Showing papers on "Cyclotomic fast Fourier transform published in 1974"
TL;DR: The CORDIC iteration is applied to several Fourier transform algorithms and a new, especially attractive FFT computer architecture is presented as an example of the utility of this technique.
Abstract: The CORDIC iteration is applied to several Fourier transform algorithms. The number of operations is found as a function of transform method and radix representation. Using these representations, several hardware configurations are examined for cost, speed, and complexity tradeoffs. A new, especially attractive FFT computer architecture is presented as an example of the utility of this technique. Compensated and modified CORDIC algorithms are also developed.
304 citations
TL;DR: The formulation is very general and includes block processing and sectioning as special cases and, when used with various fast algorithms for short length convolutions, results in improved multiplication efficiency.
Abstract: This paper presents two formulations of multi-dimensional digital signals from one-dimensional digital signals so that multidimensional convolution will implement one-dimensional convolution of the original signals. This has reduced an important word length restriction when used with the Fermat number transform. The formulation is very general and includes block processing and sectioning as special cases and, when used with various fast algorithms for short length convolutions, results in improved multiplication efficiency.
137 citations
TL;DR: This paper presents an algorithm for making use of symmetry in the fast Fourier transform in a simple and general way which is applicable to nearly all space groups and makes possible economical forward and reverse transforms of large unit cells in core.
Abstract: This paper presents an algorithm for making use of symmetry in the fast Fourier transform in a simple and general way which is applicable to nearly all space groups. This allows one to reduce storage requirements to approximately what is needed for an asymmetric unit of the electron-density function, and hence makes possible economical forward and reverse transforms of large unit cells in core.
7 citations
TL;DR: It is shown that a fast Fourier processor having an attractive cost performance ratio can be built by employing serial arithmetic in the implementation of the algorithm developed.
Abstract: An algorithm is presented that introduces two degrees of parallelism into the implementation of fast Fourier transform (FFT) processors. That is, both the radix of factorization and the number of arithmetic units may be selected to achieve the required processing speed. A serial vector multiplier that is ideally suited to the implementation of a general radix arithmetic unit is described. It is subsequently shown that a fast Fourier processor having an attractive cost performance ratio can be built by employing serial arithmetic in the implementation of the algorithm developed.
6 citations
TL;DR: This correspondence presents an improved implementation of the fast Fourier transform without sorting that is more efficient than the one presented here.
Abstract: This correspondence presents an improved implementation of the fast Fourier transform without sorting.
3 citations
01 Oct 1974
TL;DR: A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms.
Abstract: A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms. The reduced accuracy required for intermediate calculations is retained. Additionally, the fast Fourier transform can be used giving computational savings.
2 citations
TL;DR: In this paper, a simple procedure is presented to develop a fast Fourier transform (FFT) program for PQ points starting from a program for Q points, with emphasis on Q = 2M.
Abstract: A simple procedure is presented to develop a fast Fourier transform (FFT) program for PQ points starting from a program for Q points, with emphasis on Q = 2M. The transformation with respect to the factor P is followed by a transformation of P groups of Q points each using the existing subroutine, then the array is unscrambled with respect to P.
1 citations
01 Sep 1974
1 citations
15 Apr 1974
1 citations
TL;DR: A fast method is presented for simulating a class of systems that includes certain regular neural networks based on neurons that perform a weighted spatial summation as a part of their operation through high-speed convolution via the Fast Fourier Transform.
Abstract: A fast method is presented for simulating a class of systems that includes certain regular neural networks based on neurons that perform a weighted spatial summation as a part of their operation. The method employs high-speed convolution via the Fast Fourier Transform. Some important aspects are emphasized: first, even though the FFT is essential, the neurons do not need to be completely linear (they can have time varying thresholds for example); second, simulations of networks with very dense interconnections are encouraged (they take no more time then sparse ones using this method); and finally, the method is suggestive of similar but more general computational schemes.