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: The Fast Fourier Transform (FFT) as discussed by the authors is a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, and it can be used to compute an N = 210-point transform 100 times faster than using a direct approach.
Abstract: The fast Fourier transform (FFT), a computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained. Examples and detailed procedures are provided to assist the reader in learning how to use the algorithm. The savings in computer time can be huge; for example, an N = 210-point transform can be computed with the FFT 100 times faster than with the use of a direct approach.
271 citations
Journal Article•
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TL;DR: It is shown that for situations in which the relative number of zero-valued samples is quite large, significant time-saving can be obtained by pruning the FFT algorithm.
Abstract: There are basically four modifications of the N=2Mpoint FFT algorithm developed by Cooley and Tukey which give improved computational efficiency. One of these, FFT pruning, is quite useful for applications such as interpolation (in both the time and frequency domain), and least-squares approximation with trignometric polynomials. It is shown that for situations in which the relative number of zero-valued samples is quite large, significant time-saving can be obtained by pruning the FFT algorithm. The programming modifications are developed and shown to be nearly trivial. Several applications of the method for speech analysis are presented along with Fortran programs of the basic and pruned FFT algorithm. The technique described can also be applied effectively for evaluating a narrow region of the frequency domain by pruning a decimation-in-time algorithm.
270 citations
TL;DR: A new amending algorithm, poly-item cosine window interpolation, which is based on the interpolating algorithm proposed by V. Jain and T Grandke is presented, which improves the accuracy of the FFT, so it can be applied to the precision analysis for electrical harmonics.
Abstract: The fast Fourier transform (FFT) cannot be directly used in the harmonic analysis of an electric power system because of its higher errors, especially the phase error. This paper discusses the leakage phenomenon of FFT and presents a new amending algorithm, poly-item cosine window interpolation, which is based on the interpolating algorithm proposed by V. Jain and T Grandke. This new algorithm improves the accuracy of the FFT, so it can be applied to the precision analysis for electrical harmonics. The simulation result shows that applying different windows has different effects on the accuracy, and the Blackman-Harris window has the highest accuracy.
270 citations
10 Feb 2008
TL;DR: It can be formally proved that finding a collision in a randomly-chosen function from the family is at least as hard as finding short vectors in cyclic/ideal lattices in the worst case.
Abstract: We propose SWIFFT, a collection of compression functions that are highly parallelizable and admit very efficient implementations on modern microprocessors. The main technique underlying our functions is a novel use of the Fast Fourier Transform(FFT) to achieve "diffusion," together with a linear combination to achieve compression and "confusion." We provide a detailed security analysis of concrete instantiations, and give a high-performance software implementation that exploits the inherent parallelism of the FFT algorithm. The throughput of our implementation is competitive with that of SHA-256, with additional parallelism yet to be exploited.
Our functions are set apart from prior proposals (having comparable efficiency) by a supporting asymptotic security proof: it can be formally proved that finding a collision in a randomly-chosen function from the family (with noticeable probability) is at least as hard as finding short vectors in cyclic/ideal lattices in the worst case.
269 citations
TL;DR: In this article, the DC-FFT algorithm was used to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy, and a set of general formulas of the frequency response function for the elastic field was derived and verified.
Abstract: The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.
265 citations