The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
Gerard J. M. Smit - One of the best experts on this subject based on the ideXlab platform.
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ICASSP - Fourier-hermite communications; where Fourier meets Hermite
2013 IEEE International Conference on Acoustics Speech and Signal Processing, 2013Co-Authors: C. Willem Korevaar, Andre B.j. Kokkeler, Pieter-tjerk De Boer, Gerard J. M. SmitAbstract:A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency localization. Its robustness against time-frequency shifts is assessed and compared to Hermite and Fourier basis signals. The Fourier-Hermite signal set is particularly designed for communications in spectrum-scarce environments.
Mathieu Lagrange - One of the best experts on this subject based on the ideXlab platform.
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Fourier at the heart of computer music: From harmonic sounds to texture
Comptes Rendus Physique, 2019Co-Authors: Vincent Lostanlen, Joakim Andén, Mathieu LagrangeAbstract:Beyond the scope of thermal conduction, Joseph Fourier's treatise on the Analytical Theory of Heat (1822) profoundly altered our understanding of acoustic waves. It posits that any function of unit period can be decomposed into a sum of sinusoids, whose respective contribution represents some essential property of the underlying periodic phenomenon. In acoustics, such a decomposition reveals the resonant modes of a freely vibrating string. The introduction of Fourier series thus opened new research avenues on the modeling of musical timbre-a topic which was to become of crucial importance in the 1960s with the advent of computer-generated sounds. This article proposes to revisit the scientific legacy of Joseph Fourier through the lens of computer music research. We first discuss how the Fourier series marked a paradigm shift in our understanding of acoustics, supplanting the theory of consonance of harmonics in the Pythagorean monochord. Then, we highlight the utility of Fourier's paradigm via three practical problems in analysis-synthesis: the imitation of musical instruments, frequency transposition, and the generation of audio textures. Interestingly, each of these problems involves a different perspective on time-frequency duality, and stimulates a multidisciplinary interplay between research and creation that is still ongoing. To cite this article: V. Lostanlen, J. Andén, M. Lagrange, C. R. Physique X (2019). Résumé Fourier au coeur de la musique par ordinateur : des sons harmoniquesà la texture. Au-delà de son apport théorique dans le domaine de la conduction thermique, le mémoire de Joseph Fourier sur la Théorie analytique de la chaleur (1822) a révolutionné notre conception des ondes sonores. Ce mémoire affirme que toute fonction de période unitaire se décompose en une série de sinusoïdes, chacune représentant une propriété essentielle du phénomène périodiqueétudié. Dans l'acoustique, cette décomposition révèle les modes de résonance d'une corde vibrante. Ainsi, l'introduction des séries de Fourier a ouvert de nouveaux horizons en matière de modélisation du timbre musical, un sujet qui prendra une importance crucialeà partir des années 1960, avec les débuts de la musique par ordinateur. Cet article propose de thématiser l'oeuvre de Joseph Fourierà la lumière de ses implications en recherche musicale. Nous retraçons d'abord le changement de paradigme que les séries de Fourier ont opéré en acoustique, supplantant un mode de pensée fondé sur les consonances du monocorde pythagoricien. Par la suite, nous soulignons l'intérêt du paradigme de Fourierà travers trois problèmes pratiques en analyse-synthèse : l'imitation d'instruments de musique, la transposition fréquentielle, et la génération de textures sonores. Chacun de ses trois problèmes convoque une perspective différente sur la dualité temps-fréquence, et suscite un dialogue multidisciplinaire entre recherche et création qui est toujours d'actualité. Pour citer cet article : V. Lostanlen, J. Andén, M. Lagrange, C. R. Physique X (2019).
Matthew Wiersma - One of the best experts on this subject based on the ideXlab platform.
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Lp-Fourier and Fourier–Stieltjes algebras for locally compact groups
Journal of Functional Analysis, 2015Co-Authors: Matthew WiersmaAbstract:Abstract Let G be a locally compact group and 1 ≤ p ∞ . A continuous unitary representation π : G → B ( H ) of G is an L p -representation if the matrix coefficient functions s ↦ 〈 π ( s ) x , x 〉 lie in L p ( G ) for sufficiently many x ∈ H . The L p -Fourier algebra A L p ( G ) is defined to be the set of matrix coefficient functions of L p -representations. Similarly, the L p -Fourier–Stieltjes algebra B L p ( G ) is defined to be the weak*-closure of A L p ( G ) in the Fourier–Stieltjes algebra B ( G ) . These are always ideals in the Fourier–Stieltjes algebra containing the Fourier algebra A ( G ) . In this paper we investigate how these spaces reflect properties of the underlying group and study the structural properties of these algebras. As an application of this theory, we characterize the Fourier–Stieltjes ideals of SL ( 2 , R ) .
Vjekoslav Kovač - One of the best experts on this subject based on the ideXlab platform.
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Fourier restriction implies maximal and variational Fourier restriction
Journal of Functional Analysis, 2019Co-Authors: Vjekoslav KovačAbstract:Abstract We give an abstract argument that an a priori Fourier restriction estimate for a certain choice of exponents automatically implies maximal and variational Fourier restriction estimates. These, in turn, provide pointwise and quantitative interpretations of restriction of the Fourier transform to the hypersurface in question.
Robert J. Vanderbei - One of the best experts on this subject based on the ideXlab platform.
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Fast Fourier optimization
Mathematical Programming Computation, 2012Co-Authors: Robert J. VanderbeiAbstract:Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the “fast Fourier” version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.
