Pruning split-radix FFT with time shift

Yuan, Longtao; Tian, Xiang; Chen, Yaowu

doi:10.1109/icecc.2011.6066654

Cited by 6 publications

(12 citation statements)

References 17 publications

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“…It is noteworthy to stress that the SRFFT pruning− time−shift approach implicitly assumes that lengths L and N may take values equal to the power of two only. Figure 7 reports the number of required arithmetic operations to execute our proposed unified DFT COMM method and those required by the competing pruned DFTs of [14]. These results verify that our approach requires fewer arithmetic operations than those required to perform the SRFFT pruning−time−shift algorithm in all the reported tests.…”

Section: Comparisons With Pruning-based Algorithmssupporting

confidence: 63%

“…An analysis of the two alternatives (DFT DIT−DIF−Pr and DFT DIF−DIT−Pr ) verifies that the DFT DIT−DIF−Pr requires a smaller or as maximum equal number of arithmetic operations compared with the DFT DIF−DIT−Pr , so the use of the DFT DIT−DIF−Pr is strongly recommended when the decomposed and pruned transforms are required. Next, we demonstrate that our proposal requires a lower number of arithmetic operations than any of the pruning-based competing methods [3,14,23,24]. Further, we demonstrate that both decomposed transforms (DFT DIF−DIT−Pr and DFT DIT−DIF−Pr ) can be obtained from a general decomposition methodology.…”

Section: Novel Contributionsmentioning

confidence: 99%

“…Here, we use the following feasible constraints: the values of N vary as follows: N = {2 6 , 2 7 ,…, 2 20 } and k s = L o , where L o represents the number of consecutive output coefficients to be calculated. In different test scenarios, the SFFTv1, SFFTv2, and SFFTv3 algorithms deliver successful results: the first of them for N = {2 13 , 2 14 ,…, 2 20 } and k s = L o = 50, the second of them for N = {2 13 , 2 14 ,…, 2 20 } and k s = L o = 50, and finally, the third of them for N = {2 10 , 2 11 ,…, 2 20 } and k s = L o = 50, respectively. Furthermore, it was experimentally corroborated that the DFT COMM algorithm was able to deliver efficient results in all such tested sparse scenarios, as reported in Table 9.…”

Section: Comparison With the Sfft-related Algorithmsmentioning

confidence: 99%

“…Some of them prune the input of a specific FFT algorithm, others prune the output, and just a few can prune the input and output (input-output) at the same time. Markel in [1], and Skinner in [13], proposed the input pruning methods based on a radix-2 FFTs, while Yuan et al, in [14], proposed an input pruning of a split-radix FFT. The approaches of Bouguezel et al [15] and Fan et al [16] are applicable for output pruning a radix-2 FFTs, while the Xu's et al [3] proposal suggests pruning the output of a split-radix FFT.…”

Section: Related Workmentioning

confidence: 99%

“…Yuan et al, in [14], proposed another competing, the so-called SRFFT pruning−time−shift method via modifying the SRFFT pruning employing a time shifting approach that yields the input pruning algorithm based on the SRFFT methodology for L consecutive non-zero input elements. It is noteworthy to stress that the SRFFT pruning− time−shift approach implicitly assumes that lengths L and N may take values equal to the power of two only.…”

Section: Comparisons With Pruning-based Algorithmsmentioning

confidence: 99%

See 4 more Smart Citations

Unified commutation-pruning technique for efficient computation of composite DFTs

Castro-Palazuelos

Medina-Melendrez

Torres-Roman

et al. 2015

EURASIP J. Adv. Signal Process.

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An efficient computation of a composite length discrete Fourier transform (DFT), as well as a fast Fourier transform (FFT) of both time and space data sequences in uncertain (non-sparse or sparse) computational scenarios, requires specific processing algorithms. Traditional algorithms typically employ some pruning methods without any commutations, which prevents them from attaining the potential computational efficiency. In this paper, we propose an alternative unified approach with automatic commutations between three computational modalities aimed at efficient computations of the pruned DFTs adapted for variable composite lengths of the non-sparse input-output data. The first modality is an implementation of the direct computation of a composite length DFT, the second one employs the second-order recursive filtering method, and the third one performs the new pruned decomposed transform. The pruned decomposed transform algorithm performs the decimation in time or space (DIT) data acquisition domain and, then, decimation in frequency (DIF). The unified combination of these three algorithms is addressed as the DFT COMM technique. Based on the treatment of the combinational-type hypotheses testing optimization problem of preferable allocations between all feasible commuting-pruning modalities, we have found the global optimal solution to the pruning problem that always requires a fewer or, at most, the same number of arithmetic operations than other feasible modalities. The DFT COMM method outperforms the existing competing pruning techniques in the sense of attainable savings in the number of required arithmetic operations. It requires fewer or at most the same number of arithmetic operations for its execution than any other of the competing pruning methods reported in the literature. Finally, we provide the comparison of the DFT COMM with the recently developed sparse fast Fourier transform (SFFT) algorithmic family. We feature that, in the sensing scenarios with sparse/non-sparse data Fourier spectrum, the DFT COMM technique manifests robustness against such model uncertainties in the sense of insensitivity for sparsity/non-sparsity restrictions and the variability of the operating parameters.

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Section: Comparisons With Pruning-based Algorithmssupporting

confidence: 63%

Section: Novel Contributionsmentioning

confidence: 99%