Papoulis was born in Turkey in 1921, and his family moved to Athens, Greece in 1922. He earned his undergraduate degree from National Technical University of Athens. In 1945, he stowed away on a boat to escape the impending Greek Civil War and settled in the United States. He earned his Ph.D. in Mathematics at the University of Pennsylvania. 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, he became a faculty member at the Polytechnic Institute of Brooklyn (now Polytechnic Institute of New York University), where he earned the distinction of University Professor.
Papoulis contributed in the areas of signal processing, communications, 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 departments all over the world.
Two classic texts aimed at [engineering] practitioners were [first] published in 1965... [One was] Athanasios Papoulis' Probability, Random Variables, and Stochastic Processes... These books popularized a pedagogy that balanced rigor and intuition.
By staying away from complete mathematical rigor while emphasizing the physical and engineering interpretations of probability, Papoulis's book gained wide popularity.
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, mean square estimation, likelihood tests, maximum entropy methods, Monte Carlo method, spectral representations and estimation, sampling theory, bispectrum and system identification, cyclostationary processes, deterministic signals in noise (part of deterministic systems and dynamical system studies), wave optics and the Wiener and Kalman filters.
- Papoulis's generalization of the sampling theorem unified many variations of the Nyquist–Shannon sampling theorem 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.
- The Fourier Integral and its Applications by Papoulis, Athanasios, McGraw-Hill Companies (June 1, 1962), ISBN 0-07-048447-3.
- Probability, Random Variables, and Stochastic Processes by Papoulis, Athanasios 1965. McGraw-Hill Kogakusha, Tokyo, 9th edition, ISBN 0-07-119981-0.
- Signal Analysis by Athanasios Papoulis Publisher: McGraw-Hill Companies (May 1977) ISBN 0-07-048460-0 ISBN 978-0070484603
- Systems and Transforms With Applications in Optics by Athanasios Papoulis Publisher: Krieger Pub Co (June 1981) ISBN 0-89874-358-3 ISBN 978-0898743586
- Announcement of Death.
- Athanasios Papoulis and S.Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, 4th edition, McGraw Hill, 2002.
- R.J. Marks II, Handbook of Fourier Analysis and Its Applications, Oxford University Press, (2009) p. vi
- A. Papoulis, "Generalized Sampling Expansion," IEEE Transactions on Circuits and Systems, v.24, Nov. 1977
- R. F. Hoskins and J. De Sousa Pinto, "Generalized Sampling Expansions in the Sense of Papoulis," SIAM Journal on Applied Mathematics, Vol. 44, No. 3 (Jun., 1984), pp. 611-617
- J.L. Brown and S.D.Cabrera, "On well-posedness of the Papoulis generalized sampling expansion," IEEE Transactions on Circuits and Systems, May 1991 Volume: 38 , Issue 5, pp. 554-556
- A. Papoulis, "A new method of image restoration," Joint Services Technical Activity Report 39 (1973-1974).
- R. W. Gerchberg, Super-resolution through error energy reduction. Opt. Acta 21, 709-720 (1974).
- A. Papoulis, "A new algorithm in spectral analysis and bandlimited extrapolation," IEEE Transactions on Circuits and Systems, CAS-22, 735-742 (1975)
- Peter A. Jansson, Deconvolution of Images and Spectra, Second Edition, Academic Press, (1996) pp.490-494
- R.J. Marks II, op.cit., pp. 477-482
- R.J. Marks II, Ibid, p. 223
- Athanasios Papoulis, Signal Analysis, McGraw-Hill (1977)