Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: In this article, a novel transform is presented which maps continuum functions (such as probability densities) into discrete sequences and permits rapid numerical calculation of convolutions, multiple convolutions and Neumann expansions for Volterra integral equations.
77 citations
TL;DR: State variables from brain potentials are time series that are either recorded and digitized or derived from recordings by use of the Fourier and Hilbert transforms.
Abstract: State variables from brain potentials are time series that are either recorded and digitized or derived from recordings by use of the Fourier and Hilbert transforms; they provide the primary raw materials by which models of brain dynamics are constructed and evaluated.
77 citations
TL;DR: In this paper, it was shown that the Fourier transform belongs to Lq(r, da) for a certain natural measure on the su.rface of a circular cone in R3.
Abstract: Let r be the su.rface of a circular cone in R3. We show that if 1 < p < 4/3, 1/q = 3(1-1/p) and f E LP(R3), then the Fourier transform of f belongs to Lq(r, da) for a certain natural measure a on r. Following P. Tomas we also establish bounds for restrictions of Fourier transforms to conic annuli at the endpoint p = 4/3, with logarithmic growth of the bound as the thickness of the annulus tends to zero.
77 citations
TL;DR: The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT), and compare its performance to other on-chip DFT implementations.
Abstract: The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT). They show both analytically and by simulation that the circuit is guaranteed to settle into the correct values within RC time constants (on the order of hundreds of nanoseconds), and they compare its performance to other on-chip DFT implementations. >
76 citations
01 Jan 2000
TL;DR: A finite implementation of the ridgelet transform is presented that is invertible, non-redundant and achieved via fast algorithms and it is shown that this transform is orthogonal hence it allows one to use non-linear approximations for the representation of images.
Abstract: A finite implementation of the ridgelet transform is presented. The transform is invertible, non-redundant and achieved via fast algorithms. Furthermore we show that this transform is orthogonal hence it allows one to use non-linear approximations for the representation of images. Numerical results on different test images are shown. Those results conform with the theory of the ridgelet transform in the continuous domain-the obtained representation can represent efficiently images with linear singularities. Thus it indicates the potential of the proposed system as a new transform for coding of images.
76 citations