Science, Maths & Technology

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# 3.3 Quantisation

The sample values measured during sampling must be quantised to produce a digital representation of the analogue signal. That is, each value is approximated to its nearest quantisation level. Quantisation levels are pre-determined levels, like the rungs of a ladder, between the lowest possible sample value and the highest. The closeness of the approximation between a sample value and its nearest quantisation level depends on the number of quantisation levels available. For example, using a thousand levels involves less approximation than using a hundred levels.

Each quantisation level is represented by a unique binary number. The number of levels is therefore related to the number of bits, n, used in the binary numbers that represent the quantisation levels. For example, using 3 bits provides eight (23) discrete levels represented by: 000, 001, 010, …, 111. Eight bits and twelve bits will quantise the signal into 256 (28) and 4096 (212) levels respectively. In general, an n-bit analogue-to-digital converter (ADC) provides 2n quantisation levels.

## Activity 3.2 Self assessment

Compact disc audio uses 16-bit quantisation.

• a.How many quantisation levels are there?
• b.One quantisation level is designated as zero. Can there be equal numbers of levels for positive and negative values?