Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. 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 grayscale image to black and white, such that the density of black dots in the new image approximates the average gray level in the original.
Etymology
The term dither was published in books on analog computation and hydraulically controlled guns shortly after World War II. Though he did not use the term dither, the concept of dithering to reduce quantization patterns was first applied by Lawrence G. Roberts in his 1961 MIT master's thesis and 1962 article. By 1964 dither was being used in the modern sense described in this article. The technique was in use at least as early as 1915, though not under the name dither.
In digital processing and waveform analysis
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.
Quantization yields error. 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. The ear is therefore very sensitive to distortion, or additional frequency content, but far less sensitive to additional random noise at all frequencies such as found in a dithered signal.
Digital audio
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.
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, this must be reduced to 16 bits to make the CD.
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.
Examples
Take, for example, a waveform that consists of the following values:
1 2 3 4 5 6 7 8
If the waveform is reduced by 20%, then the following are the new values:
0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4
If these values are truncated it results in the following data:
0 1 2 3 4 4 5 6
If these values are rounded instead it results in the following data:
1 2 2 3 4 5 6 6
For any original waveform, the process of reducing the waveform amplitude by 20% results in regular errors. Take for example a sine wave that, for some portion, matches the values above. Every time the sine wave's value hit 3.2, the truncated result would be off by 0.2, as in the sample data above. Every time the sine wave's value hit 4.0, there would be no error since the truncated result would be off by 0.0, also shown above. The magnitude of this error changes regularly and repeatedly throughout the sine wave's cycle. It is precisely this error that 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.