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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 827509, 12 pages
Research Article

Multiple Memory Structure Bit Reversal Algorithm Based on Recursive Patterns of Bit Reversal Permutation

1Group of Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany
2Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany
3Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka

Received 6 April 2014; Revised 4 June 2014; Accepted 5 June 2014; Published 17 July 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 K. K. L. B. Adikaram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With the increasing demand for online/inline data processing efficient Fourier analysis becomes more and more relevant. Due to the fact that the bit reversal process requires considerable processing time of the Fast Fourier Transform (FFT) algorithm, it is vital to optimize the bit reversal algorithm (BRA). This paper is to introduce an efficient BRA with multiple memory structures. In 2009, Elster showed the relation between the first and the second halves of the bit reversal permutation (BRP) and stated that it may cause serious impact on cache performance of the computer, if implemented. We found exceptions, especially when the said index mapping was implemented with multiple one-dimensional memory structures instead of multidimensional or one-dimensional memory structure. Also we found a new index mapping, even after the recursive splitting of BRP into equal sized slots. The four-array and the four-vector versions of BRA with new index mapping reported 34% and 16% improvement in performance in relation to similar versions of Linear BRA of Elster which uses single one-dimensional memory structure.