Issue No. 01 - January (1974 vol. 23)
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.
Bit reversal, fast Fourier transform, unscrambling.
R.J. Polge, J.M. Carswell, B.K. Bhagavan, "Fast Computational Algorithms for Bit Reversal", IEEE Transactions on Computers, vol. 23, no. , pp. 1-9, January 1974, doi:10.1109/T-C.1974.223771