Page 483 - Invited Paper Session (IPS) - Volume 2

IPS355 Georg Lindgren
theory with the different applications. Many are those who have witnessed
about his kindness and helpfulness, to young PhD students as well as to
established researchers.

3. An overview of his work
Steve Rice published sixty-four scientific papers during his career. In the
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list they are categorized into three groups according to focus: Computation,
mathematics, and statistics; Physics and communication systems; Signal
processing.
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“Mathematical analysis of random noise”, with its 162 pages, belongs to
all three categories. Its significance for radio communication and general
signal processing is obvious – it was written for engineers in an engineering
environment. Rice was quite familiar with the work by Norbert Wiener on
correlation functions, harmonic analysis, and filtering of certain “random”
functions, written as mathematics with electrical engineering applications in
mind. Rice embraced explicitly the idea of a “stationary stochastic process”
as an ensemble of functions with a statistical distribution in the sense of
Khintchine and Cramer. Wiener, as prestigious mathematician, helped to
advocate the statistical´ viewpoint, when he claimed that information is not
only what has been said, but also what might have been said. It has been
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argued that Rice’s “Random noise”, Shannon’s “Information theory”, and
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Wiener’s book on smoothing and prediction, are the three most important
publications from USA during the 1940s to establish the statistical radio
communication theory.
“Mathematical analysis of random noise” has four main parts: (I) on shot
noise, (II) on power spectra and correlation, (III) on the statistical properties
of correlated noise, (IV) on non-linear filters. Part
(II) presented a stationary process as a random Fourier sum, with discrete
spectrum,

() = ∑ cos + sin = ∑ cos( − ), (1)

with random ( , ) and ( , ). In part (III) the discrete spectrum is replaced

by a continuous one and the signal () assumed to be Gaussian.
It took only a decade before the statistical content of parts (I, II, IV) was
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included in advanced textbooks for radio engineers. But what makes Rice’s
random noise paper important for statistics research is part (III), and the
statistics community was slow to recognize its challenges, namely the
statistical properties of the number and location of level crossings by a
stationary process. We will deal with some of these challenges later in this
paper.
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