Spectrum estimation and the Fourier transform in imaging and spectroscopy

Abstract

This work aims at two purposes: tutoring and reference. It is an introductory, concise text for the newcomers to Fourier transform NMR, and it is a reference source for those who are involved in NMR spectroscopy and imaging and who have already made themselves familiar with the concepts of frequency and spectrum. The work attempts to help the reader understand the natural meaning of Fouriertransform theory, beginning with basicconceptsand proceeding to more complicated ones, step by step, covering almost every aspect of interest in the area. It also introduces two new concepts in NMR signal-processing theory: time-frequency representations and the temporal autocorrelation function. New algorithms of spectral estimation and image reconstruction, based on this original material, are proposed. The new techniques fully exploit the special characteristics of the N M R signal. The tutoring material is presented qualitatively, and it includes only fundamental mathematics Throughout the text, an effort is made to explain important concepts in simple terms, usually through examples, so that the introduction of new information flows smoothlyand no extensive spiritual endeavor is required from the reader.