#research See also: [[Fourier Transform]] # Gibbs Ringing Motivation: Explaining some filtering artifacts Gibbs Ringing, or more generally the Gibbs Phenomenon, is an artifact that occurs due to the nature of mapping an oscillatory function onto a piecewise-continuous function's jump discontinuity. This is most commonly explained using a [[Fourier Transform]] on the boxcar function.  Taking This can be extended into the field of imaging that inolves using a filtering process to create an image. In this process, at discontinuities in an aimge, there may be some general "wave-like" image artifacts. Here are two examples from MRI imaging:   In both images we can observe this light and dark alternative pattern near the boundaries of the image features.