James William Cooley (1926 – June 29, 2016) was an

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, pe ...

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 ...

. Cooley received a B.A. degree in 1949 from

Manhattan College Manhattan College is a private, Catholic, liberal arts university in the Bronx, New York City. Originally established in 1853 by the Brothers of the Christian Schools (De La Salle Christian Brothers) as an academy for day students, it was la ...

, Bronx, NY, an M.A. degree in 1951 from

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

, New York, NY, and a Ph.D. degree in 1961 in

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

from

. He was a

programmer A computer programmer, sometimes referred to as a software developer, a software engineer, a programmer or a coder, is a person who creates computer programs — often for larger computer software. A programmer is someone who writes/creates ...

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

's computer at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, Princeton, NJ, from 1953 to 1956, where he notably programmed the Blackman–Tukey transformation. He worked on quantum mechanical computations at the

Courant Institute The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

, New York University, from 1956 to 1962, when he joined the Research Staff at the

IBM Watson Research Center The Thomas J. Watson Research Center is the headquarters for IBM Research. The center comprises three sites, with its main laboratory in Yorktown Heights, New York, Yorktown Heights, New York (state), New York, U.S., 38 miles (61 km) north ...

, Yorktown Heights, NY. Upon retirement from IBM in 1991, he joined the Department of

Electrical Engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

University of Rhode Island The University of Rhode Island (URI) is a public land-grant research university with its main campus in Kingston, Rhode Island, United States. It is the flagship public research as well as the land-grant university of the state of Rhode Island ...

, Kingston, where he served on the faculty of the

computer engineering Computer engineering (CoE or CpE) is a branch of electrical engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers ...

program. His most significant contribution to the world of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...

is re-discovering the

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...

, which he co-developed with

John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...

(see

Cooley–Tukey FFT algorithm The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size N = N_1N_2 in terms of ''N''1 ...

) while working for the research division of IBM in 1965. The motivation for it was provided by Dr.

Richard L. Garwin Richard Lawrence Garwin (born April 19, 1928) is an American physicist, best known as the author of the first hydrogen bomb design. In 1978, Garwin was elected a member of the National Academy of Engineering for contributing to the application ...

at IBM Watson Research who was concerned about verifying a

nuclear arms A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions (thermonuclear bomb), producing a nuclear explosion. Both bomb ...

treaty with the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...

for the SALT talks. Garwin thought that if he had a very much faster

Fourier Transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

he could plant sensors in the ground in countries surrounding the Soviet Union. He suggested to both Cooley and

Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the Cooley–Tukey FFT algorithm, fast Fourier Transform (FFT) algorithm and box plot. The Tukey's range test ...

how Fourier transforms could be programmed to be much faster. They did the work, the sensors were planted, and he was able to locate

nuclear explosions A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, tho ...

to within 15 kilometers of where they were occurring. J. W. Cooley was a member of the ''Digital Signal Processing Committee'' of the

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

, was elected a Fellow of IEEE for his work on the FFT, and received the

IEEE Centennial Medal The IEEE Centennial Medal was a medal minted and awarded in 1984 ''to persons deserving of special recognition for extraordinary achievement'' to celebrate the Centennial of the founding of the Institute of Electrical and Electronics Engineers (I ...

. In 2002 he received the

IEEE Jack S. Kilby Signal Processing Medal The IEEE Jack S. Kilby Signal Processing Medal is presented "for outstanding achievements in signal processing" theory, technology or commerce. The recipients of this award will receive a gold medal, together with a replica in bronze, a certificat ...

. He considerably contributed to the establishing of terminology in

Publications

* James W. Cooley (1961): "An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields", Math. Comput. 15, 363–374. DOI
10.1090/S0025-5718-1961-0129566-X
This describes the so-called Numerov-Cooley method for numerically solving one-dimensional

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

s. * James W. Cooley & John W. Tukey (1965):
An algorithm for the machine calculation of complex Fourier series
, Math. Comput. 19, 297–301. *Cooley, James W., Timothy M. Toolan and Donald W. Tufts. "A Subspace Tracking Algorithm Using the Fast Fourier Transform." IEEE Signal Processing Letters. 11(1):30–32. January 2004. *Real, Edward C., Donald W. Tufts and James W. Cooley. "Two Algorithms for Fast Approximate Subspace Tracking." IEEE Transactions on Signal Processing. 47(7):1936–1945. July 1999. *Tufts, D. W., E. C. Real and J. W. Cooley. "Fast Approximate Subspace Tracking (FAST)." IN: Proceedings of the 1997 IEEE

International Conference on Acoustics, Speech, and Signal Processing ICASSP, the International Conference on Acoustics, Speech, and Signal Processing, is an annual flagship conference organized of IEEE Signal Processing Society. All papers included in its proceedings have been indexed by Ei Compendex. The first ICAS ...

. IEEE. 1997. I:547–550.

References

External links

* {{DEFAULTSORT:Cooley, James 1926 births 2016 deaths 20th-century American mathematicians 21st-century American mathematicians IBM employees Manhattan College alumni Columbia School of Engineering and Applied Science alumni University of Rhode Island faculty Members of the United States National Academy of Engineering Courant Institute of Mathematical Sciences faculty Fellow Members of the IEEE IEEE Centennial Medal laureates

Publications

See also

References

External links