Title: Fourier synthesis methods for identification and control of ensembles
Description: In this thesis we study problems where dispersions in parameters which govern the dynamics of members of a physical ensemble make measurement of desired quantities difficult. Physical parameters of interest get hidden due to the dispersions across the ensemble. The unifying theme throughout this work is the development of Fourier synthesis based methods to correct for such dispersions. Nuclear Magnetic Resonance (NMR) spectroscopy and imaging in inhomogeneous magnetic fields motivate the models and problems studied in the thesis. We provide explicit methods to overcome and compensate for dispersions in several well known experiments. Additionally, we give a new procedure to identify the complete spatial profile of an unknown inhomogeneity in the static field B 0 in an NMR experiment, and subsequently to compensate for it. Another interesting and related problem studied in the thesis is the design of control laws to prepare the final state of the ensemble as a function of the dispersion parameters which govern the dynamics of its members. The solutions to these problems have importance in the fields of magnetic resonance imaging and coherent spectroscopy.