Dither
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226186994
2008-07-17T06:17:07Z
Dicklyon
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Reverted 1 edit by [[Special:Contributions/84.27.155.161|84.27.155.161]]; Back to singular die. ([[WP:TW|TW]])
{{otheruses}}
'''Dither''' is an intentionally applied form of [[noise]], used to randomize [[quantization error]], thereby preventing large-scale patterns such as contouring that are more objectionable than uncorrelated noise. Dither is routinely used in processing of both digital audio and digital video data, and is often one of the last stages of audio production to [[compact disc]].
[[Image:Dither def 1788.png|thumb|right|350px|Provincial definition of "to dither" from ''The Rural Economy of Yorkshire: Comprizing the Management of Landed Estates, and the Present Practice of Husbandry in the Agricultural Districts of that County'', by Mr. Marshall (William), Vol. II, London: T. Cadell, 1788.]]
== Origin of the word "dither" ==
[[Image:Didder def 1707.png|right|thumb|250px|The first dictionary definition of "didder," from [[Thomas Blount (lexicographer)|Thomas Blount]], ''Glossographia Anglicana Nova: Or, A Dictionary, Interpreting Such Hard Words of whatever Language, as are at present used in the English Tongue, with their Etymologies, Definitions, &c. Also, The Terms of Divinity, Law, Physick, Mathematics, History, Agriculture, Logick, Metaphysicks, Grammar, Poetry, Musick, Heraldry, Architecture, Painting, War, and all other Arts and Sciences are herein explain'd, from the best Modern Authors, as, Sir Isaac Newton, Dr. Harris, Dr. Gregory, Mr. Lock, Mr. Evelyn, Mr. Dryden, Mr. Blunt, &c.'', London, 1707.]]
<blockquote>
…one of the earliest [applications] of dither came in World War II from Hrant H. Papazian. Airplane bombers used mechanical computers to perform navigation and bomb trajectory calculations. Curiously, these computers (boxes filled with hundreds of gears and cogs) performed more accurately when flying on board the aircraft, and less well on ground. Engineers realized that the vibration from the aircraft reduced the error from sticky moving parts. Instead of moving in short jerks, they moved more continuously. Small vibrating motors were built into the computers, and their vibration was called dither from the Middle English verb "didderen," meaning "to tremble." Today, when you tap a mechanical meter to increase its accuracy, you are applying dither, and modern dictionaries define dither as a highly nervous, confused, or agitated state. In minute quantities, dither successfully makes a digitization system a little more analog in the good sense of the word. – Ken Pohlmann, ''Principles of Digital Audio''<ref>{{cite book | title = Principles of Digital Audio | author = Ken C. Pohlmann | publisher = McGraw-Hill Professional | year = 2005 | ibsn = 0071441565 | url = http://books.google.com/books?id=VZw6z9a03ikC&pg=PA49&dq=didderen+dither+intitle:Principles+intitle:of+intitle:Digital+intitle:Audio&lr=&as_brr=0&ei=yS0bSNDOM4-msgO2u8WJAg&sig=Ivn61B3TyFFY6rlq5SVVRT5V8c4 }}</ref>
</blockquote>
The term dither was published in books on analog computation and control shortly after the war.<ref>{{cite book | title = Ordnance Field Guide: Restricted | author = William C. Farmer | publisher = Military service publishing company | year = 1945 | url = http://books.google.com/books?id=15ffO4UVw8QC&q=dither&pgis=1 }}</ref><ref>{{cite book | title = Electronic Analog Computers: (d-c Analog Computers) | author = Granino Arthur Korn and Theresa M. Korn | publisher = McGraw-Hill | year = 1952 | url = http://books.google.com/books?id=dwsuAAAAIAAJ&q=dither&pgis=1 }}</ref> The concept of dithering to reduce quantization patterns was first applied by Lawrence G. Roberts<ref>{{cite book | title = Data Compression: Techniques and Applications | author = Thomas J. Lynch | publisher = Lifetime Learning Publications | year = 1985 | url = http://books.google.com/books?id=E7EmAAAAMAAJ&q=first+suggested+by+Roberts+in+1962&dq=first+suggested+by+Roberts+in+1962&pgis=1 }}</ref> in his 1961 [[MIT]] master's thesis<ref>Lawrence G. Roberts, ''Picture Coding Using Pseudo-Random Noise'', MIT, S.M. thesis, 1961 [http://www.packet.cc/files/pic-code-noise.html online]</ref> and 1962 article<ref>{{cite journal | title = Picture Coding Using Pseudo-Random Noise | author = Lawrence G. Roberts | journal = IEEE Trans. Information Theory | volume = 8 | issue = 2 | date = February 1962 | pages = 145–154 | url = http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1057702 | format = abstract | doi = 10.1109/TIT.1962.1057702}}</ref> though he did not use the term ''dither''. By 1964 dither was being used in the modern sense described in this article.<ref>{{cite journal | title = Dither Signals and Their Effect on Quantization Noise | author = L. Schuchman | journal = IEEE Trans. Communications | volume = 12 | issue = 4 | date = Dec 1964 | pages = 162–165 | url = http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1088973 | doi = 10.1109/TCOM.1964.1088973 | format = abstract}}</ref>
== Dither in digital processing and waveform analysis ==
Dither most often surfaces in the fields of digital audio and video, where it is applied to rate conversions and (usually optionally) to bit-depth transitions; it is utilized in many different fields where digital processing and analysis is used — especially waveform analysis. These uses include systems using [[digital signal processing]], such as [[digital audio]], [[digital video]], [[digital photography]], [[seismology]], [[radar|RADAR]], [[weather forecasting]] systems and many more.
The premise is that [[quantization]] and re-quantization of digital data yields error. If that error is repeating and ''[[correlation|correlated]]'' to the signal, the error that results is repeating, cyclical, and mathematically determinable. In some fields, especially where the receptor is sensitive to such artifacts, cyclical errors yield undesirable artifacts. In these fields dither results in less determinable artifacts. The field of audio is a primary example of this — the human [[ear]] functions much like a [[Fourier transform]], wherein it hears individual frequencies. The ear is therefore very sensitive to ''[[distortion]],'' or additional frequency content that "colors" the sound differently. The ear is far less sensitive to random noise at all frequencies.
== Digital audio ==
{{main|Quantization (sound processing)}}
In a seminal paper published in the AES Journal, Lipshitz and Vanderkooy pointed out that different noise types, with different probability density functions (PDF's) behave differently when used as dither signals, and suggested optimal levels of dither signal for audio.<ref>S.P. Lipshitz, J. Vanderkooy and R.A. Wannamaker. 1991. Minimally-audible noise shaping. J. Audio Eng. Soc. 39, 836-852. and J. Vanderkooy and S.P. Lipshitz. 1987. Dither in digital audio. J. Audio Eng. Soc. 35, 966-975</ref>
<blockquote>
In an analog system, the signal is ''continuous'', but in a [[PCM]] digital system, the amplitude of the signal out of the digital system is limited to one of a set of fixed values or numbers. This process is called [[quantization]]. Each coded value is a discrete step... if a signal is quantized without using dither, there will be quantization distortion related to the original input signal... In order to prevent this, the signal is "dithered", a process that mathematically removes the harmonics or other highly undesirable distortions entirely, and that replaces it with a constant, fixed noise level.<ref>Mastering Audio: The Art and the Science by [[Bob Katz]], pages 49-50, ISBN 978-0-24-080545-0</ref></blockquote>
The final version of audio that goes onto a [[compact disc]] contains only 16 [[bit]]s per sample, but throughout the production process a greater number of bits are typically used to represent the sample. In the end, the digital data must be resampled to 16 bits for pressing onto a CD and distributing.
There are multiple ways in which one can resample the data to 16 bits. They can, for example, simply lop off the excess bits — called ''truncation.'' They can also ''round'' the excess bits to the nearest value. Each of these methods, however, results in predictable and determinable errors in the result. Take, for example, a waveform that consists of the following values:
1 2 3 4 5 6 7 8
If we reduce our waveform by, say, 20% then we end up with the following values:
0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4
If we truncate these values we end up with the following data:
0 1 2 3 4 4 5 6
If we instead round these values we end up with the following data:
1 2 2 3 4 5 6 6
If any waveform, comprising the original values, were to be processed by multiplying each value by .8, the result would contain errors. A repeating sine wave quantized to the original sample values, for example, would experience the same error every time its supposed value was "3.4" in that the truncated result would be off by .4. Any time the supposed value was "5" the error after processing and truncation would be 0. Therefore, the error amount would change repeatedly as the values change. The result is cyclical behavior in the error, which manifests itself as additional frequency content on the waveform ([[harmonic distortion]]). The ear hears this as [[distortion]], or the presence of additional frequency content.
A plausible solution would be to take the 2 digit number (say, 4.8) and round it one direction or the other. For example, we could round it to 5 one time and then 4 the next time. This would make the long-term average 4.5 instead of 4, so that over the long-term the value is closer to its actual value. This, on the other hand, still results in determinable (though more complicated) error. Every other time the value 4.8 comes up the result is an error of .2, and the other times it is – .8. This still results in repeating, quantifiable error.
Another plausible solution would be to take 4.8 and round it so that the first four times out of five it rounded up to 5, and the fifth time it rounded to 4. This would average out to exactly 4.8 over the long term. Unfortunately, however, it still results in repeatable and determinable errors, and those errors still manifest themselves as distortion to the ear (though [[oversampling]] can reduce this).
This leads to the ''dither'' solution. Rather than predictably rounding up or down in a repeating pattern, what if we rounded up or down in a random pattern? If we came up with a way to randomly toggle our results between 4 and 5 so that 80% of the time it ended up on 5 then we would average 4.8 over the long run but would have random, unrepeating error in the result. This is done through dither.
We calculate a series of random numbers between 0 and .9 (ex: .6, .4, .5, .3, .7, etc.) and we add these random numbers to the results of our equation. Two times out of ten the result will truncate back to 4 (if 0 or .1 are added to 4.8) and the rest of the times it will truncate to 5, but each given situation has a random 20% chance of rounding to 4 or 80% chance of rounding to 5. Over the long haul this will result in results that average to 4.8 and a quantization error that is random — or noise. This "noise" result is less offensive to the ear than the determinable distortion that would result otherwise.
[[Image:plot small.png|center]]
{{-}}
<!-- Image with unknown copyright status removed: [[Image:440Hz0dB10secs16bitsNoDithering_wav.png|right|thumb|Spectrum of a 440Hz sine wave audio signal without dithering]] -->
<!-- Deleted image removed: [[Image:440Hz0dB10secs16bitsDithered wav.png|right|thumb|Spectrum of same signal with TPDF dithering applied]] -->
Audio samples:
{{multi-listen start}}
{{multi-listen item|filename=16bit sine.ogg|title=16-bit sine wave|format=[[Ogg]]}}
{{multi-listen item|filename=6bit sine truncated.ogg|title=truncated to 6 bits|format=[[Ogg]]}}
{{multi-listen item|filename=6bit sine dithered.ogg|title=dithered to 6 bits|format=[[Ogg]]}}
{{multi-listen end}}
==== When to add dither ====
Dither must be added before any quantization or re-quantization process, in order to prevent non-linear behavior (distortion); the lesser the bit depth, the greater the dither must be. The results of the process still yield distortion, but the distortion is of a random nature so its result is effectively noise. Any bit-reduction process should add dither to the waveform before the reduction is performed.
=== Different types of dither ===
'''RPDF''' stands for "Rectangular Probability Density Function," equivalent to a roll of a [[dice|die]]. Any number has the same random [[probability]] of surfacing.
'''TPDF''' stands for "[[Triangular distribution|Triangular Probability Density Function]]," equivalent to a roll of two dice (the sum of two independent samples of RPDF).
'''Gaussian PDF''' is equivalent to a roll of a large number of dice. The relationship of probabilities of results follows a bell-shaped, or [[Gaussian curve]].
'''Colored Dither''' is sometimes mentioned as dither that has been filtered to be different from [[white noise]]. Some dither algorithms use noise that has more energy in the higher frequencies so as to lower the energy in the critical audio band.
'''[[Noise shaping]]''' is not actually dither, but rather a feedback process that has dither within it. It is used for the same purposes.
==== Which dither to use ====
If the signal being dithered is to undergo further processing, then it should be processed with TPDF dither (see paper by J. Vanderkooy and S.P. Lipshitz in references) that has an amplitude of two quantization steps (so that the dither values computed range from, say, – 1 to +1, or 0 to 2). This is the lower power ideal dither, in that it does not introduce noise modulation (constant noise floor) and completely eliminates the harmonic distortion from *quantization*. If colored dither is used at these intermediate processing stages then the frequency content can "bleed" into other, more noticeable frequency ranges and become distractingly audible.
If the signal being dithered is to undergo no further processing — it is being dithered to its final result for distribution — then colored dither or noiseshaping is appropriate, and can effectively lower the audible noise level by putting most of that noise in areas where it is less critical.
== Digital photography and image processing ==
[[Image:Dithering example red blue.png|frame|left|An illustration of dithering. Red and blue are the only colors used, but as the pixels become smaller, the patch appears violet.]]
'''Dithering''' is a technique used in [[computer graphics]] to create the illusion of [[color]] depth in images with a limited [[color palette]] ([[color quantization]]). In a dithered image, colors not available in the palette are approximated by a diffusion of colored [[pixel]]s from within the available palette. The human eye perceives the diffusion as a mixture of the colors within it (see [[color vision]]). Dithering is analogous to the [[halftone]] technique used in [[printing]]. Dithered images, particularly those with relatively few colors, can often be distinguished by a characteristic graininess, or speckled appearance.
=== Dithering examples ===
<div style="float:right; width: 260px; margin: 0 0 1em 1em">
[[Image:Dithering example undithered.png|frame|Figure 1. Original photo; note the smoothness in the detail.]]
[[Image:Dithering example undithered web palette.png|frame|Figure 2. Original image using the web-safe color palette with no dithering applied. Note the large flat areas and loss of detail.]]
[[Image:Dithering example dithered web palette.png|frame|Figure 3. Original image using the web-safe color palette with [[Floyd-Steinberg dithering]]. Note that even though the same palette is used, the application of dithering gives a better representation of the original.]]
[[Image:Dithering example dithered 256color.png|frame|Figure 4. Here, the original has been reduced to a 256-color optimized palette with [[Floyd-Steinberg dithering]] applied. The use of an optimized palette, rather than a fixed palette, allows the result to better represent the colors in the original image.]]
[[Image:Dithering example undithered 16color.png|frame|Figure 5. Depth is reduced to a 16-color optimized palette in this image, with no dithering. Colors appear muted, and color banding is pronounced.]]
[[Image:Dithering example dithered 16color.png|frame|Figure 6. This image also uses the 16-color optimized palette, but the use of dithering helps to reduce banding.]]
</div>
Reducing the color depth of an image can often have significant visual side-effects. If the original image is a photograph, it is likely to have thousands, or even millions of distinct colors. The process of constraining the available colors to a specific ''color palette'' effectively throws away a certain amount of color information.
A number of factors can affect the resulting quality of a color-reduced image. Perhaps most significant is the color palette that will be used in the reduced image. For example, an original image (''Figure 1'') may be reduced to the 216-color "[[Web colors#Web-safe colors|web-safe]]" color palette. If the original pixel colors are simply translated into the closest available color from the palette, no dithering occurs (''Figure 2''). Typically, this approach results in flat areas (contours) and a loss of detail, and may produce patches of color that are significantly different from the original. Shaded or gradient areas may appear as ''color bands'', which may be distracting. The application of dithering can help to minimize such visual artifacts, and usually results in a better representation of the original (''Figure 3''). Dithering helps to reduce [[color banding]] and flatness.
One of the problems associated with using a fixed color palette is that many of the needed colors may not be available in the palette, and many of the available colors may not be needed; a fixed palette containing mostly shades of green would not be well-suited for images that do not contain many shades of green, for instance. The use of an optimized color palette can be of benefit in such cases. An optimized color palette is one in which the available colors are chosen based on how frequently they are used in the original source image. If the image is reduced based on an optimized palette, the result is often much closer to the original (''Figure 4'').
The number of colors available in the palette is also a contributing factor. If, for example, the palette is limited to only 16 colors, the resulting image could suffer from additional loss of detail, and even more pronounced problems with flatness and color banding (''Figure 5''). Once again, dithering can help to minimize such artifacts (''Figure 6'').
=== Applications ===
Display hardware, including early computer [[graphics card|video adapters]] and many modern [[Liquid crystal display|LCDs]] used in [[mobile phone]]s and inexpensive [[digital camera]]s, are only capable of showing a smaller color range than more advanced displays. One common application of dithering is to more accurately display graphics containing a greater range of colors than the hardware is capable of showing. For example, dithering might be used in order to display a photographic image containing [[truecolor|millions of colors]] on video hardware that is only capable of showing 256 colors at a time. The 256 available colors would be used to generate a dithered approximation of the original image. Without dithering, the colors in the original image might simply be "rounded off" to the closest available color, resulting in a new image that is a poor representation of the original. Dithering takes advantage of the human eye's tendency to "mix" two colors in close proximity to one another.
Some LCDs may use '''[[temporal dithering]]''' to achieve a similar effect. By alternating each pixel's color value rapidly between two approximate colors in the panel's color space (also known as [[frame rate control]]), a display panel which natively supports 18-bit color (6 bits per channel) can represent a 24-bit "true" color image (8 bits per channel).<ref>6-Bit vs. 8-Bit....PVA/MVA vs. TN+Film
Are Things Changing? [http://www.tftcentral.co.uk/articles/6bit_8bit.htm]</ref>
Dithering such as this, in which the computer's display hardware is the primary limitation on [[color depth]], is commonly employed in software such as [[web browser]]s. Since a web browser may be retrieving graphical elements from an external source, it may be necessary for the browser to perform dithering on images with too many colors for the available display. It was due to problems with dithering that a color palette known as the "[[Web colors#Web-safe colors|web-safe color palette]]" was identified, for use in choosing colors that would not be dithered on displays with only 256 colors available.
But even when the total number of available colors in the display hardware is high enough when rendering full color digital photographs, as those 15- and 16-bit RGB [[Highcolor|Hicolor]] 32,768/65,536 color modes, banding can be evident to the eye, especially in large areas of smooth shade transitions (although the original image file has no banding at all). Dithering the 32 or 64 RGB levels will result in a pretty good "pseudo [[truecolor]]" display approximation, which the eye cannot resolve as ''grainy''. Furthermore, images displayed on 24-bit RGB hardware (8 bits per RGB primary) can be dithered to simulate somewhat higher bit depth, and/or to minimize the loss of hues available after a [[gamma correction]]. High-end still image processing software, as [[Adobe Photoshop]], commonly uses these techniques for improved display.
Another useful application of dithering is for situations in which the [[graphics file format|graphic file format]] is the limiting factor. In particular, the commonly-used [[GIF]] format is restricted to the use of 256 or fewer colors in many graphics editing programs. Images in other file formats, such as [[Portable Network Graphics|PNG]], may also have such a restriction imposed on them for the sake of a reduction in file size. Images such as these have a fixed color palette defining all the colors that the image may use. For such situations, [[bitmap graphics editor|graphical editing software]] may be responsible for dithering images prior to saving them in such restrictive formats.
<div style="clear: right" ></div>
=== Dithering algorithms ===
There are several [[algorithm]]s designed to perform dithering. One of the earliest, and still one of the most popular, is the [[Floyd-Steinberg dithering]] algorithm, developed in [[1975]]. One of the strengths of this algorithm is that it minimizes visual artifacts through an [[Error diffusion|error-diffusion]] process; error-diffusion algorithms typically produce images that more closely represent the original than simpler dithering algorithms.<ref name=dhalf>{{cite web
|url = http://www.efg2.com/Lab/Library/ImageProcessing/DHALF.TXT
|title = Digital Halftoning
|accessdate = 2007-09-10
|last = Crocker
|first = Lee Daniel
|authorlink = Lee Daniel Crocker
|coauthors = Boulay, Paul & Morra, Mike
|date = [[1991-06-20]]
|work = Computer Lab and Reference Library
}} ''Note: this article contains a minor mistake: “(To fully reproduce our 256-level image, we would need to use an''
'''8x8''' ''pattern.)” The bold part should read “16x16”.''</ref>
Dithering methods include:
* Thresholding (also average dithering<ref>{{cite web
|url = http://www.visgraf.impa.br/Courses/ip00/proj/Dithering1/
|title = Average Dithering
|accessdate = 2007-09-10
|last = Silva
|first = Aristófanes Correia
|coauthors = Lucena, Paula Salgado & Figuerola, Wilfredo Blanco
|date = [[2000-12-13]]
|work = Image Based Artistic Dithering
|publisher = Visgraf Lab
}}</ref>): each pixel value is compared against a fixed threshold. This may be the simplest dithering algorithm there is, but it results in immense loss of detail and contouring.<ref name=dhalf />
* Random dithering was the first attempt (at least as early as 1951) to remedy the drawbacks of thresholding. Each pixel value is compared against a random threshold, resulting in a staticky image. Although this method doesn't generate patterned artifacts, the noise tends to swamp the detail of the image.<ref name=dhalf />
* [[Ordered dithering]]: dithers using a fixed pattern. For every pixel in the image the value of the pattern at the corresponding location is used as a threshold. Different patterns can generate completely different dithering effects.
**[[Halftone]] dithering looks similar to halftone screening in newspapers. This is a form of clustered dithering, in that dots tend to cluster together. This can help hide the adverse effects of blurry pixels found on some older output devices.
**[[Bayer dithering]] produces a cross-hatch pattern. This is a form of dispersed dithering. Because the dots don't cluster, the result looks much less grainy.<ref name=dhalf />
{|
!(Original)
!Threshold
!Random
!Halftone
!Bayer
|-
|[[Image:Michelangelo's David - 63 grijswaarden.png]]
|[[Image:Michelangelo's David - drempel.png]]
|[[Image:Michelangelo's David - ruis.png]]
|[[Image:Michelangelo's David - halftoon.png]]
|[[Image:Michelangelo's David - Bayer.png]]
|}
* [[Error diffusion|Error-diffusion]] dithering: diffuses the quantization error to neighbouring pixels.
**[[Floyd-Steinberg dithering]] only diffuses the error to neighbouring pixels. This results in very fine-grained dithering.
**[[Jarvis, Judice, and Ninke dithering]] diffuses the error also to pixels one step further away. The dithering is coarser, but has less visual artifacts. It is much slower than [[Floyd-Steinberg dithering]].
**[[Stucki dithering]] is based on the above, but is slightly faster. Its output tends to be clean and sharp.
**[[Burkes dithering]] is a simplified form of Stucki dithering that is faster, but less clean than Stucki dithering.
**Scolorq is an experimental spatial [[color quantization]] algorithm that combines color quantization and dithering to produce an optimal image. Because of this nature, the example image shown below is not strictly black&white, but has two gray tones instead. <ref>See [[color quantization]] for a description of Spatial color quantization algorithm (scolorq). The website which describes it in more detail is at [http://www.moonflare.com/code/scolorq/].</ref>
{|
!Floyd-Steinberg
!Jarvis, Judice & Ninke
!Stucki
!Burkes
!Scolorq
|-
|[[Image:Michelangelo's David - Floyd-Steinberg.png]]
|[[Image:Michelangelo's David - Jarvis, Judice & Ninke.png]]
|[[Image:Michelangelo's David - Stucki.png]]
|[[Image:Michelangelo's David - Burkes.png]]
|[[Image:Michelangelo's David - Scolorq.png]]
|}
* Error-diffusion dithering (continued):
**[[Sierra dithering]] is based on Jarvis dithering, but it's faster while giving similar results.
**Two-row Sierra is the above method modified by Sierra to improve its speed.
**Filter Lite is an algorithm by Sierra that is much simpler and faster than Floyd-Steinberg, while still yielding similar (according to Sierra, better) results.
**[[Atkinson dithering]] resembles Jarvis dithering and Sierra dithering, but it's faster. Another difference is that it doesn't diffuse the entire quantization error, but only three quarters. It tends to preserve detail well, but very light and dark areas may appear blown out.
***[http://www.tinrocket.com/software/hyperdither/ History]
***[http://verlagmartinkoch.at/software/dither/index.html Algorithm]
**[[Riemersma dithering]] [http://www.compuphase.com/riemer.htm]
***[[Hilbert-Peano dithering]] is a [http://www.imagemagick.org/Usage/quantize/#dither_error variant] of Riemersma dithering, used by [[Imagemagick]]. <ref>Imagemagick source code, file magick/quantize.c, and online manual which mentions the dithering method by name: [http://www.imagemagick.org/script/command-line-options.php]</ref>
**Even toned screening is a patented modification of Floyd-Steinberg dithering intended to reduce visual artifacts, in particular to produce more even dot patterns in highlights and shadows. [http://www.artofcode.com/eventone/]
{|
!Sierra
!Two-row Sierra
!Filter Lite
!Atkinson
!Hilbert-Peano
|-
|[[Image:Michelangelo's David - Sierra.png]]
|[[Image:Michelangelo's David - tweerijig Sierra.png]]
|[[Image:Michelangelo's David - Sierra's Filter Lite.png]]
|[[Image:Michelangelo's David - Atkinson.png]]
|[[Image:Michelangelo's David - Hilbert-Peano.png]]
|}
== Dithering in optical fiber systems ==
Stimulated [[Brillouin scattering|Brillouin Scattering]] (SBS) is a [[Nonlinear optics|nonlinear optical effect]] that limits the launched optical power in [[fiber optic]] systems. This power limit can be increased by dithering the transmit optical center frequency, typically implemented by modulating the laser's bias input.
== References ==
<references/>
More recent research in the field of dither for audio was done by Lipshitz, Vanderkooy, and Wannamaker at the [[University of Waterloo]].[http://audiolab.uwaterloo.ca/stan.htm]
== See also ==
* [[Digital audio]]
* [[Quantization (signal processing)]]
* [[Anti-aliasing]]
== External links ==
*[http://www.prosoundweb.com/studyhall/rane/dd/dd2.php "Dither - Not All Noise Is Bad"]
*[http://www.hifi-writer.com/he/dvdaudio/dither.htm What is Dither?] Article previously published in ''Australian HI-FI'' with visual examples of how audio dither sharply reduces high order harmonic distortion.
Other well-written papers on the subject at a more elementary level are available by:
*Aldrich, Nika. "[http://www.users.qwest.net/%7Evolt42/cadenzarecording/DitherExplained.pdf Dither Explained (pdf)]"
*Katz, Bob. [http://www.digido.com/portal/pmodule_id=11/pmdmode=fullscreen/pageadder_page_id=27/ The Secrets of Dither]"
Both Nika Aldrich and [[Bob Katz]] are esteemed experts in the field of digital audio and have books available as well, each of which are far more comprehensive in their explanations:
*Aldrich, Nika. "[http://www.cadenzarecording.com Digital Audio Explained]"
*Katz, Bob. "[http://www.digido.com/portal/pmodule_id=11/pmdmode=fullscreen/pageadder_page_id=66/?PHPSESSID=62e494f55b80063f2bf090bf60c0253b Mastering Audio]"
*[http://www.vibrationdata.com/Newsletters/May2006_NL.pdf Dither Vibration Example]
[[Category:Audio engineering]]
[[Category:Digital signal processing]]
[[Category:Computer graphic artifacts]]
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