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

TL;DR

This paper introduces the Direct Fourier Permutation Algorithm and its generalization for vectorial digit reversal, offering faster alternatives for bit and digit reversal computations in signal processing.

Contribution

It presents novel algorithms for efficient bit and digit reversal, with implementations and comparisons supporting their integration into MATLAB's toolbox.

Findings

Algorithms outperform existing MATLAB functions in speed

Implementation in MATLAB demonstrates practical efficiency

Generalization to arbitrary radix enhances versatility

Abstract

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.