Showing papers on "Rader's FFT algorithm published in 1982"
TL;DR: An algorithm that reduces the computational effort to two-thirds of the effort required by most radix-2 algorithms and its structure is particularly appealing when transforming pure real or imaginary sequences and/or symmetric or antisymmetric sequences.
Abstract: This paper develops and presents a radix-2 fast Fourier transform (FFT) algorithm that reduces the computational effort (as measured by the number of multiplications) to two-thirds of the effort required by most radix-2 algorithms. The resulting algorithm is similar to one obtained by applying a principle suggested by Rader and Brenner; however, its structure is particularly appealing when transforming pure real or imaginary sequences and/or symmetric or antisymmetric sequences; furthermore, memory requirements (other than those for storing the input data) do not grow with the size of the transform.
43 citations
TL;DR: A time-efficient algorithm for calculating the discrete Fourier transform is developed which uses a prime factor decomposition of the DFT into multiple short prime length DFT's which are converted into cyclic convolutions by an index permutation based on number theory.
Abstract: A time-efficient algorithm for calculating the discrete Fourier transform is developed. It uses a prime factor decomposition of the DFT into multiple short prime length DFT's which are converted into cyclic convolutions by an index permutation based on number theory. The convolutions are evaluated by table look-up using distributed arithmetic. When programmed on a Z80 microprocessor, the algorithm is 2-20 times faster than conventional algorithms. The approach also makes it possible to add simple external logic to a micro-processor system to further increase the speed.
18 citations
TL;DR: It is shown that Singleton's mixed radix algorithm (MFFT) is the most flexible and uses the least memory, while the Winograd Fourier transform algorithm (WFTA) and Kolba-Parks prime factor algorithm (PFA) are the most efficient.
Abstract: The number of real operations and memory is presented for three efficient Fortran algorithms which compute the mixed radix discrete Fourier transform (DFT). It is shown that Singleton's mixed radix algorithm (MFFT) is the most flexible and uses the least memory, while the Winograd Fourier transform algorithm (WFTA) and Kolba-Parks prime factor algorithm (PFA) are the most efficient.
11 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