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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01 Jun 1975
TL;DR: The finite word length used in the computer causes round-off error in the calculation of Fourier coefficients in the decimation-in-time algorithm, which causes the statistical mean-square error to be determined.
Abstract: The finite word length used in the computer causes round-off error in the calculation of Fourier coefficients. When the fast Fourier transform method is used, the statistical mean-square error has been previously determined [3] for the case of the decimation-infrequency algorithm. This letter treats the same problem for the decimation-in-time algorithm.
6 citations
27 Apr 1993
TL;DR: The idea of RTA is extended to the M-D Cooley-Tukey (C-T) FFT algorithm and M-d Good-Thomas (G-Thomas) prime factor algorithm and a new implementation strategy for these algorithms that requires no interprocessor communication is discussed.
Abstract: To reduce or eliminate the interprocessor communications, I. Gertner, R. Tolimieri, and their colleagues proposed an M-D fast Fourier transform (FFT) algorithm, called the reduced transform algorithm (RTA). In the present work, the idea of RTA is extended to the M-D Cooley-Tukey (C-T) FFT algorithm and M-D Good-Thomas (G-T) prime factor algorithm. A new implementation strategy for these algorithms that requires no interprocessor communication is discussed. A hybrid algorithm which combines the C-T or G-T algorithm with RTA is also described. >
6 citations
25 May 1992
TL;DR: This paper shows a fast implementation method of a two dimensional (2D) filter based on fast convolution related to the fast Fourier transform (FFT) look up table that gives a good accurate selection of the desired frequency.
Abstract: This paper shows a fast implementation method of a two dimensional (2D) filter. The filter design is based on fast convolution related to the fast Fourier transform (FFT) look up table. This is then extended to the 2D FFT. The design and implementation of the system gives a good accurate selection of the desired frequency. The system has a step advantage of a reduction in the operation time. >
6 citations
24 Aug 2011
TL;DR: A "precision cache" method is proposed as the supplement of the mixed precision method to calculate of twiddle factor, and a work group split method is used to reduce the latency of access global memory frequently.
Abstract: In order to solve the low accuracy problem of GPU-based FFT, a mixed precision method is employed in this paper. A "precision cache" method is proposed as the supplement of the mixed precision method to calculate of twiddle factor. A work group split method is used to reduce the latency of access global memory frequently. The mixed precision FFT achieves 3 times accuracy improvement compared to CUFFT3.2 and 4 times peak performance to MKL FFT. The experiment shows that mixed precision method on CPU-GPU heterogeneous platform achieves high accuracy and efficient Fast Fourier Transform.
6 citations
TL;DR: This paper reports on the application of a new FFT algorithm, first described by Winograd, to the calculation of diffraction OTF that yields the same accuracy as that obtained by the Cooley-Tukey method but is up to four times faster.
Abstract: Although fast Fourier transform (FFT) algorithms based on the Cooley-Tukey method have been widely used for the computation of optical transfer function (OTF), the need for yet faster algorithms remains. This is particularly so since desk-top computers with modest speed and memory size have become essential tools in optical design. In this paper we report on the application of a new FFT algorithm, first described by Winograd, to the calculation of diffraction OTF. The algorithm is compared both in speed and in accuracy with the commonly used radix-2 FFT and with an autocorrelation method employing the Gaussian quadrature integration technique. It is found that the new algorithm yields the same accuracy as that obtained by the Cooley-Tukey method but is up to four times faster. Some other advantages and drawbacks are discussed.
6 citations