Abstract
This chapter reviews parallel fast Fourier transform (FFT) algorithms. The sequence of length N to be transformed is distributed across P processors, and in each stage every processor performs independent computations on its respective subsequences in the local memory. The operation count of O(N log2 N/P) is similar to that of the serial algorithm, but is inversely proportional to the number of processors. For the most part, the sequences have complex elements, but recently developed parallel algorithms for sequences of real and conjugate symmetric elements are also reviewed. A new parallel algorithm for the discrete cosine transform (DCT), or sequences of real symmetric elements, is presented. We discuss radix-2 algorithms for the most part, but extensions to nonradix-2 transforms and the Bluestein FFT for arbitrary length sequences are also covered. The communication schemes used, are transposes and i-cycles. For simplification of the implementation, the multidimensional transform is presented first as an extension of the one-dimensional transform. Intrinsically multidimensional transforms are presented as a further extension.
This research was supported by the Office of Naval Research under grant N00014-89-J 1320.
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Pelz, R.B. (1997). Parallel FFTs. In: Keyes, D.E., Sameh, A., Venkatakrishnan, V. (eds) Parallel Numerical Algorithms. ICASE/LaRC Interdisciplinary Series in Science and Engineering, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5412-3_9
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