Quantization

Quantization is the process of mapping a large or continuous set of values to a finite set of discrete levels. In signal processing and digital electronics, quantization typically refers to converting a continuous-time, continuous-amplitude signal into a discrete-time, discrete-amplitude representation as part of analog-to-digital conversion. The result is a staircase approximation of the original signal, with exact values lost within a range determined by the quantization step size.

Quantization involves two related ideas: the number of levels (or bits) and how the levels are spaced. Uniform quantization uses evenly spaced levels over a specified dynamic range, while nonuniform quantization uses uneven spacing to allocate more levels where the signal is more likely to occur (for example, mu-law or A-law companding in audio). The quantization error, or quantization noise, is the difference between the input and its quantized value and is often modeled as a random variable with power inversely related to the number of levels. Dithering adds a controlled amount of noise before quantization to reduce perceptual artifacts.

In digital systems, quantization is paired with sampling. After sampling, an analog-to-digital converter assigns each sample to one of the discrete levels. Quantization limits dynamic range and introduces distortion, but increasing the number of levels reduces error at the cost of larger data size and higher circuit complexity. Techniques such as dithering and noise shaping can improve perceptual quality in audio and other signals.

In physics, quantization denotes the discrete eigenvalues of certain observables, such as energy levels in atoms or the angular momentum of particles, a fundamental consequence of quantum mechanics. Planck's constant sets the scale for these discrete values.