Quantization maps a continuum of possible amplitudes to a finite set of representation levels.

For a uniform quantizer with step size $\Delta$, values within one interval are mapped to the same output level. The quantization error is

$$e_q=x-Q(x),$$

where $Q(x)$ is the quantized value.

Away from overload, a rounding quantizer has approximately

$$|e_q|\le \frac{\Delta}{2}.$$

Using more levels reduces the step size over a fixed input range and therefore reduces typical quantization error, but increases the amount of information needed to identify the selected level.

If the input exceeds the representable range, overload or clipping occurs and the error can be much larger than one quantization step.

Quantization makes amplitude discrete. Sampling instead makes the independent time variable discrete. A digital representation of an analog waveform commonly applies both operations.