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 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.
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.
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 n 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 or indirectly. 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.
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, Spectral Analysis, and neuroscience.
Norbert Wiener was an American computer scientist, mathematician and philosopher. He became 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.
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem.
NWC may stand for:
Szolem Mandelbrojt was a Polish-French mathematician who specialized in mathematical analysis. He was a professor at the Collège de France from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.
Cornelius (Cornel) Lanczos was a Hungarian-Jewish, Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians.
Raymond Edward Alan Christopher Paley was an English mathematician who made significant contributions to mathematical analysis before dying young in a skiing accident.
In applied mathematics, the Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known 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 spectral density of that process.
In signal processing, the adjoint filter mask of a filter mask is reversed in time and the elements are complex conjugated.
Gisiro Maruyama was a Japanese mathematician, noted for his contributions to the study of stochastic processes. The Euler–Maruyama method for the numerical solution of stochastic differential equations bears his name.
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 63 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.
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.
Donald Lyman Burkholder was an American mathematician known for his contributions to probability theory, particularly the theory of martingales. The Burkholder–Davis–Gundy inequality is co-named after him. Burkholder spent most of his professional career as a professor in the Department of Mathematics of the University of Illinois at Urbana-Champaign. After his retirement in 1998, Donald Burkholder remained a professor emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign. He was a member of the U.S. National Academy of Sciences and a fellow of the American Mathematical Society.
Carl-Gustav Esseen was a Swedish mathematician. His work was in the theory of probability. The Berry–Esseen theorem is named after him.
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. All of these topics have received a large degree of attention from machine learning researchers, with SampTA serving as bridge between these two communities.
Eitan Tadmor is a distinguished university professor at the University of Maryland, College Park. His work has featured contributions to the theory and computation of Partial differential equations with diverse applications to shock wave, kinetic transport, incompressible flows, image processing, and self-organized collective dynamics.
Kenneth Irwin Gross was an American mathematician.
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