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Fast Computational Algorithms for Bit Reversal
January 1974 (vol. 23 no. 1)
pp. 1-9
R.J. Polge, Department of Electrical Engineering, University of Alabama
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.
Index Terms:
Bit reversal, fast Fourier transform, unscrambling.
R.J. Polge, B.K. Bhagavan, J.M. Carswell, "Fast Computational Algorithms for Bit Reversal," IEEE Transactions on Computers, vol. 23, no. 1, pp. 1-9, Jan. 1974, doi:10.1109/T-C.1974.223771
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