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Dither is routinely used in processing of both digital audio and video data, and is often one of the last stages of mastering audio to a CD.

A common use of dither is converting a greyscale image to black and white, such that the density of black dots in the new image approximates the average grey level in the original.

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.

In minute quantities, dither successfully makes a digitization system a little more analog in the good sense of the word. The term dither was published in books on analog computation and hydraulically controlled guns shortly after World War II.

Dither is utilized in many different fields where digital processing and analysis are used. These uses include systems using digital signal processing , such as digital audio , digital video , digital photography , seismology , radar and weather forecasting systems.

If that error is correlated to the signal, the result is potentially cyclical or predictable. In some fields, especially where the receptor is sensitive to such artifacts, cyclical errors yield undesirable artifacts.

In these fields introducing dither converts the error to random noise. The field of audio is a primary example of this.

The human ear functions much like a Fourier transform , wherein it hears individual frequencies. 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 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.

The final version of audio that goes onto a compact disc contains only 16 bits 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 reduced to 16 bits for pressing onto a CD and distributing. There are multiple ways to do this. One can, for example, simply discard the excess bits — called truncation.

One can also round the excess bits to the nearest value. Each of these methods, however, results in predictable and determinable errors in the result.

Using dither replaces these errors with a constant, fixed noise level. Take, for example, a waveform that consists of the following values:.

Take for example a sine wave that, for some portion, matches the values above. It is precisely this error which manifests itself as distortion.

What the ear hears as distortion is the additional content at discrete frequencies created by the regular and repeated quantization error.

A plausible solution would be to take the 2 digit number say, 4. For example, it could be rounded to 5 one time and then 4 the next time. This would make the long-term average 4.

This, on the other hand, still results in determinable though more complicated error. Every other time the value 4. This still results in a repeating, quantifiable error.

Another plausible solution would be to take 4. This would average out to exactly 4. 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, it is possible to round up or down in a random pattern.

If a series of random numbers between 0. Over the long haul this will result in results that average to 4. This "noise" result is less offensive to the ear than the determinable distortion that would result otherwise.

Dither should be added to any low-amplitude or highly periodic signal before any quantization or re-quantization process, in order to de-correlate the quantization noise from the input signal and to prevent non-linear behavior distortion ; the lesser the bit depth, the greater the dither must be.

The result of the process still yields distortion, but the distortion is of a random nature so the resulting noise is, effectively, de-correlated from the intended signal.

Any bit-reduction process should add dither to the waveform before the reduction is performed. In a seminal paper published in the AES Journal, Lipshitz and Vanderkooy pointed out that different noise types, with different probability density functions PDFs behave differently when used as dither signals, and suggested optimal levels of dither signal for audio.

Dither can be useful to break up periodic limit cycles , which are a common problem in digital filters. Random noise is typically less objectionable than the harmonic tones produced by limit cycles.

Any number has the same random probability of surfacing. 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 , typical of dither generated by analog sources such as microphone preamplifiers.

If the bit depth of a recording is sufficiently great, that preamplifier noise will be sufficient to dither the recording. 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 a filtering process that shapes the spectral energy of quantisation error, typically to either de-emphasise frequencies to which the ear is most sensitive or separate the signal and noise bands completely.

If dither is used, its final spectrum depends on whether it is added inside or outside the feedback loop of the noise shaper: In this case, the final noise floor is the sum of the flat dither spectrum and the shaped quantisation noise.

While real-world noise shaping usually includes in-loop dithering, it is also possible to use it without adding dither at all, in which case the usual harmonic-distortion effects still appear at low signal levels.

If a colored dither is used instead at these intermediate processing stages, then frequency content may "bleed" into other frequency ranges that are more noticeable, which could become distractingly audible.

If the signal being dithered is to undergo no further processing — if it is being dithered to its final result for distribution — then a "colored" dither or noise shaping is appropriate.

This can effectively lower the audible noise level, by putting most of that noise in a frequency range where it is less critical. Dithering is used in computer graphics to create the illusion of " color depth" in images with a limited color palette - a technique also known as color quantization.

In a dithered image, colors that are not available in the palette are approximated by a diffusion of colored pixels from within the available palette.

The human eye perceives the diffusion as a mixture of the colors within it see color vision. Dithered images, particularly those with relatively few colors, can often be distinguished by a characteristic graininess or speckled appearance.

By its nature, dithering introduces pattern into an image - the theory being that the image will be viewed from such a distance that the pattern is not discernible to the human eye.

Unfortunately this is often not the case, and often the patterning is visible - for example, often with images found on the web.

In these circumstances it has been shown that a blue noise dither pattern is the least unsightly and distracting. However, other techniques such as ordered dithering can also generate blue noise dithering without the tendency to degenerate into areas with artifacts.

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 color " web-safe " color palette.

If the original pixel colors are simply translated into the closest available color from the palette, no dithering will occur Figure 2. It has roots in a piece of classical Latin literature from 45 BC, making it over years old.

Richard McClintock, a Latin professor at Hampden-Sydney College in Virginia, looked up one of the more obscure Latin words, consectetur, from a Lorem Ipsum passage, and going through the cites of the word in classical literature, discovered the undoubtable source.

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