Parts of the body, which extend beyond the Field of view in the phase encoding direction may still be visible in the image as artifacts.
Please note that aliasing in the frequency direction is also possible but can be eliminated in the same manner or by applying frequency specific filters to the received signal.

See Aliasing Artifact.

Conversion of the analog signal to a series of digital values by measurement at a set of particular times; this utilizes the analog to digital converter. If the rate of sampling is less than twice the highest frequency in the signal, aliasing will occur. The duration of sampling determines how small a difference of frequencies can be separated.

See also Aliasing.

A wrap around artifact (also called backfolding artifact or aliasing artifact) is produced by inadequate sampling or digitization. Wrap around artifacts result from digitizing fewer than two samples per period in a periodic function. Aliasing can occur in MR imaging whenever the scanned area extends beyond the field of view. These areas extending beyond the field of view boundaries are aliased back into the image to appear at artifactual locations.

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

Backfolding always occurs due to wrong phase encoding caused by objects outside the planned FOV. Phase encoding gradients are scaled for the field of view only. Tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image. The Backfolding artifact projects image contents which fall outside the imaging FOV back into the image; the back folded information thus reappearing on the other side of the image. In fact, information along the phase encoding direction can be viewed as projected onto a cylindrical screen with a circumference corresponding to the linear field of view dimension in the phase encoding direction.

See also Aliasing Artifact.

Filtering is any process that alters the relative frequency content. This can be done with an analog (conventional electrical) filter, e.g. to remove higher frequency components so as to avoid aliasing in digitizing. Filtering can be carried out numerically on the digitized data. Raw data can be filtered prior to the image calculation. The Hanning filter is provided with various weightings, e.g. for the reduction of edge oscillation.