NMR Signals 119
Introduction 119
General theory of the Padé-Laplace method 120
Padé-Laplace analysis of multiexponential curves 126
The particular case of Padé-Laplace analysis of NMR FID 129
Conclusion 135
References 136
Chapter 6. Digital filtering 139
Introduction: why use digital filtering 139
Mathematical background 140
Computational pitfalls 144
Applications 150
Conclusion 158
References 160
Appendix A: Glossary of symbols and abbreviations 160
Appendix B: PASCAL code for tan Butterworth filter 161
Appendix C: The M'th roots of - 1 163
Chapter 7. Binomial Filters 164
Introduction 164
Theory. 164
Postacquisition filters 168
Chemical shift filters 172
Multiple quantum filters 176
J filters 179
Conclusion 180
Appendix 180
References 180
Chapter 8. Linear Prediction and Singular Value Decomposition in NMR Signal Analysis 183
Linear Prediction. Elementary theory 183
Linear Prediction of NMR signals 187
SVD and its properties 188
Solving the prediction coefficients 190
LPSVD 196
HSVD (State Space Approach) 200
Conclusion 207
References 208
Part II: Applications in the time-domain 210
Chapter 9. A Windows Program for Relaxation Parameter Estimation 210
Introduction 210
Marquardt method of nonlinear parameter estimation 211
File menu 220
Acquisition menu 222
Simulate menu 223
Calculate menu 224
View menu 228
Plot menu 231
Convert menu 234
Options menu 235
Help menu 235
References 236
Chapter 10. Continuous Relaxation Time Distribution Decomposition by MEM 237
Introduction 237
The Maximum Entropy Method 239
Validation of MEM by simulation 243
Validation of MEM with experimental data 247
Conclusion 251
References 251
Chapter 11. Examples of the Use of Padé-Laplace in NMR 254
Introduction 254
Experimental conditions 255
Study of a model 261
Study of a starch suspension 262
Conclusion 264
References 264
Chapter 12. Analysis and interpretation of NMR water relaxation and diffusion data 267
Introduction 267
Relaxation in spatially homogeneous solutions and gels 267
Exchange in spatially heterogeneous systems 281
Activity coefficients and NMR water relaxation 291
Electrical conductivity and NMR water relaxation 295
Conclusion 296
Appendix 297
References 298
Chapter 13. Scattering Wavevector Analysis of Pulsed Gradient Spin Echo Data 300
The Pulsed Gradient Spin Echo Method 300
Restricted diffusion 303
Direct imaging of molecular motion 313
Conclusion 320
References 322
Chapter 14. Accuracy and Precision of Intensity Determinations in Quantitative NMR 325
Introduction 325
Relaxation times and relaxation delays 326
Baseline and phase anomalies 327
Integration algorithms and integration range 330
Noise in NMR spectrometers 331
Precision of imegrals 332
Least squares methods 335
Linear Prediction 337
Maximum Emropy Methods 338
The use of modulus or power spectra 338
Precision of derived parameters 339
Conclusion 340
References 340
Part III: Applications in the frequency-domain 349
Chapter 15. Least Squares Estimation of Parameters Affecting NMR Line-shapes in Multi-Site Chemical Exchange 349
Introduction 349
General equations for signal shape 349
Least Squares method 350
Computer program 352
Problems in Least Squares optimisation 353
Symbols 361
References 363
Chapter 16. Reference Deconvolution in NMR 365
Reference deconvolution 365
Practical implementation 369
Applications 373
Conclusions 377
Acknowledgments 379
References 379
Chapter 17. Continuous Wave and Rapid Scan Correlation NMR 381
Introduction 381
The principles of CW NMR 381
Rapid scan methods 384
Applications of Rapid Scan Correlation NMR 389
Conclusions 391
References 392
Chapter 18. Data processing in High-Resolution Multidimensional NMR 393
Introduction 393
Nature of multidimensional data set - some mathematics 393
Basic processing 398
Display 404
Quality improvement 405
Non-FT spectral analysis 409
Alternate samplings 414
Parameter evaluation 415
Minimisation of the computer burden 416
References 418
Chapter 19. Neural Networks for 2D NMR Spectroscopy 426
Introduction 426
Pattern recognition and Neural Networks 427
Data abstraction and Neural Networks 432
Assignment of protein spectra 437
Acknowledgements 439
References 439
Chapter 20. Analysis of Nuclear Magnetic Resonance Spectra of Mixtures Using Multivariate Techniques 441
Introduction 441
Carbon-13 Nuclear Magnetic Resonance Spectroscopy 443
Data pretreatment 447
Multivariate Analysis 450
Applications 458
Conclusions 467
References 467
Part IV: Applications in the spatial-domain 471
Chapter 21. Quantitative Magnetic Resonance Imaging: Applications and Estimation of Errors 471
Introduction 471
The uses of quantitative imaging 472
Practical problems in quantitative imaging 476
Data fitting 477
Random errors 482
Systematic errors 490
Conclusion 501
Acknowledgements 502
References 502
Chapter 22. Stochastic Spectroscopic Imaging 508
Introduction 508
Noise 509
Processing of the linear response 512
Nonlinear response 515
Processing of the nonlinear response 517
Experimental examples 519
Summary 528
References 528
Chapter 23. Application of Multivariate Data Analysis Techniques to NMR Imaging 532
Summary 532
Introduction 533
Tomography, MR Imaging and MR Spectra 534
Multivariate Images 539
The experiment 542
Experimental Design 542
Multivariate Image Analysis 543
Acknowledgements 551
References 551
Acronyms 554
Index 556