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Parallel Architecture for Fast Transforms with Trigonometric Kernel
October 1994 (vol. 5 no. 10)
pp. 1091-1099

We present an unified parallel architecture for four of the most important fast orthogonal transforms with trigonometric kernel: Complex Valued Fourier (CFFT), Real Valued Fourier (RFFT), Hartley (FHT), and Cosine (FCT). Out of these, only the CFFT has a data flow coinciding with the one generated by the successive doubling method, which can be transformed on a constant geometry flow using perfect unshuffle or shuffle permutations. The other three require some type of hardware modification to guarantee the constant geometry of the successive doubling method. We have defined a generalized processing section (PS), based on a circular CORDIC rotator, for the four transforms. This PS section permits the evaluation of the CFFT and FCT transforms in n data recirculations and the RFFT and FHT transforms in n-1 data recirculations, with n being the number of stages of a transform of length N=r/sup n/. Also, the efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms.

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Index Terms:
Index Termsparallel architectures; transforms; Fourier transforms; multiprocessor interconnectionnetworks; parallel algorithms; mathematics computing; parallel architecture; fasttransforms; trigonometric kernel; fast orthogonal transforms; Complex Valued FourierTransform; Real Valued Fourier Transform; Hartley Transform; Cosine Transform;successive doubling method; constant geometry flow; perfect unshuffle; shuffle;hardware modification; circular CORDIC rotator; data recirculations; partitioned parallelarchitecture; cycle loss; systolic computation; butterflies; systolic array
Citation:
F. Argüello, J.D. Bruguera, R. Doallo, E.L. Zapata, "Parallel Architecture for Fast Transforms with Trigonometric Kernel," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 10, pp. 1091-1099, Oct. 1994, doi:10.1109/71.313124
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