The Norbert Wiener Center for Harmonic Analysis and Applications (NWC) is a division of the Mathematics Department in the University of Maryland College of Computer, Mathematical, and Natural Sciences devoted to research and education in pure and applied harmonic analysis. The center, named after acclaimed scientist Norbert Wiener was founded in 2004 and is based out of the Mathematics Building on the University of Maryland, College Park campus. It is supported by the University of Maryland, the National Science Foundation, and local industries with which it interacts.
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms. In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience.
Norbert Wiener was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.
The University of Maryland, College Park is a public research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the University System of Maryland, and is the largest university in both the state and the Washington metropolitan area, with more than 41,000 students representing all fifty states and 123 countries, and a global alumni network of over 360,000. Its twelve schools and colleges together offer over 200 degree-granting programs, including 92 undergraduate majors, 107 master's programs, and 83 doctoral programs. UMD is a member of the Association of American Universities and competes in intercollegiate athletics as a member of the Big Ten Conference.
Currently, the Norbert Wiener Center is actively involved in research project involved with waveform design, dimension reduction, geospatial terrain and image processing, data fusion, phase retrieval frames, and analysis on graphs.
February Fourier Talks
The Norbert Wiener Center hosts the annual conference, the February Fourier Talks (FFT). The first FFT was held in 2002 and 2003, and then annually since 2006. The aim of the annual FFT is to bring together researchers from academia, government, and industry, as a means to spur innovation and foster interaction in Harmonic Analysis and its Applications. The FFT lasts two days and consists of approximately 15 half-hour talks, a distinguished lecture, a colloquium, and a keynote lecture. The speakers are top researchers in pure and applied harmonic analysis in academia, government, and industry.
Current Personnel
The Director of the NWC is John Benedetto. The faculty members include: John Benedetto, Radu Balan, Wojciech Czaja, and Kasso Okoudjou. The current Scientific Development Officers include Michael Dellomo, Jeffrey Sieracki, and Alfredo Nava-Tudela. The current postdoctoral fellows include Xuemei Chen and Benjamin Manning. The associate director of the center is Matthew Begué. A list of all other members, including all graduate students, can be found on the center's official website.
John Joseph Benedetto is a Professor of Mathematics at the University of Maryland, College Park and is a leading researcher in wavelet analysis and Director of the Norbert Wiener Center for Harmonic Analysis and Applications. He was named Distinguished Scholar-Teacher by the University of Maryland in 1999 and has directed 58 Ph.D students. The volume Harmonic Analysis and Applications: In Honor of John Benedetto, edited by Christopher Heil, describes his influence:
John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field.
Kasso Akochayé Okoudjou is a Professor of Mathematics at the University of Maryland, College Park. He works on pure and harmonic analysis, differential equations and fractals at the Norbert Wiener Center for Harmonic Analysis and Applications. He is the 2018 Martin Luther King Visiting Professor at Massachusetts Institute of Technology.
A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection.
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 to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse factors. As a result, it manages to reduce the complexity of computing the DFT from , which arises if one simply applies the definition of DFT, to , where is the data size. The difference in speed can be enormous, especially for long data sets where N may be in the thousands or millions. In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly. There are many different FFT algorithms based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory.
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data. The concept of deconvolution is widely used in the techniques of signal processing and image processing. Because these techniques are in turn widely used in many scientific and engineering disciplines, deconvolution finds many applications.
Hua Luogeng or Hua Loo-Keng was a Chinese mathematician and politician famous for his important contributions to number theory and for his role as the leader of mathematics research and education in the People's Republic of China. He was largely responsible for identifying and nurturing the renowned mathematician Chen Jingrun who proved Chen's theorem, the best known result on the Goldbach conjecture. In addition, Hua's later work on mathematical optimization and operations research made an enormous impact on China's economy. He was elected a foreign associate of the US National Academy of Sciences in 1982. He was elected a member of the standing Committee of the first to sixth National people's Congress, Vice-Chairman of the sixth National Committee of the Chinese People's Political Consultative Conference and Vice-Chairman of the China Democratic League (1979). He joined the Communist Party of China in 1979.
Raymond Edward Alan Christopher Paley was an English mathematician. Paley was born in Bournemouth, England. He was educated at Eton. From there he entered Trinity College, Cambridge where he showed himself as a brilliant student. He won a Smith's Prize in 1930 and was elected a fellow of Trinity College.
In applied mathematics, the Wiener–Khinchin theorem, also known as the Wiener–Khintchine theorem and sometimes as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary random process has a spectral decomposition given by the power spectrum of that process.
Jerrold Eldon Marsden was a mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.
In signal processing, the adjoint filter mask of a filter mask is reversed in time and the elements are complex conjugated.
Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington. His areas of interest are harmonic analysis, differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres".
Audrey Anne Terras is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions.
Ahmed I. Zayed is an Egyptian American mathematician. His research interestes include Sampling Theory, Wavelets, Medical Imaging, Fractional Fourier transform，Sinc Approximations, Boundary Value Problems, Special Functions and Orthogonal polynomials, Integral transforms.
In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by A(T), is the space of absolutely convergent Fourier series. Here T denotes the circle group.
Hans Georg Feichtinger is an Austrian mathematician. He is Professor in the mathematical faculty of the University of Vienna. He is editor-in-chief of the Journal of Fourier Analysis and Applications (JFAA) and associate editor to several other journals. He is one of the founders and head of the Numerical Harmonic Analysis Group (NuHAG) at University of Vienna. Today Feichtinger's main field of research is harmonic analysis with a focus on time-frequency analysis.
SampTA is a biennial interdisciplinary conference for mathematicians, engineers, and applied scientists. The main purpose of SampTA is to exchange recent advances in sampling theory and to explore new trends and directions in the related areas of application. The conference focuses on such fields as signal processing and image processing, coding theory, control theory, real analysis and complex analysis, harmonic analysis, and the theory of differential equations. SampTA features plenary talks by prominent speakers, special sessions on selected topics reflecting the current trends in sampling theory and its applications to the engineering sciences, as well as regular sessions about traditional topics in sampling theory. Contributions from authors attending the SampTA conferences are usually published in special issues of Sampling Theory in Signal and Image Processing, an international journal dedicated to sampling theory and its applications. The proceedings of SampTA 2015 were indexed in IEEE Xplore.
Rajendra Bhatia is an Indian mathematician, author, and educator.
Kenneth Irwin Gross was an American mathematician.
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