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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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07 Jul 2013
TL;DR: The broadband accuracy of the mixed-form fast multipole algorithm (MF-FMA) is improved by applying rotation techniques using the coordinate system rotation technique and the pseudospectral projection based on fast Fourier transform (FFT).
Abstract: In this paper, the broadband accuracy of the mixed-form fast multipole algorithm (MF-FMA) is improved by applying rotation techniques. Two kinds of rotation methods are employed respectively. One is the coordinate system rotation technique. The other one is the pseudospectral projection based on fast Fourier transform (FFT). Either of them has certain advantages depending on the number of multipoles. Through rotation, translation matrices become very sparse, which enables us to save the storage as well as the CPU time. Hence, we can increase the number of multipoles in the low frequency regime to shift up the transition region of MF-FMA. The overall accuracy is thereby improved significantly.
TL;DR: A method for the computation of the Stokes formula using the Fast Hartley Transform CFHT techniques, which shows that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of F HT techniques is about two times faster than that of F FT techniques.
Abstract: This paper presents a method for the computation of the Stokes formula using the Fast Hartley Transform CFHT) techniques. The algorithm is most suitable for the computation of real sequence transform, while the Fast Fourier Transform (FFT) techniques are more suitable for the computa ton of complex sequence transform. A method of spherical coordinate transformation is presented in this paper. By this method the errors, which are due to the approximate term in the convolution of Stokes formula, can be effectively eliminated. Some numerical tests are given. By a comparison with both FFT techniques and numerical integration method, the results show that the resulting values of geoidal undulations by FHT techniques are almost the same as by FFT techniques, and the computational speed of FHT techniques is about two times faster than that of FFT techniques.
Patent•
22 Jul 2010TL;DR: In this paper, a fast Fourier transform (FFT) was proposed to reduce the amount of computation and the complexity of an FFT in a frequency division multiplexing (FDM) system.
Abstract: A fast Fourier transform (FFT) apparatus and method. The FFT method may include finding a number of subcarriers carrying valid data in reception data, determining a Fourier transform order on the basis of the number of subcarriers, performing complex multiplication on the reception data, and then performing a Fourier transform of the determined Fourier transform order. Using the FFT method, it is possible to reduce the amount of computation and the complexity of an FFT in a frequency division multiplexing (FDM) system and simplify a hardware structure.
TL;DR: The commenter states that the fast Fourier transform (FFT) processor of the aforementioned paper by C.C. Hui et al., contains many interesting and novel features, but it is pointed out that bit reversed input/output FFT algorithms, matrix transposers, and bit reversers have been noted in the literature.
Abstract: For the original paper see ibid., vol. 31, no. 11, p. 1751-61 (Nov. 1996). The commenter states that the fast Fourier transform (FFT) processor of the aforementioned paper by C.C. Hui et al., contains many interesting and novel features. However, it is pointed out that bit reversed input/output FFT algorithms, matrix transposers, and bit reversers have been noted in the literature. In addition, lower radix algorithms can be modified to be made computationally equivalent to higher radix algorithms. Many FFT ideas, including those of the above paper, can also be applied to other important algorithms and architectures.
01 Jan 1999
TL;DR: In this article, a new implementation of the two-dimensional FFT (2-D FFT) is proposed, which enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators.
Abstract: In this correspondence, a new implementation of the two- dimensional FFT (2-D FFT) is proposed. Compared with the usual separable solution, the new realization of the 2-D FFT has reduced arithmetic complexity. Computational savings are achieved because the 2- D case enables, after some modifications of the basic separable algorithm, scaling and inverse scaling of butterfly operators. The new improvement is also applied to other 2-D transforms: DCT-IV, DCT, and lapped transforms.