Editing Quantization (signal processing) (section)

===Additive noise model===
A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of additive [[white noise]] – having negligible correlation with the signal and an approximately flat [[power spectral density]].<ref name=Bennett/><ref name=GrayNeuhoff/><ref name=Widrow1>{{cite journal | last=Widrow | first=B. |author-link=Bernard Widrow| title=A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory | journal=IRE Transactions on Circuit Theory | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=3 | issue=4 | year=1956 | issn=0096-2007 | doi=10.1109/tct.1956.1086334 | pages=266–276| hdl=1721.1/12139 | s2cid=16777461 | hdl-access=free }}</ref><ref name=Widrow2>[[Bernard Widrow]], "[http://www-isl.stanford.edu/~widrow/papers/j1961statisticalanalysis.pdf Statistical analysis of amplitude quantized sampled data systems]", ''Trans. AIEE Pt. II: Appl. Ind.'', Vol. 79, pp. 555–568, Jan. 1961.</ref> The additive noise model is commonly used for the analysis of quantization error effects in digital filtering systems, and it can be very useful in such analysis. It has been shown to be a valid model in cases of high-resolution quantization (small <math>\Delta</math> relative to the signal strength) with smooth PDFs.<ref name=Bennett/><ref name=MarcoNeuhoff>{{cite journal | last1=Marco | first1=D. | last2=Neuhoff | first2=D.L. | title=The Validity of the Additive Noise Model for Uniform Scalar Quantizers | journal=IEEE Transactions on Information Theory | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=51 | issue=5 | year=2005 | issn=0018-9448 | doi=10.1109/tit.2005.846397 | pages=1739–1755| s2cid=14819261 }}</ref>

Additive noise behavior is not always a valid assumption. Quantization error (for quantizers defined as described here) is deterministically related to the signal and not entirely independent of it. Thus, periodic signals can create periodic quantization noise.  And in some cases, it can even cause [[limit cycle]]s to appear in digital signal processing systems. One way to ensure effective independence of the quantization error from the source signal is to perform ''[[dither]]ed quantization'' (sometimes with ''[[noise shaping]]''), which involves adding random (or [[pseudo-random]]) noise to the signal prior to quantization.<ref name=GrayNeuhoff/><ref name=Widrow2/>