Editing Analog-to-digital converter (section)

====Quantization error====
[[File:Conversion AD DA.png|thumb|Analog to digital conversion as shown with fig. 1 and fig. 2]]

Quantization error is introduced by the [[quantization (signal processing)|quantization]] inherent in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The error is nonlinear and signal-dependent. In an ideal ADC, where the quantization error is uniformly distributed between −{{Fraction|1|2}} LSB and +{{Fraction|1|2}} LSB, and the signal has a uniform distribution covering all quantization levels, the [[signal-to-quantization-noise ratio]] (SQNR) is given by

:<math>\mathrm{SQNR} = 20 \log_{10}(2^Q) \approx 6.02 \cdot Q\ \mathrm{dB} \,\!</math><ref>{{cite book|last=Lathi|first=B.P.|title=Modern Digital and Analog Communication Systems|year=1998|publisher=Oxford University Press|edition=3rd}}</ref>

where Q is the number of quantization bits.  For example, for a [[audio bit depth|16-bit]] ADC, the quantization error is 96.3&nbsp;dB below the maximum level.

Quantization error is distributed from DC to the [[Nyquist frequency]]. Consequently, if part of the ADC's bandwidth is not used, as is the case with [[oversampling]], some of the quantization error will occur [[out-of-band]], effectively improving the SQNR for the bandwidth in use.  In an oversampled system, [[noise shaping]] can be used to further increase SQNR by forcing more quantization error out of band.