Showing papers on "Prime-factor FFT algorithm published in 1969"

An algorithm for computing the mixed radix fast Fourier transform

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.

The chirp z-transform algorithm and its application

Abstract: We discuss a computational algorithm for numerically evaluating the z-transform of a sequence of N samples. This algorithm has been named the chirp z-transform algorithm. Using this algorithm one can efficiently evaluate the z-transform at M points in the z-plane which lie on circular or spiral contours beginning at any arbitrary point in the z-plane. The angular spacing of the points is an arbitrary constant; M and N are arbitrary integers. The algorithm is based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N + M) log 2 (N + M) as opposed to being proportional to N · M for direct evaluation of the z-transform at M points. Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fourier transform program.

Fast fourier integration of piecewise polynomial functions

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.

A Fast Fourier Trans- form Algorithm for a Global, Highly Parallel Processor

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.

Comments on "A High-Speed Algorithm for the Computer Generation of Fourier Transforms"

Abstract: The efficiency (in terms of both execution time and storage requirements) of a recently presented algorithm for computing the fast Fourier transform is compared to that of alternative algorithms.