Quantizer

A quantizer is a device or algorithm that maps a continuous range of input values to a finite set of output levels. It is a key component of the quantization stage in analog-to-digital and digital-to-analog conversion, converting amplitudes into discrete representations. Quantization introduces an error, known as quantization error, which is the difference between the input and the quantized output.

Quantizers can be categorized by how they operate and by their level spacing. Scalar quantizers process individual samples, while vector quantizers operate on blocks of samples using a codebook of representative levels. Uniform quantizers use evenly spaced levels, typically described by a fixed step size. Nonuniform quantizers use non-equidistant levels to better match the statistical distribution of the input signal, often achieving lower distortion for signals with known statistics. Adaptive or dynamic quantizers adjust their step size in response to the input.

Quantization performance is often described by the quantization error and the signal-to-quantization-noise ratio (SQNR). For a uniform, ideal N-bit quantizer with a full-scale sine input, the SQNR is approximately 6.02N + 1.76 dB. The quantization error is commonly modeled as a uniform random variable in the range [-Δ/2, Δ/2], where Δ is the quantization step size, yielding a mean squared error of Δ^2/12. Dithering can be applied to decorrelate quantization noise from the signal.

Practical implementations include analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). ADC architectures include flash, successive-approximation register (SAR), pipeline, and sigma-delta (ΔΣ) designs; sigma-delta quantizers use oversampling and noise shaping to improve resolution for audio. Nonuniform quantization commonly employs companding (μ-law or A-law) to compress dynamic range before quantization. Vector quantization uses a learned codebook for efficient representation in compression tasks.