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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 article, a 3D Fourier transform of a linear function with triangular support is derived in its coordinate-free representation, which is applied to the near-field computation, yielding accurate numerical solutions.
Abstract: A three-dimensional Fourier transform (FT) of a linear function with triangular support is derived in its coordinate-free representation. The Fourier transform of this distribution is derived in three steps. First, the 2-D FT of a constant (top hat) function is obtained. Next, the distribution is generalized to a linearly varying function. Finally, the formulation is extended to a coordinate-free representation which is the 3-D FT of the 2-D function defined over a surface. This formulation is applied to the near-field computation, yielding accurate numerical solutions. >
24 citations
TL;DR: A new fast radix-p-algorithm for the discrete cosine transform (DCT) and its inverse is presented, based on the divide-and-conquer method and on the arithmetic with Chebyshev polynomials.
Abstract: A new fast radix-p-algorithm (p ≧ 2) for the discrete cosine transform (DCT) and its inverse is presented. It is based on the divide-and-conquer method and on the arithmetic with Chebyshev polynomials. The algorithm can be applied for the efficient calculation of DCT's of arbitrary transform lengths and for the implementation of other discrete Vandermonde transforms withO(N logN) arithmetical operations.
24 citations
TL;DR: In this article, the convergence of Fourier continuations with truncation of the singular value decomposition (SVD) is analyzed. But the convergence is limited by a parameter that depends only on the parameters of the Fourier continuation and the points over which it is applied.
24 citations
TL;DR: A decomposition of the Cooley-Tukey algorithm is proposed to allow efficient utilization of core memory and mass storage and the number of input/output operations is greatly reduced, with no increase in the computational burden.
Abstract: We consider the problem of performing a two-dimensional fast Fourier transform (FFT) on a very large matrix in limited core memory. We propose a decomposition of the Cooley-Tukey algorithm to allow efficient utilization of core memory and mass storage. The number of input/output operations is greatly reduced, with no increase in the computational burden. The method is suitable for nonsquare matrices and arrays of three or more dimensions.
24 citations
21 Apr 1997
TL;DR: By studying a 90 degree rotation, an algorithm to compute a prime-length discrete Fourier transform (DFT) based on convolutions and multiplications of discrete, periodic chirps is formulated, providing a further connection between the DFT and the discrete Wigner distribution based on group theory.
Abstract: The concept of rotations in continuous-time, continuous-frequency is extended to discrete-time, discrete-frequency as it applies to the Wigner distribution. As in the continuous domain, discrete rotations are defined to be elements of the special orthogonal group over the appropriate (discrete) field. Use of this definition ensures that discrete rotations will share many of the same mathematical properties as continuous ones. A formula is given for the number of possible rotations of a prime-length signal, and an example is provided to illustrate what such rotations look like. In addition, by studying a 90 degree rotation, we formulate an algorithm to compute a prime-length discrete Fourier transform (DFT) based on convolutions and multiplications of discrete, periodic chirps. This algorithm provides a further connection between the DFT and the discrete Wigner distribution based on group theory.
24 citations