Athanasios Papoulis /ref> ( el, Αθανάσιος Παπούλης; 1921 – April 25, 2002) was a
Greek
Greek may refer to:
Greece
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 ...
engineer
Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limit ...
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, structure, space, models, and change.
History
On ...
.
Life
Papoulis was born in modern day
Turkey
Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a transcontinental country located mainly on the Anatolian Peninsula in Western Asia, with a small portion on the Balkan Peninsula in ...
in 1921, and his family was moved to
Athens
Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...
,
Greece
Greece,, or , romanized: ', officially the Hellenic Republic, is a country in Southeast Europe. It is situated on the southern tip of the Balkans, and is located at the crossroads of Europe, Asia, and Africa. Greece shares land borders ...
in 1922 as a consequence of the
Population exchange between Greece and Turkey
The 1923 population exchange between Greece and Turkey ( el, Ἡ Ἀνταλλαγή, I Antallagí, ota, مبادله, Mübâdele, tr, Mübadele) stemmed from the "Convention Concerning the Exchange of Greek and Turkish Populations" signed at ...
. He earned his undergraduate degree from
National Technical University of Athens
The National (Metsovian) Technical University of Athens (NTUA; el, Εθνικό Μετσόβιο Πολυτεχνείο, ''National Metsovian Polytechnic''), sometimes known as Athens Polytechnic, is among the oldest higher education institution ...
. In 1945, he stowed away on a boat to escape the impending
Greek Civil War
The Greek Civil War ( el, ο Eμφύλιος όλεμος}, ''o Emfýlios'' 'Pólemos'' "the Civil War") took place from 1946 to 1949. It was mainly fought against the established Kingdom of Greece, which was supported by the United Kingdom and ...
and settled in the United States. He studied under the supervision of John Robert Kline at the
University of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
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 liberal arts college in Schenectady, New York. Founded in 1795, it was the first institution of higher learning chartered by the New York State Board of Regents, and second in the state of New York, after Columbia Co ...
, 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 Sta ...
), 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 sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
,
communications
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
, and
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
and system theory. His classic book ''Probability, Random Variables, and Stochastic Processes'' is used as a textbook in many graduate-level probability courses in electrical engineering departments all over the world.
By staying away from complete mathematical rigor while emphasizing the physical and engineering interpretations of
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
, 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 determi ...
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 p ...
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 ca ...
dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
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 effe ...
Kalman filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...
s.
Contributions
* Papoulis's generalization of the sampling theorem unified many variations of the
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that per ...
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 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)