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: A diagrammatic representation of mixed radix and highest radix FFT algorithms is derived, and two broad classes of FFT hard-ware are explored, from the point of view of speed, parallelism, radix number, and type of memory.
Abstract: The fast Fourier transform algorithm is derived by means of successive fracturing of one-dimensional data strings into two-dimensional arrays. Using this formulation, a diagrammatic representation of mixed radix and highest radix FFT algorithms is derived. Using this representation, two broad classes of FFT hard-ware are explored, from the point of view of speed, parallelism, radix number, and type of memory.
106 citations
TL;DR: In this article, a method for calculating structure factors by Fourier inversion of a model electron density map is presented, which is 3½ to 7 times less expensive than conventional methods for non-centrosymmetric space groups.
Abstract: A method is presented for calculating structure factors by Fourier inversion of a model electron density map. The cost of this method and of the standard methods are analyzed as a function of number of atoms, resolution, and complexity of space group. The cost functions were scaled together by timing both methods on the same problem, with the same computer. The FFT method is 3½ to 7 times less expensive than conventional methods for non-centrosymmetric space groups.
105 citations
TL;DR: In this paper, the fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description, and a stochastic decomposition technique facilitates utilization of the FFT algorithm.
Abstract: The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, p...
104 citations
TL;DR: The twiddle factor from the feedback in a traditional SDFT resonator is removed and thus the finite precision of its representation is no longer a problem and the accumulated errors and potential instabilities are drastically reduced in the mSDFT.
Abstract: This article presented a novel method of computing the SDFT that we call the modulated SDFT (mSDFT). The sliding discrete Fourier transform (SDFT) is a recursive algorithm that computes a DFT on a sample-by-sample basis. The accumulated errors and potential instabilities inherent in traditional SDFT algorithms are drastically reduced in the mSDFT. We removed the twiddle factor from the feedback in a traditional SDFT resonator and thus the finite precision of its representation is no longer a problem.
103 citations
TL;DR: A novel adaptable accurate way for calculating polar FFT and log-polar FFT is developed in this paper, named multilayer fractional Fourier transform (MLFFT), which provides a mechanism to increase the accuracy by increasing the user-defined computing level.
Abstract: A novel adaptable accurate way for calculating polar FFT and log-polar FFT is developed in this paper, named multilayer fractional Fourier transform (MLFFT). MLFFT is a necessary addition to the pseudo-polar FFT for the following reasons: It has lower interpolation errors in both polar and log-polar Fourier transforms; it reaches better accuracy with the nearly same computing complexity as the pseudo-polar FFT; it provides a mechanism to increase the accuracy by increasing the user-defined computing level. This paper demonstrates both MLFFT itself and its advantages theoretically and experimentally. By emphasizing applications of MLFFT in image registration with rotation and scaling, our experiments suggest two major advantages of MLFFT: 1) scaling up to 5 and arbitrary rotation angles, or scales up to 10 without rotation can be recovered by MLFFT while currently the result recovered by the state-of-the-art algorithms is the maximum scaling of 4; 2) No iteration is needed to obtain large rotation and scaling values of images by MLFFT, hence it is more efficient than the pseudopolar-based FFT methods for image registration.
103 citations