For years, rumors have been circulating about quantization noise:
(a) The noise is additive and white and uncorrelated with the signal being quantized, and
(b) The noise is uniformly distributed between plus and minus half a quanta, having zero mean and a mean square of one twelveth the square of a quanta.

Yet, simple reasoning tells another story:
(a) The noise is related to the signal being quantized,
(b) The probability distribution of the noise depends on the probability distribution of the signal being quantized, and
(c) The noise will be correlated over time if the signal being quantized is correlated over time. 

In spite of the simple reasoning, the rumors turn out to be true when quantizing theorems, analogous to the well known sampling theorem, are satisfied. Quantization, a nonlinear process, can be analyzed by linear sampling theory applied to the probability density distribution of the signal being quantized. In practice, the quantizing theorems are almost never perfectly satisfied (by analogy, signals are almost never perfectly band-limited so the sampling theorem is almost never perfectly satisfied). However, the rumors about quantization noise turn out to be extremely close to being true for a wide practical range of signal characteristics.  

When the rumors are true, signal processing, communication, and control systems containing nonlinear quantization behave like noisy linear systems and are easy to analyze. The original theory was developed by B. Widrow in his 1956 MIT doctoral thesis, applied to fixed-point (uniform) quantization. The theory was extended by Widrow and I. Kollar in the 1990's to apply to floating-point quantization. Their work on these subjects was published in a Cambridge University Press book in 2008 entitled "Quantization Noise".

Dr. Bernard Widrow (M'56, SM'70, F'76, LF’06) received from MIT the S.B. degree in 1951, the S.M. degree in 1953, and the Sc.D. degree in 1956, all in electrical engineering. At MIT from 1956 -1959, he taught classes in digital signal processing and started research in what was to become the field of adaptive signal processing. In 1959, he joined the faculty at Stanford University.

At Stanford, he introduced graduate courses in digital signal processing, adaptive signal processing, and artificial neural networks. During his 50 years at Stanford, he was the principal advisor to 85 Ph.D. students. His students have become workers in industry, founders of companies, professors, deans, provosts, medical doctors, and admirals in the U.S. Navy.

In 1959, together with his first Ph.D. student, M.E. Hoff, Jr., he invented the LMS algorithm (least mean square), still considered to be the world's most widely used learning algorithm. It is used in all modems for channel equalization and echo cancelling. It is one of the key technologies that make the internet possible. LMS is used in adaptive neural networks, controls, noise cancelling, antenna arrays, speech recognition, face recognition, devices for the hearing impaired, and in other medical applications.

This research has led to several hundred journal publications, twenty patents, and four books. One of his papers, "Adaptive Antenna Systems", published in December 1967 in the Proceedings of the IEEE, became a citation classic. His four  books are B.Widrow and S.D.Stearns, "Adaptive Signal Processing", Prentice-Hall, 1985; B.Widrow and E.Walach, "Adaptive Inverse Control", Prentice-Hall, 1996; S. Haykin and B.Widrow, eds.,"Least-Mean-Square Adaptive Filters", Wiley-Interscience, 2003; B.Widrow and I.Kollar,"Quantization Noise", Cambridge University Press, 2008.

Dr. Widrow is a Life Fellow of the IEEE and a Fellow of AAAS. He received the IEEE Centennial Medal in 1984, the IEEE Alexander Graham Bell Medal in 1986, the IEEE Neural Networks Pioneer Medal in 1991, the IEEE Signal Processing Society Medal in 1998, the IEEE Millennium Medal in 2000, and the Benjamin Franklin Medal from the Franklin Institute in 2001. He was inducted into the National Academy of Engineering in 1995, and into the Silicon Valley Engineering Hall of Fame in 1999. He is currently Chairman of the Santa Clara Valley Chapter of the IEEE Computational Intelligence Society. 

http://www-isl.stanford.edu/~widrow/

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Sponsored by the Santa Clara Valley Chapters of the IEEE Computational Intelligence Society, IEEE Control Systems Society, and IEEE Signal Processing Society.