This article describes the use of time-domain processing for analyzing spectra acquired in vivo. The theoretical basis of processing in the time domain is presented, emphasizing that this is also the acquisition domain. Some of the drawbacks of using the Fourier transform (FT) and analyzing data in the frequency domain are presented. A brief historical perspective is provided and algorithms are described for time-domain processing. The importance of accurate prior knowledge and calculating the limits of error estimation (Cramer Rao Bounds) are emphasized. The generation of prior knowledge using quantum- mechanical calculations of spin systems, enabling a wide range of pulse sequences and timing parameters to be simulated, is described. Problems associated with estimating background signals, such as from lipids, macromolecules, and membrane components, are considered and the theoretical breakdown of the Cramer Rao assumptions, if these are modelled nonparametrically, is discussed. Methods to mitigate these consequences, such as Monte-Carlo simulation and Bayesian estimation, are briefly considered. The jMRUI suite of software, featuring AMARES, QUEST, and AQSES, is used throughout to illustrate the steps involved, and practical examples of processing 31P magnetic resonance spectroscopy kinetic data and short echo brain H-1 spectra are provided.
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