Topic
Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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TL;DR: This application note from Motorola provides both an excellent tutorial on the FFT itself and describes how it can be implemented using a general-purpose digital signal processor.
11 citations
TL;DR: The spline-interpolation-based fast Fourier transform (FFT) algorithm, designated as the SFFT algorithm, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes.
Abstract: The spline-interpolation-based fast Fourier transform (FFT) algorithm, designated as the SFFT algorithm, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes. The proposed SFFT algorithm first introduces the spline interpolation technique to reduce the number of the Cholesky decomposition of a spectral density matrix and subsequently uses the FFT algorithm to further enhance the computational speed. In order to highlight the superiority of the SFFT algorithm, the simulations of the multivariate stationary longitudinal wind velocity fluctuations have been carried out, respectively, with resorting to the SFFT-based and FFT-based spectral representation SR methods, taking into consideration that the elements of cross-power spectral density matrix are the complex values. The numerical simulation results show that though introducing the spline interpolation approximation in decomposing the cross-power spectral density matrix, the SFFT algorithm can achieve the results without a loss of precision with reference to the FFT algorithm. In comparison with the FFT algorithm, the SFFT algorithm provides much higher computational efficiency. Likewise, the superiority of the SFFT algorithm is becoming more remarkable with the dividing number of frequency, the number of samples, and the time length of samples going up.
11 citations
TL;DR: This correspondence presents details of a new implementation of the prime factor FFT algorithm (PFA) for computing the discrete Fourier transform (DFT) that saves about 40 percent of the execution time of the conventional one.
Abstract: This correspondence presents details of a new implementation of the prime factor FFT algorithm (PFA) for computing the discrete Fourier transform (DFT). This implementation applies a program generation technique to the PFA algorithm and saves about 40 percent of the execution time of the conventional one.
11 citations
03 Aug 2010
TL;DR: This paper describes a novel data reordering technique based on the vector calculation of size r that reduces memory usage by eliminating the look-up table traditionally employed in the computation of bit-reversal indexes.
Abstract: The Fast Fourier Transform (FFT) is a key role in signal processing applications that is useful for the frequency domain analysis of signals. The FFT computation requires an indexing scheme at each stage to address input/output data and coefficient multipliers properly. Most of these indexing schemes are based on bit-reversal techniques that are boosted by a look-up table requiring extra memory storage. This paper describes a novel data reordering technique based on the vector calculation of size r. FFTs are considered in-place (or in situ) algorithms that transform a data structure by using a constant amount of memory storage. We demonstrate that our proposed method reduces memory usage by eliminating the look-up table traditionally employed in the computation of bit-reversal indexes.
11 citations
16 Jul 2000
TL;DR: The present algorithm is motivated by the multilevel fast multipole algorithm (MLFMA), but is different from that described by Brandt (1991), where the restriction of the Fourier data to an Ewald sphere is lifted so that it can be arbitrarily distributed as well.
Abstract: The nonuniform fast Fourier transform (FFT) on a line has been of interest to a number of scientists for its practical applications. However, not much has been written on Fourier transforming sparse spatial data where the Fourier transform is needed at only sparse data points in the Fourier space in 2D or 3D. It finds applications in remote sensing, inverse problems, and synthetic aperture radar where the scattered field is related to the Fourier transform of the scatterers. We outline an algorithm to perform this transform in NlogN operations, where N is the number of spatial data available, and we assume that the number of Fourier data desired is also of O(N). The algorithm described here is motivated by the multilevel fast multipole algorithm (MLFMA), but is different from that described by Brandt (1991). In MLFMA, an embedded fast Fourier transform algorithm is inherent, where the spatial data is arbitrarily distributed, but the Fourier data is required on the Ewald sphere. In the present algorithm, the restriction of the Fourier data to an Ewald sphere is lifted so that it can be arbitrarily distributed as well. The present algorithm can be easily generalized to 3D.
11 citations