Quantization is the process of mapping input values from a large set (often a continuous set) to output values in a smaller set, often with a finite number of elements). It involves constraining an input from a continuous or otherwise large set of values to a discrete set. Quantization is used in various fields, including mathematics, digital signal processing, physics, computing, and music production).

In digital signal processing, quantization is involved in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding). Quantization also forms the core of essentially all lossy compression algorithms). In physics, quantization refers to the process of constraining an input from a continuous or otherwise large set of values (such as the real numbers) to a discrete set (such as the integers) . In computing, quantization is used in virtual memory compression. In music production, quantizing means moving notes recorded into a MIDI sequencer or DAW in line with the “grid,” which makes a rhythmically imprecise performance end up perfect.

Quantization introduces various sources of error in algorithms, such as rounding errors, underflow or overflow, computational noise, and limit cycles. The difference between an input value and its quantized value is referred to as quantization error). To manage the effects of quantization, one needs to choose the right data types to represent the real-world signals and consider the precision, range, and scaling of the data type used to encode the signal.

In summary, quantization is the process of mapping continuous infinite values to a smaller set of discrete finite values. It is used in various fields and introduces various sources of error in algorithms.