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.
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 the real line, or by Fourier series for periodic functions. 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 and neuroscience.
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.
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. 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 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 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 Stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling the filter coefficients by a factor of in the th level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. This algorithm is more famously known as "algorithme à trous" in French which refers to inserting zeros in the filters. It was introduced by Holschneider et al.
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 is the current 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.
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.
Vitold Belevitch was a Belgian mathematician and electrical engineer of Russian origin who produced some important work in the field of electrical network theory. Born to parents fleeing the Bolsheviks, he settled in Belgium where he worked on early computer construction projects. Belevitch is responsible for a number of circuit theorems and introduced the now well-known scattering parameters.
Ahmed I. Zayed is an Egyptian American mathematician. His research interests include Sampling Theory, Wavelets, Medical Imaging, Fractional Fourier transform，Sinc Approximations, Boundary Value Problems, Special Functions and Orthogonal polynomials, Integral transforms.
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.
