In reality, any microphone systems or other sensors used to detect sound pressure changes (and hence used to record music, speech, etc), will also pick up and create themselves some random noise. By ‘noise’ here I don’t mean interference like someone whistling in another room, or using a drill in an nearby studio, I mean that the air molecules will be rattling about with random thermal movements, and that the electrons in wires also rattle about in similar random ways. This noise level may be quite small, but its effect is very important. The amount of information (how much detail, etc) in a real analog signal contains is always finite, and limited by the amount of noise that is always present. The formal details of this are laid out in the papers published by Claude Shannon and others, and repeated in many textbooks on this topic.

The quantisation problem we described earlier comes from the perfect regularity of the series of bands and how these affect our waveform. We assumed the waveform was a perfect sinewave with no noise or other contributions. Yet in reality any sound measurement will have random noise covering or fogging the tiniest details. Since noise varies unpredictably the effect varies from one sample to another in a random way, breaking up the statistical regularity of the quantisation. This limits how precisely we can make a meaningful measurement or take a sample. It also has another quite remarkable and surprising effect that turns out to be very useful.

This result arises because the added noise breaks up the tendency for every sinewave cycle to be distorted into exactly the same (incorrect) shape as all its neighbours. A regular and repetitive distortion is replaced by a noise background. When we record signals which come with a natural noise level that is larger than the step between bands (quantisation level) of the sampling process then we may not have to deliberately add any noise. However when the signal is almost free of noise we end up with the curious result that deliberately adding some noise can improve the results by removing the unwanted distortion.

The deliberate addition of a random (or pseudo-random) pattern to achieve this effect is called ‘dithering’. Although I am not trying to cover all the details here, this technique can be applied in various ways, but the simplest to understand is just to ensure we have some ‘noise’ along with the signal, and make sure the noise is big enough to waggle up and down over at least a couple of bands between sample values. In some cases this pseudo-random addition is deliberately modified in response to the signal as it arrives and/or is designed to produce a sequence of sample values signal whose noise spectrum is not uniform but has lower noise at the frequencies where human hearing is most sensitive. These methods are often called ‘noise shaping’. Hence in many cases the techniques used to remove distortion and minimise the audibility of the resulting noise are lumped together.

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