Athanasios Papoulis was a Greek

Greek American

Greek Americans are Americans of Greek descent also described as Hellenic descent. According to the 2007 U.S. Census Bureau estimation, there were 1,380,088 people of Greek ancestry in the United States, while the State Department mentions that around 3,000,000 Americans claim to be of Greek descent...

-American

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 engineer

Engineer

An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

 and applied mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

.

Life

Papoulis was born in Athens

Athens

Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...

, Greece

Greece

Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....

 in 1921 and graduated from National Technical University of Athens

National Technical University of Athens

The National Technical University of Athens , sometimes simply known as Athens Polytechnic, is among the oldest and most prestigious higher education institutions of Greece....

. Papoulis was a member of the faculty of the Polytechnic institute of Brooklyn (now Polytechnic Institute of New York University) since 1952.

Studies

Papoulis contributed in the areas of signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, communications

Information theory

Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

, and signal 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

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

 departments all over the world.
By staying away from complete mathematical rigor while emphasizing the physical and engineering interpretations of probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

, 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

Stochastic simulation

Stochastic simulation algorithms and methods were initially developed to analyse chemical reactions involving large numbers of species with complex reaction kinetics. The first algorithm, the Gillespie algorithm was proposed by Dan Gillespie in 1977...

, mean square estimation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

, likelihood tests, maximum entropy methods

Principle of maximum entropy

In Bayesian probability, the principle of maximum entropy is a postulate which states that, subject to known constraints , the probability distribution which best represents the current state of knowledge is the one with largest entropy.Let some testable information about a probability distribution...

, Monte Carlo method

Monte Carlo method

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

, spectral representations

Diffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 and estimation, sampling theory

Sampling theory

sampling theory may mean:* Nyquist–Shannon sampling theorem, digital signal processing * Statistical sampling* Fourier sampling...

, bispectrum

Bispectrum

In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum...

 and system identification, cyclostationary processes, deterministic signals in noise (part of deterministic systems

Deterministic system (mathematics)

In mathematics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.-Examples:...

 and dynamical system

Dynamical system

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...

 studies), wave optics and the Wiener

Wiener filter

In signal processing, the Wiener filter is a filter proposed by Norbert Wiener during the 1940s and published in 1949. Its purpose is to reduce the amount of noise present in a signal by comparison with an estimation of the desired noiseless signal. The discrete-time equivalent of Wiener's work was...

 and Kalman filter

Kalman filter

In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...

s.

Contributions

• Papoulis's generalization of the sampling theorem unified many variations of the Nyquist–Shannon sampling theorem
  Nyquist–Shannon sampling theorem
  The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...
  
   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.

External links

• The Athanasios Papoulis Award, one of the IEEE LI Section Awards