Fast Fourier Transforms: for fun and profit
AFIPS '66 (Fall) Proceedings of the November 7-10, 1966, fall joint computer conference
Notes on Shuffle/Exchange-Type Switching Networks
IEEE Transactions on Computers
Efficient Fast Fourier Transform Programs for Arbitary Factors with One Step Loop Unscrambling
IEEE Transactions on Computers
Implementation of Permutation Functions in Illiac IV-Type Computers
IEEE Transactions on Computers
Unified Matrix Treatment of the Fast Walsh-Hadamard Transform
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
A Fast Recursive Algorithm and Architecture for Pruned Bit-reversal Interleavers
Journal of Signal Processing Systems
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Radix 2 fast Fourier transform programs of the Gentleman-Sande type leave the transformed array in a scrambled order of frequencies. Unscrambling is accomplished by moving each element from its present location into a new location obtained by bit reversal. Bit reversal can be interpreted as an exchange of groups of bits symmetric with respect to a pivot. Two formulas are developed for simultaneous and sequential exchanging in place, with negligible auxiliary storage. Programs for one-step and sequential unscrambling were implemented. Binary unscrambling is useful to unscramble large arrays in peripheral storage. The one-step unscrambling program presented is more efficient than other programs available in the literature.