### 2012 Events:

Note: the linked titles for some events are the presentations speakers provided which can be viewed online or downloaded.

# January 26, 2012: "Quantization Noise" by Prof. Bernard Widrow, Stanford University

**Abstract:** 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".

**Bio:** Bernard Widrow received the S.B., S.M., and Sc.D. degrees in Electrical Engineering from
the Massachusetts Institute of Technology in 1951, 1953, and 1956, respectively. He joined the MIT faculty and
taught there from 1956 to 1959. In 1959, he joined the faculty of Stanford University, where he is Professor of
Electrical Engineering.

He began research on adaptive filters, learning processes, and artificial neural models in 1957. Together with M.E. Hoff, Jr., his first doctoral student at Stanford, he invented the LMS algorithm in the autumn of 1959. Today, this is the most widely used learning algorithm, used in every MODEM in the world. He has continued working on adaptive signal processing, adaptive controls, and neural networks since that time.

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 Signal Processing Society Medal in 1986, the IEEE Neural Networks Pioneer Medal in 1991, the IEEE Millennium Medal in 2000, and the Benjamin Franklin Medal for Engineering from the Franklin Institute of Philadelphia in 2001. He was inducted into the National Academy of Engineering in 1995 and into the Silicon Valley Engineering Council Hall of Fame in 1999.

Dr. Widrow is a past president and member of the Governing Board of the International Neural Network Society. He is associate editor of several journals and is the author of over 125 technical papers and 21 patents. He is co-author of Adaptive Signal Processing and Adaptive Inverse Control, both Prentice-Hall books. A new book, Quantization Noise, was published by Cambridge University Press in June 2008.