page_title: Ringing artifacts
section_title: Ringing and ripple
hierarchical_section_title: Ringing artifacts / Related phenomena / Ringing and ripple
context_page_description: In signal processing, particularly digital image processing, ringing artifacts are artifacts that appear as spurious signals near sharp transitions in a signal. Visually, they appear as bands or "ghosts" near edges; audibly, they appear as "echos" near transients, particularly sounds from percussion instruments; most noticeable are the pre-echos. The term "ringing" is because the output signal oscillates at a fading rate around a sharp transition in the input, similar to a bell after being struck. As with other artifacts, their minimization is a criterion in filter design.
context_section_description: In signal processing and related fields, the general phenomenon of time domain oscillation is called ringing, while frequency domain oscillations are generally called ripple, though generally not "rippling".
  A key source of ripple in digital signal processing is the use of window functions: if one takes an infinite impulse response (IIR) filter, such as the sinc filter, and windows it to make it have finite impulse response, as in the window design method, then the frequency response of the resulting filter is the convolution of the frequency response of the IIR filter with the frequency response of the window function. Notably, the frequency response of the rectangular filter is the sinc function (the rectangular function and the sinc function are Fourier dual to each other), and thus truncation of a filter in the time domain corresponds to multiplication by the rectangular filter, thus convolution by the sinc filter in the frequency domain, causing ripple. In symbols, the frequency response of  is  In particular, truncating the sinc function itself yields  in the time domain, and  in the frequency domain, so just as low-pass filtering (truncating in the frequency domain) causes ringing in the time domain, truncating in the time domain (windowing by a rectangular filter) causes ripple in the frequency domain.
caption: Frequency response of a 5th order Chebyshev filter, exhibiting ripple.