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# Quantization

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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.

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.

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

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