Quantization

Quantization is the property of being constrained to a set of discrete values, rather than varying continuously.

Quantisation (in digital signal processing) refers to the process of approximating a continuous signal by a set of discrete symbols or integer values. In general, a quantization operator can be represented as

Q(x) = round(f(x))

where x is a real number, Q(x) an integer, and f(x) is an arbitrary real-valued function that controls the 'quantization law' of the particular coder.

For example, in digital telephony, two popular quantization schemes are the 'A-law' and 'µ-law', each mapping an analog signal to an integer value represented by an 8-bit binary number, but each with a different function f.

See also:

• information theory
• rate distortion theory

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Quantization is also used, in quantum physics to describe the process by which a physical system exhibits quantized behavior, rather than continuous, or 'classical' behavior.

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In music software, quantization is the altering of the times and durations of notes so they fit the beat or subbeat perfectly.