Bit Reversal through Direct Fourier Permutation Method and Vectorial Digit Reversal Generalization

This paper describes the Direct Fourier Permuation Algorithm, an efficient method of computing Bit Reversal of natural indices [1, 2, 3, ..., 2^k] in a vectorial manner (k iterations) and also proposes the Vectorial Digit Reversal Algorithm, a natural generalization of Direct Fourier Permutation Algorithm that is enabled to compute the r-digit reversal of natural indices [1, 2, 3, ..., r^k] where r is an arbitrary radix. Matlab functions implementing these two algo- rithms and various test and comparative results are presented in this paper to support the idea of inclusion of these two algorithms in the next Matlab Signal Processing Toolbox official distribution package as much faster alternatives to current Matlab functions bitrevorder and digitrevorder.