Multidimensional Random Sampling for Fourier Transform Estimation

......................................................................................................................... I Acknowledgments .......................................................................................................... II Author Declaration ........................................................................................................ IV Associated Publications .................................................................................................. V Glossary .......................................................................................................................... IX Chapter 1: Introduction ................................................................................................ 1 1.1 NMR Spectroscopy ................................................................................. 2 1.2 The Adopted Sampling Methodology .................................................... 6 1.3 Summary of the Contributions .............................................................. 12 1.4 Thesis Outline ........................................................................................ 14 Chapter 2: Sampling Techniques and Fourier Analysis ............................................ 15 2.1 Preliminary on Multidimensional Sampling and Fourier Analysis ......... 19 2.2 Nonuniform Sampling Techniques and Processing Algorithms .............. 25 2.2.1 Least-Square Spectral Analysis ................................................... 25 2.2.2 Compressive Sensing ................................................................... 26 2.2.3 Periodic Nonuniform Sampling ................................................... 28