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 a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.
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, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time, as in time series. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids at the frequency components of the signal. Although it is common to refer to the magnitude portion as the frequency response of a signal, the phase portion is required to uniquely define the signal.
Stéphane Georges Mallat is a French applied mathematician, concurrently appointed as Professor at Collège de France and École normale supérieure. He made fundamental contributions to the development of wavelet theory in the late 1980s and early 1990s. He has additionally done work in applied mathematics, signal processing, music synthesis and image segmentation.
Baroness Ingrid Daubechies is a Belgian-American physicist and mathematician. She is best known for her work with wavelets in image compression.
Yves F. Meyer is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017.
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image. Further, it purveys a high degree of shift-invariance in its magnitude, which was investigated in. However, a drawback to this transform is that it exhibits redundancy compared to a separable (DWT).
In mathematics, a wavelet series is a representation of a square-integrable function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.
Martin Vetterli was president of École polytechnique fédérale de Lausanne (EPFL) in Switzerland, succeeding Patrick Aebischer. He's a professor of engineering and was formerly the president of the National Research Council of the Swiss National Science Foundation.
Ali Naci Akansu is a Turkish-American professor of electrical & computer engineering and scientist in applied mathematics.
Robert Jackson Marks II is an American electrical engineer, computer scientist and Distinguished Professor at Baylor University. His contributions include the Zhao-Atlas-Marks (ZAM) time-frequency distribution in the field of signal processing, the Cheung–Marks theorem in Shannon sampling theory and the Papoulis-Marks-Cheung (PMC) approach in multidimensional sampling. He was instrumental in the defining of the field of computational intelligence and co-edited the first book using computational intelligence in the title. A Christian and an old earth creationist, he is a subject of the 2008 pro-intelligent design motion picture, Expelled: No Intelligence Allowed.
Abdul Jabbar Hassoon Jerri is an Iraqi American mathematician, most recognized for his contributions to Shannon Sampling Theory, It's Generalizations, Error Analysis, and Historical Reviews, and in particular his establishment in 2002 of the journal Sampling Theory in Signal and Image Processing with over thirty top international experts as its editors, besides establishing its Sampling Publishing, also his contribution to the general understanding of the Gibbs Phenomenon, where he wrote the first book ever on the subject, published by Springer - Verlag, then he followed it by editing another book on Advances in Gibbs Phenomenon published by Sampling Publishing.
Fedor (Fedya) L'vovich Nazarov is a Russian mathematician working in the United States. He has done research in mathematical analysis and its applications, in particular in functional analysis and classical analysis.
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.
Peter Balazs is an Austrian mathematician working at the Acoustics Research Institute Vienna of the Austrian Academy of Sciences.
Akram Aldroubi is an American mathematician known for his work in sampling theory, harmonic analysis, and their applications to signal and image processing as well as biomedical data analysis.
Gitta Kutyniok is a German applied mathematician known for her research in harmonic analysis, deep learning, compressed sensing, and image processing. She has a Bavarian AI Chair for "Mathematical Foundations of Artificial Intelligence" in the institute of mathematics at the Ludwig Maximilian University of Munich.
Maamar Bettayeb is a control theorist, educator and inventor. He is the author of publications on understanding the singular value decomposition and model order reduction. Bettayeb is also a promoter of scientific research.
Albert Cohen is a French mathematician, specializing in approximation theory, numerical analysis, and digital signal processing.
