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.

In terms of the time domain, the cause of this type of ringing is the ripples in the sinc function,[1] which is the impulse response (time domain representation) of a perfect low-pass filter.

One may distinguish overshoot (and undershoot), which occurs when transitions are accentuated – the output is higher than the input – from ringing, where after an overshoot, the signal overcorrects and is now below the target value; these phenomena often occur together, and are thus often conflated and jointly referred to as "ringing".

This occurs most severely when the impulse response or step response of a filter has oscillations – less formally, if for a spike input, respectively a step input (a sharp transition), the output has bumps.

Ringing is closely related to overshoot and undershoot, which is when the output takes on values higher than the maximum (respectively, lower than the minimum) input value: one can have one without the other, but in important cases, such as a low-pass filter, one first has overshoot, then the response bounces back below the steady-state level, causing the first ring, and then oscillates back and forth above and below the steady-state level.

If one has a linear time invariant (LTI) filter, then one can understand the filter and ringing in terms of the impulse response (the time domain view), or in terms of its Fourier transform, the frequency response (the frequency domain view).

These ringing artifacts are not results of imperfect implementation or windowing: the ideal low-pass filter, while possessing the desired frequency response, necessarily causes ringing artifacts in the time domain.

Thus the basic solution from the time domain perspective is to use filters with nonnegative impulse response.

On the other hand, if the cause is a band-limited signal, as in JPEG, one cannot simply replace a filter, and ringing artifacts may prove hard to fix – they are present in JPEG 2000 and many audio compression codecs (in the form of pre-echo), as discussed in the examples.

In the time domain, the cause is an impulse response that oscillates, assuming negative values.

This can be resolved by using a filter whose impulse response is non-negative and does not oscillate, but shares desired traits.

However, it is not as good as a low-pass filter: it rolls off in the passband, and leaks in the stopband: in image terms, a Gaussian filter "blurs" the signal, which reflects the attenuation of desired higher frequency signals in the passband.

Flat response in the passband is desirable, so one windows with functions whose Fourier transform has fewer oscillations, so the frequency domain behavior is better.

[6] In the frequency domain, the cause can be interpreted as due to the sharp (brick-wall) cut-off, and ringing reduced by using a filter with smoother roll-off.

Thus, among these the, first-order filter rolls off slowest, and hence exhibits the fewest time domain artifacts, but leaks the most in the stopband, while as order increases, the leakage decreases, but artifacts increase.

[4] While ringing artifacts are generally considered undesirable, the initial overshoot (haloing) at transitions increases acutance (apparent sharpness) by increasing the derivative across the transition, and thus can be considered as an enhancement.

[8] Another artifact is overshoot (and undershoot), which manifests itself not as rings, but as an increased jump at the transition.

If the signal is bounded, for instance an 8-bit or 16-bit integer, this overshoot and undershoot can exceed the range of permissible values, thus causing clipping.

Clipping can also occur for unrelated reasons, from a signal simply exceeding the range of a channel.

Some modern JPEG codecs, such as mozjpeg and ISO libjpeg, use such a trick to reduce ringing by deliberately causing overshoots in the IDCT results.

JPEG compression can introduce ringing artifacts at sharp transitions, which are particularly visible in text.

This is a due to loss of high frequency components, as in step response ringing.

In cases where these cause circular artifacts around point sources, these may be referred to as "rings" due to the round shape (formally, an annulus), which is unrelated to the "ringing" (oscillatory decay) frequency phenomenon discussed on this page.

[4] Many special functions exhibit oscillatory decay, and thus convolving with such a function yields ringing in the output; one may consider these ringing, or restrict the term to unintended artifacts in frequency domain signal processing.

Fraunhofer diffraction yields the Airy disk as point spread function, which has a ringing pattern.

In cameras, a combination of defocus and spherical aberration can yield circular artifacts ("ring" patterns).

However, the pattern of these artifacts need not be similar to ringing (as discussed on this page) – they may exhibit oscillatory decay (circles of decreasing intensity), or other intensity patterns, such as a single bright band.

Visual illusions can occur at transitions, as in Mach bands, which perceptually exhibit a similar undershoot/overshoot to the Gibbs phenomenon.