Topic
Split-radix FFT algorithm
About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.
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01 Mar 1973
TL;DR: In this article, it was shown that the classes of modular rings of integers in which the FFT may be computed is completely characterized by the prime decomposition of the modulus.
Abstract: : The paper presents several results relating modular arithmetic schemes and the Fast Fourier transform. In particular, the classes of modular rings of integers in which the FFT may be computed is completely characterized by the prime decomposition of the modulus. Also, an extension of this result for computation structures similar to modular rings of integers yields a sufficiency hypothesis for the computation of FFT.
7 citations
TL;DR: In this article, the authors compared the performance of different interpolation fast Fourier transform (FFT) algorithms under white Gaussian noises and showed that the trade-off between biases and variances of frequency estimation is unavoidable.
Abstract: This paper compares performances of frequency estimations provided by different interpolation fast Fourier transform (FFT) algorithms under white Gaussian noises. Firstly, accuracies of frequency estimation algorithms are evaluated by deriving analytical expressions of variances of frequency estimation. Then, theoretical results are validated by means of computer simulations. It is shown that the trade-off between biases and variances of frequency estimation is unavoidable. From both theoretical and simulation results, it can be concluded that variances of frequency estimation are proportional to the noise variance and inverse proportional to the length of FFT.
7 citations
TL;DR: A fast algorithm for computing multilinear integrals which are defined through Fourier multipliers, based on generating a hierarchical decomposition of the summation domain into squares, and applying an FFT based fast convolution algorithm for the computation associated with each square.
7 citations
TL;DR: The interaction between the grid size factorization and the symmetry operators and its influence on the algorithm design are discussed and the central idea is a recursive reduction of the problem to a series of transforms on grids with no special points.
Abstract: Algorithms are presented for maximally efficient computation of the crystallographic fast Fourier transform (FFT). The approach is applicable to all 230 space groups and allows reduction of both the computation time and the memory usage by a factor equal to the number of symmetry operators. The central idea is a recursive reduction of the problem to a series of transforms on grids with no special points. The maximally efficient FFT for such grids has been described in previous papers by the same authors. The interaction between the grid size factorization and the symmetry operators and its influence on the algorithm design are discussed.
7 citations
Patent•
03 Jun 1986TL;DR: In this article, a fast Fourier transform (FFT) data address pre-scrambler technique and cuit for selectively generating prescrambled bit reversed, data address sequences needed to perform radix 2, radix 4, and mixed radix-2/4 FFT transforms are presented.
Abstract: A fast Fourier transform (FFT) data address pre-scrambler technique and cuit for selectively generating pre-scrambled bit reversed, data address sequences needed to perform radix-2, radix-4 and mixed radix-2/4 fast Fourier transforms.
7 citations