Showing papers on "Split-radix FFT algorithm published in 1969"
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Abstract: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.
534 citations
01 Apr 1969
TL;DR: A technique is presented which utilizes the FFT and its associated computational speed, and computes the Fourier transform of "smooth" functions with better accuracy than the F FT alone.
Abstract: The fast Fourier transform (FFT) is a high-speed technique for computing the discrete Fourier transform of a function. The FFT is exact only for discrete (sampled) functions. A technique is presented which utilizes the FFT and its associated computational speed, and computes the Fourier transform of "smooth" functions with better accuracy than the FFT alone. In particular, algorithms using the FFT for transformation of piecewise polynomial functions are presented.
2 citations
01 Jan 1969
TL;DR: A fast Fourier transform (FFT) algorithm is presented for an unstructured, parallel ensemble of computing elements with global control that makes efficient use of a fixed-size memory and minimizes data transmission between computing elements.
Abstract: A fast Fourier transform (FFT) algorithm is presented for an unstructured, parallel ensemble of computing elements with global control. The procedure makes efficient use of a fixed-size memory and minimizes data transmission between computing elements. Included are some practical considerations of the trade-offs between element utilization and gain of computing speed via parallelism.
1 citations