MR imaging techniques in which the image is built up from successive lines through the object. In various schemes, the lines are isolated by oscillating magnetic field gradients or selective excitation, and then the NMR signals from the selected line are encoded for position by detecting the FID or spin echo in the presence of a magnetic field gradient along the line; the Fourier transformation of the detected signal then yields the distribution of emitted NMR signal along the line.

Optional component of the computer system used to perform Fourier transformations to accelerate the processing of the received numerical data relative to the MR imaging process, to speed them up.

Quadrature detection is used in magnetic resonance imaging as well as in Doppler ultrasound and is also called quadrature demodulation or phase quadrature technique.
With this phase sensitive demodulation technique the complex demodulated signal is separated into two components. One is called the real channel; the second part is called the imaginary channel and is located 90° away from the real channel. The signals from both channels are combined to produce a single set of quadrature detected real and imaginary spectra. In MRI, the parts of the demodulated MR signal are further processed by Fourier transformation analysis. All information on the MR signal components e.g. amplitude, phase, and frequency is given by this quadrature detection combined with Fourier analysis.

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.