A better FFT bit-reversal algorithm without tables

Yong, A.

doi:10.1109/78.91199

Cited by 20 publications

(3 citation statements)

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“…This permutation will be referred further in this paper as Fourier Permutation and is sometimes named the Buterfly Permutation [1], or Bit Reversal Permutation [2]- [9] due to the fact that the reversed bit representation of the permuted index of the initial 0-based index (see the following example) is implicitly sorted in ascending order. The Fourier Permutation of the 1-based index [1,2,3,4,5,6,7,8] is [1,5,3,7,2,6,4,8]. The stages leading to this permutation through the explicit calls in (1) are the following: [1,2,3,4,5,6,7,8] → [1,3,5,7,2,4,6,8] → [1,5,3,7,2,6,4,8] → [1,5,3,7,2,6,…”

Section: Introductionmentioning

confidence: 99%

“…The Fourier Permutation of the 1-based index [1,2,3,4,5,6,7,8] is [1,5,3,7,2,6,4,8]. The stages leading to this permutation through the explicit calls in (1) are the following: [1,2,3,4,5,6,7,8] → [1,3,5,7,2,4,6,8] → [1,5,3,7,2,6,4,8] → [1,5,3,7,2,6,4,8], where a left to right reading shows the permutations operated from the first to the last (the innermost) call.…”

Section: Introductionmentioning

confidence: 99%

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

Popescu-Bodorin

2011

Preprint

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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 algorithms 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Popescu-Bodorin

2011

Preprint

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“…Splitting the summation, applying (58) to π n (j) and π n (j +1), then adjusting missing terms for j = k/2 − 1 and j = k − 1, we obtainV (k, a, b) = k 23) is applied twice. Next, multiplying out terms and using property(23), the above expression simplifies toV (k, a, b) = 2k 1 (π n−1 (b/2)−1)−a k − (π n−1 (a/2)+1)−b k − 2π n−1 (π n−1 (a/2)+1)−b kwhich is equivalent to(37) with a = a, b = b, a = 2π n−1 (π n−1 (a/2)+1)−b, b = 2π n−1 (π n−1 (b/2)−1)−a, and e = 1. PROOF OF LEMMA 14 Assume a, b are both even.…”

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confidence: 99%

Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures

Mansour

2013

IEEE Trans. Signal Process.

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A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is presented, and closed-form expressions for BRP statistics including descents/ascents, major index, excedances/descedances, inversions, and serial correlations are derived. It is shown that BRP sequences have weak correlation properties. Moreover, a new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2-D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardware-efficient architectures for the proposed algorithms are developed. Simulation results of interleavers employed in modern communication standards demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.

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A Fast Recursive Algorithm and Architecture for Pruned Bit-reversal Interleavers

Mansour

2013

J Sign Process Syst

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A better FFT bit-reversal algorithm without tables

Cited by 20 publications

References 4 publications

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

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

Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures

A Fast Recursive Algorithm and Architecture for Pruned Bit-reversal Interleavers

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