quantisation

Quantisation is the process of mapping a continuous range of values to a finite set of discrete levels. In signal processing, it is part of analog-to-digital conversion, where a sampled signal's amplitudes are rounded to the nearest available level. The result is quantisation error, or noise, whose properties depend on the quantiser design. A uniform quantiser uses evenly spaced levels; non-uniform quantisers allocate levels nonlinearly, as in companding schemes (mu-law, A-law) to better match perceptual sensitivity or dynamic range.

The number of levels is determined by the word length in digital systems, commonly 8, 12, 16, 24 bits, yielding 2^N levels. Quantisation affects dynamic range and resolution; in communications, it limits accuracy and can interact with other distortions. A standard benchmark is that, for a full-scale sine wave, the signal-to-quantisation-noise ratio is approximately 6.02N + 1.76 dB.

In physics, quantisation refers to the discrete nature of certain physical quantities, such as energy levels in atoms, angular momentum, or electric charge, a foundational concept of quantum mechanics. The term can also describe discrete lattices in mathematics or digital systems, where continuous signals or variables are approximated by discrete representatives.

Applications include audio and image encoding, digital communications, and control systems, where quantisation is inevitable in converting analogue signals to digital form. Techniques such as dithering and proper quantiser design help reduce perceptible artefacts and improve linearity.