Athanasios Papoulis /ref> (; 1921 – April 25, 2002) was a
Greek
Greek may refer to:
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group
*Greek language, a branch of the Indo-European language family
**Proto-Greek language, the assumed last common ancestor of all kno ...
-
American
American(s) may refer to:
* American, something of, from, or related to the United States of America, commonly known as the "United States" or "America"
** Americans, citizens and nationals of the United States of America
** American ancestry, p ...
engineer
Engineers, as practitioners of engineering, are professionals who Invention, invent, design, build, maintain and test machines, complex systems, structures, gadgets and materials. They aim to fulfill functional objectives and requirements while ...
and applied
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
.
Life
Papoulis was born in modern day
Turkey
Turkey, officially the Republic of Türkiye, is a country mainly located in Anatolia in West Asia, with a relatively small part called East Thrace in Southeast Europe. It borders the Black Sea to the north; Georgia (country), Georgia, Armen ...
in 1921, and his family was moved to
Athens
Athens ( ) is the Capital city, capital and List of cities and towns in Greece, largest city of Greece. A significant coastal urban area in the Mediterranean, Athens is also the capital of the Attica (region), Attica region and is the southe ...
,
Greece
Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to th ...
in 1922 as a consequence of the
Population exchange between Greece and Turkey
The 1923 population exchange between Greece and Turkey stemmed from the "Convention Concerning the Exchange of Greek and Turkish Populations" signed at Lausanne, Switzerland, on 30 January 1923, by the governments of Greece and Turkey. It involv ...
. He earned his undergraduate degree from
National Technical University of Athens
The National (Metsovian) Technical University of Athens (NTUA; , ''National Metsovian Polytechnic''), sometimes known as Athens Polytechnic, a university in Athens, Greece. It is named in honor of its benefactors Nikolaos Stournaris, Eleni Tosi ...
. In 1945, he stowed away on a boat to escape the impending
Greek Civil War
The Greek Civil War () took place from 1946 to 1949. The conflict, which erupted shortly after the end of World War II, consisted of a Communism, Communist-led uprising against the established government of the Kingdom of Greece. The rebels decl ...
and settled in the United States. He studied under the supervision of John Robert Kline at the
University of Pennsylvania
The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...
and earned his Ph.D. in Mathematics in 1950. His dissertation was titled ''On the Strong Differentiation of the Indefinite Integral.''
He married Caryl Engwall in New York, New York in 1953, and had five children: Irene, Helen, James, Ann, and Mary. In 1952, after teaching briefly at
Union College
Union College is a Private university, private liberal arts college in Schenectady, New York, United States. Founded in 1795, it was the first institution of higher learning chartered by the New York State Board of Regents, and second in the s ...
, he became a faculty member at the Polytechnic Institute of Brooklyn (now
Polytechnic Institute of New York University
The New York University Tandon School of Engineering (commonly referred to as Tandon) is the engineering and applied sciences school of New York University. Tandon is the second oldest private engineering and technology school in the United St ...
), where he earned the distinction of University Professor.
Studies
Papoulis contributed in the areas of
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...
,
communications
Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether Intention, unintentional or failed transmissions are included and whether communication not onl ...
, and
signal
A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology.
In ...
and
system theory
Systems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, defined by its structur ...
. His classic book ''Probability, Random Variables, and Stochastic Processes'' is used as a textbook in many graduate-level probability courses in
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
departments all over the world.
By staying away from complete mathematical rigor while emphasizing the physical and engineering interpretations of
probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
, Papoulis's book gained wide popularity.
Theory
Athanasios Papoulis specialized in engineering mathematics, his work covers probability, statistics, and estimation in the application of these fields to modern engineering problems. Papoulis also taught and developed subjects such as
stochastic simulation A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.DLOUHÝ, M.; FÁBRY, J.; KUNCOVÁ, M.. Simulace pro ekonomy. Praha : VŠE, 2005.
Realizations of these ...
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
sampling theory
In this statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole ...
,
bispectrum In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions.
Definitions
The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional po ...
and system identification,
cyclostationary process
A cyclostationary process is a signal having statistical properties that vary cyclically with time.
A cyclostationary process can be viewed as multiple interleaved stationary processes. For example, the maximum daily temperature in New York City c ...
dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...
studies),
wave optics
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
and the
Wiener
Wiener (from German: "Viennese") may refer to:
Food
* A Vienna sausage of German origin, in German ''Wiener'', named after the capital of Austria
* A hot dog, a cooked sausage, traditionally grilled or steamed and served in a sliced bun
* A Po ...
and
Kalman filter
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...
s.
Contributions
* Papoulis's generalization of the sampling theorem unified many variations of the
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample r ...
into one theorem.
* The Papoulis–Gerchberg algorithm is an iterative signal restoration algorithm that has found widespread use in signal and image processing.
* "Papoulis's eloquent proof" of the conventional
sampling theorem
Sampling may refer to:
*Sampling (signal processing), converting a continuous signal into a discrete signal
*Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components
*Sampling (music), the reuse of a soun ...
requires only two equations.
Bibliography
* ''The Fourier Integral and its Applications'' by Papoulis, Athanasios, McGraw-Hill Companies (June 1, 1962), , .
* ''Probability, Random Variables, and Stochastic Processes'' by Papoulis, Athanasios 1965. McGraw-Hill Kogakusha, Tokyo, 9th edition,
* ''Signal Analysis'' by Athanasios Papoulis Publisher: McGraw-Hill Companies (May 1977)
* ''Systems and Transforms With Applications in Optics'' by Athanasios Papoulis Publisher: Krieger Pub Co (June 1981)
* ''Probability and Statistics'' by Athanasios Papoulis Publisher: Prentice Hall (September 1989)
* ''Circuits and Systems – A modern approach'' by Athanasios Papoulis Publisher: Holt, Rinehart and Winston, Inc. (1980)