An Adaptation of the Fast Fourier Transform for Parallel Processing
Journal of the ACM (JACM)
Algorithms: Algorithm 338: algol procedures for the fast Fourier transform
Communications of the ACM
Algorithms: Algorithm 339: an algol procedure for the fast Fourier transform with arbitrary factors
Communications of the ACM
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IEEE Transactions on Computers
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IEEE Transactions on Computers
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IEEE Transactions on Computers
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IEEE Transactions on Computers
Radix-4 FFT algorithms with ordered input and output data
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
FFT algorithms for vector computers
Parallel Computing
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A procedure for factoring of the N脳N matrix representing the discrete Fourier transform is presented which does not produce shuffled data. Exactly one factor is produced for each factor of N, resulting in a fast Fourier transform valid for any N. The factoring algorithm enables the fast Fourier transform to be implemented in general with four nested loops, and with three loops if N is a power of two. No special logical organization, such as binary indexing, is required to unshuffle data. Included are two sample programs, one which writes the equations of the matrix factors employing the four key loops, and one which implements the algorithm in a fast Fourier transform for N a power of two. The algorithm is shown to be most efficient for Na power of two.