Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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TL;DR: In this paper, the wavelet transform was applied to the interpretation of extended x-ray absorption fine structure spectra concerning the complexation of Uranium(VI) with the carboxylic groups acetic-, formic-, and glycolic acid.
Abstract: Extended x-ray absorption fine structure data evaluation usually begins with the Fourier transform of the spectrum. We suggest the wavelet transform as a complement to the Fourier transform. While the Fourier transform analyzes the distances to the backscattering atoms, wavelet transform additionally reveals the wavenumber dependence of the scattering. Thus wavelet analysis can differentiate between heavier and lighter backscattering atoms, even if they are almost equidistant from the central atom. First the method of operation and the advantage of the wavelet analysis will be demonstrated by simple models. Then it is applied to the interpretation of extended x-ray absorption fine structure spectra concerning the complexation of Uranium(VI) with the carboxylic groups acetic-, formic-, and glycolic acid. The wavelet transform analysis suggests clearly for the system Uranium-formic acid both, U-U and U-C-C, structural elements. In contrast to the clear separation of different scattering paths by wavelet transform, Fourier transform analysis was not able to resolve the two different backscattering processes.
26 citations
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30 Dec 1899TL;DR: The Cooley-Tukey Algorithm as discussed by the authors was developed to compute the Discrete Fourier Transform for a large number of input points in relatively reasonable times, however, for certain uses a demand developed for computing the Fourier transform in a very short time or even in real time.
Abstract: With the advent of digital computers it became possible to compute the Discrete Fourier Transform for a large number of input points in relatively reasonable times. However, for certain uses a demand developed to compute the Discrete Fourier Transform in a very short time or even in real time. Also, a demand developed for computing the Fourier Transform for a very large number of input points. These demands resulted in a requirement for computing the Fourier Transform in the fastest time possible. A very economical way for computing the Fourier Transform was developed a few years ago and is known as the Cooley-Tukey Algorithm. This article describes another algorithm for computing the Discrete Fourier Transform where the required number of additions and subtractions is the same as in the Cooley-Tukey Algorithm; but the required number of multiplications is only one half of that in the Cooley-Tukey Algorithm.
26 citations
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TL;DR: The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform, and readily generalizes to higher dimensions and to piecewise smooth functions.
26 citations
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TL;DR: In this paper, the discrete inverse Radon transform of a function sampled on the product space of two two-dimensional spheres is determined as the solution of a minimization problem, which is iteratively solved using fast Fourier techniques for and SO(3).
Abstract: The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem which applies to x-ray tomography with polycrystalline materials. This paper presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space of two two-dimensional spheres is determined as the solution of a minimization problem, which is iteratively solved using fast Fourier techniques for and SO(3). The favorable complexity and stability of the algorithm based on these techniques has been confirmed with numerical tests.
26 citations
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TL;DR: A large interval can be selected as the threshold to obtain almost optimal filtering results and once the selected threshold is suitable, it is almost optimal.
Abstract: A simple phase unwrapping approach based on windowed Fourier filtering was proposed recently [K. Qian et al. A simple phase unwrapping approach based on filtering by windowed Fourier transform. Opt Laser Technol 2005;37:458–62]. The windowed Fourier filtering algorithm is an essential ingredient that suppresses the noise effectively and makes the phase unwrapping trivial. This paper adds a note on the threshold selection in the windowed Fourier filtering algorithm. A large interval can be selected as the threshold to obtain almost optimal filtering results. Once the selected threshold is suitable, it is almost optimal. This makes the threshold selection in the windowed Fourier filtering algorithm extremely easy.
26 citations