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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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Journal ArticleDOI
He Wen1, Zhaosheng Teng1, Yong Wang1, Bo Zeng1, Xiaoguang Hu2 
TL;DR: The interpolated FFT algorithm based on the minimized sidelobe window is considered, and its calculate procedure and formulas are given, which is free of solving high-order equations, making the method a good choice for real-time applications.
Abstract: This paper focuses on the low-computation harmonic-analysis procedure with sufficient suppression of spectral leakage and picket-fence effect. The interpolated FFT algorithm based on the minimized sidelobe window is considered, and its calculate procedure and formulas are given, which is free of solving high-order equations. The implementation of the proposed algorithm in the digital-signal-processor (DSP) based three-phase harmonic ammeter is also introduced. The proposed algorithm has the major advantages that the calculate formulas for harmonic parameters can be easily implemented by hardware multipliers, making the method a good choice for real-time applications. The simulation and application results validate the accuracy and efficiency of the proposed algorithm.

62 citations

Journal ArticleDOI
TL;DR: Empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time and it is shown that FAD FT-2 not only generally outperforms F ADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals.
Abstract: In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.

61 citations

Journal ArticleDOI
Maria Eleftheriou1, Blake G. Fitch1, Aleksandr Rayshubskiy1, T. J. C. Ward1, R. S. Germain1 
TL;DR: The volumetric FFT outperforms a port of the FFTW Version 2.1.5 library on large-node-count partitions and compared with that of the Fastest Fourier Transform in the West (FFTW) library.
Abstract: This paper presents results on a communications-intensive kernel, the three-dimensional fast Fourier transform (3D FFT), running on the 2,048-node Blue Gene®/L (BG/L) prototype. Two implementations of the volumetric FFT algorithm were characterized, one built on the Message Passing Interface library and another built on an active packet Application Program Interface supported by the hardware bring-up environment, the BG/L advanced diagnostics environment. Preliminary performance experiments on the BG/L prototype indicate that both of our implementations scale well up to 1,024 nodes for 3D FFTs of size 128 × 128 × 128. The performance of the volumetric FFT is also compared with that of the Fastest Fourier Transform in the West (FFTW) library. In general, the volumetric FFT outperforms a port of the FFTW Version 2.1.5 library on large-node-count partitions.

61 citations

Journal ArticleDOI
TL;DR: This work proposes a nonequispaced hyperbolic cross FFT based on onehyperbolicCross FFT and a dedicated interpolation by splines on sparse grids and allows for the efficient evaluation of trigonometric polynomials with Fourier coefficients supported on the hyperbolics cross at arbitrary spatial sampling nodes.
Abstract: A straightforward discretization of problems in $d$ spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives. We propose a nonequispaced hyperbolic cross FFT based on one hyperbolic cross FFT and a dedicated interpolation by splines on sparse grids. Analogously to the nonequispaced FFT for trigonometric polynomials with Fourier coefficients supported on the full grid, this allows for the efficient evaluation of trigonometric polynomials with Fourier coefficients supported on the hyperbolic cross at arbitrary spatial sampling nodes.

61 citations

Journal ArticleDOI
TL;DR: In this article, a group-harmonic weighting distribution is proposed for system-wide interharmonic evaluation in power systems, which can restore the dispersing spectral leakage energy caused by the fast Fourier transform, and calculate the power distribution proportion around the adjacent frequencies at each harmonic to determine the inter harmonic frequency.
Abstract: The fast Fourier transform (FFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals with power system harmonics in power systems. However, the misapplications of FFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of group-harmonic weighting distribution is proposed for system-wide inter-harmonic evaluation in power systems. The proposed algorithm can restore the dispersing spectral leakage energy caused by the FFT, and calculate the power distribution proportion around the adjacent frequencies at each harmonic to determine the inter-harmonic frequency. Therefore, not only high-precision in integer harmonic measurement by the FFT can be retained, but also the inter-harmonics can be identified accurately, particularly under system frequency drift. The numerical examples are presented to verify the performance of the proposed algorithm.

60 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202224
20211
20188
201757
201692