Edward Purcell and Felix Bloch discovered the basic of spectroscopy in 1946 (see MRI History). Nuclear magnetic resonance spectroscopy (NMR Spectroscopy or MRS) is an analytical tool, based on nuclei that have a spin (nuclei with an odd number of neutrons and/or protons) like 1H, 13C, 17O, 19F, 31P etc.
Through nuclear magnetic principles as precession, chemical shift, spin spin coupling etc., the analysis of the content, purity, and molecular structure of a sample is possible. The spectrum produced by this process contains a number of peaks; the highs and the positions of these peaks allow the exact analysis. Unknown compounds can be matched against spectral libraries. Even very complex organic compounds as enzymes and proteins can be determined. For the wide uses of NMR spectroscopy (from mineralogy to medicine) there is a variety of different techniques available.
See Spectroscopic Imaging Techniques.

Quick Overview
Please note that there are different common names for this artifact.

A data truncation artifact may occur when the interface between high and low signal intensities is encountered in one imaging plane. The 2D-FT techniques transform the MR signal to spatial intensity image data with frequency and phase information encoding each axis in the plane of the scan. This artifact is found in both frequency and phase axes. Artifactual ripples adjacent to edges in an image or sharp features in a spectrum, caused by omission of higher frequency terms in Fourier transformation, particularly with the use of zero filling to replace unsampled higher frequencies.
Complex shapes are specified by series of sine and cosine waves of various frequencies, phase and amplitude. Some shapes are more difficult to encode than others. The most difficult shapes to represent with Fourier series of terms are waveforms with instantaneous transitions, tissue discontinuities or edges. The low-frequency components of the series describe the overall shape of the step function. Higher frequency components are needed to describe the corners if the step function more accurately. If not enough samples are taken, these areas cannot be accurately represented. The truncation of the infinite data series results in a ringing artifact because of the inability to accurately approximate this tissue discontinuity with a shorter truncated data set. Therefore, the ringing that occurs at all tissue boundaries on MR is called truncation artifact.

This problem can be easily resolved by taking more samples - a higher acquisition matrix and/or a smaller FOV. See Gibbs Artifact and Gibbs Phenomenon.

Undersampling is the decrease in data to increase image acquisition speed (shorter scan times without loss of quality - increased productivity - reduced cost of equipment). There are different strategies to decrease data without losing quality (e.g. reduction of the FOV in one or more spatial directions - RFOV).
Reduction in data normally is associated with an increase in aliasing (degradation of the SNR through backfolding of the entire noise spectrum), or with other artifact caused by missing data, which results in fine lines.

The selective excitation of spins in only a limited region of space. This can be particularly useful for spectroscopy as well as imaging. Spatial localization of the signal source may be achieved through spatially selective excitation and the resulting signal may be analyzed directly for the spectrum corresponding to the excited region. It is usually achieved with selective excitation.
Typically, a single dimension of localization can be achieved with one selective RF excitation pulse (and a magnetic field gradient along a desired direction), while a localized volume (3D) can be excited with a stimulated echo produced with three selective RF pulses whose selective magnetic field gradients are mutually orthogonal, having a common intersection in the desired region. Similar 'crossed plane' excitation can be used with selective 180° refocusing pulses and conventional spin echoes.
A degree of spatial localization of excitation can alternatively be achieved with depth pulses, e.g. when using surface coils for excitation as well as signal detection. An indirect application of selective excitation for volume-selected spectroscopy is to use appropriate combinations of signals acquired after selective inversion of different regions, in order to subtract away the signal from undesired regions.