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: An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transform.
Abstract: An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transform
96 citations
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TL;DR: The capabilities and flexibility of a discrete-dipole code implementing the two-dimensional fast Fourier transform technique are demonstrated with scattering results from circuit features on surfaces.
Abstract: A two-dimensional fast Fourier transform technique is proposed for accelerating
the computation of scattering characteristics of features on surfaces by using
the discrete-dipole approximation. The two-dimensional fast Fourier transform
reduces the CPU execution time dependence on the number of dipoles N from O(N2) to O(N log N). The capabilities and flexibility of a discrete-dipole
code implementing the technique are demonstrated with scattering results from
circuit features on surfaces.
96 citations
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TL;DR: Fast Fourier transform (FFT)-based computations can be far more accurate than the slow transforms suggest, but these results depend critically on the accuracy of the FFT software employed, which should generally be considered suspect.
Abstract: Fast Fourier transform (FFT)-based computations can be far more accurate than the slow transforms suggest. Discrete Fourier transforms computed through the FFT are far more accurate than slow transforms, and convolutions computed via FFT are far more accurate than the direct results. However, these results depend critically on the accuracy of the FFT software employed, which should generally be considered suspect. Popular recursions for fast computation of the sine/cosine table (or twiddle factors) are inaccurate due to inherent instability. Some analyses of these recursions that have appeared heretofore in print, suggesting stability, are incorrect. Even in higher dimensions, the FFT is remarkably stable.
96 citations
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TL;DR: This paper compares least square approximations of real and complex series, analyzes their properties for sample count towards infinity as well as estimator behaviour, and shows the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case.
Abstract: In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.
95 citations
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TL;DR: In this paper, the authors considered the inversion of the 3D X-ray transform with a limited data set containing the line integrals which have two intersections with the lateral surface of a cylindrical detector.
Abstract: We consider the inversion of the three-dimensional (3D) X-ray transform with a limited data set containing the line integrals which have two intersections with the lateral surface of a cylindrical detector The usual solution to this problem is based on 3D filtered-backprojection, but this method is slow This paper presents a new algorithm which factors the 3D reconstruction problem into a set of independent 2D radon transforms for a stack of parallel slices Each slice is then reconstructed using standard 2D filtered-backprojection The algorithm is based on the application of the stationary-phase approximation to the 2D Fourier transform of the data, and is an extension to three dimensions of the frequency-distance relation derived by Edholm et al(1986) for the 2D radon transform Error estimates are also obtained
95 citations