# Glossary definition of 'Dither'

There are many points in a digital audio signal path where precision can be lost. For example, in a digital transfer from 24-bits to 16-bits, or in an analogue to digital conversion. In this situation it is not sufficient just to discard low-order bits - this causes truncation distortion, characterised by aharmonic frequency components and unnatural, harsh decays. Instead, it is preferable to use some sort of 'dithering' process, whereby the truncation process is linearized by modulating the signal prior to the truncation, usually by the addition of a small amount of noise.

By adding a random element to the truncation decision, small components as far as 30dB below the noise floor can be accurately represented, and an analogue-like low-signal performance can be realised. This is achieved at the expense of slightly raising of the noise floor, although with some dithering schemes such as noise shaping, linearization can be achieved with no noticeable increase in noise.

How can dithering allow information to be preserved below the least-significant bit? It seems impossible. Consider a simple example where the audio samples are numbers between one and six, and we are going to 'truncate' them (i.e. reduce their resolution) so that numbers from one to three become zero, and those from four to six become one. Clearly much information will be lost, and all excursions of the signal between one and three and between four and six will not affect the output at all. But if we throw a die for each sample, add the number of spots to that sample, and translate totals of six and below to zero and totals of seven and above to one, we have a simple dithering scheme. Input samples of three will be more likely to result in outputs of one than will inputs of one. The throw of the die is our dither noise. Since all the faces of the die have an equal chance of occurring, this is known as 'rectangular probability distribution function' (RPDF) dither, which in fact does not produce perfect linearization. We actually use 'triangular probability distribution function' (TPDF) dither, which is like throwing two dice with a resultant increase in the probability of medium sized numbers - totals of two and twelve occur much less often than seven.