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快速傅里葉變換中計(jì)算倒序的新思路

劉大慶,  林浩然,  陳樹越

劉大慶, 林浩然, 陳樹越. 快速傅里葉變換中計(jì)算倒序的新思路[J]. 電子與信息學(xué)報(bào), 2018, 40(3): 758-762. doi: 10.11999/JEIT170595
引用本文: 劉大慶, 林浩然, 陳樹越. 快速傅里葉變換中計(jì)算倒序的新思路[J]. 電子與信息學(xué)報(bào), 2018, 40(3): 758-762. doi: 10.11999/JEIT170595
LIU Daqing, LIN Haoran, CHEN Shuyue. New Approach for Calculating Inversed Order Sequence in FFT[J]. Journal of Electronics & Information Technology, 2018, 40(3): 758-762. doi: 10.11999/JEIT170595
Citation: LIU Daqing, LIN Haoran, CHEN Shuyue. New Approach for Calculating Inversed Order Sequence in FFT[J]. Journal of Electronics & Information Technology, 2018, 40(3): 758-762. doi: 10.11999/JEIT170595

快速傅里葉變換中計(jì)算倒序的新思路

doi: 10.11999/JEIT170595
基金項(xiàng)目: 

國家自然科學(xué)基金(51176016)

New Approach for Calculating Inversed Order Sequence in FFT

Funds: 

The National Natural Science Foundation of China (51176016)

  • 摘要: 為了提高快速傅里葉變換的運(yùn)算效率，減少運(yùn)算時(shí)間，該文研究了FFT中倒序序列的計(jì)算。研究發(fā)現(xiàn)不同長度的倒序序列不相互獨(dú)立，它們之間有深刻的聯(lián)系，長度為N的倒序序列可以由長度為N/2的倒序序列生成。根據(jù)不同長度的倒序序列之間的相互關(guān)聯(lián)性，給出了新的倒序序列的計(jì)算方法及相應(yīng)的算法流程。通過計(jì)算仿真，驗(yàn)證了算法的正確性。該算法實(shí)現(xiàn)簡單，而且運(yùn)算效率高。與傳統(tǒng)算法相比，新算法可將計(jì)算效率提高3個(gè)數(shù)量級。
    Abstract: In order to improve the efficiency of Fast Fourier Transform (FFT) and reduce the computation time, an algorithm of inversed order sequence in FFT is studied. It is revealed that the inversed order sequences with different length N are not independent but have a deep connection, that is, the inversed order sequence with length N can be produced by the one with length N/2 according to a specific schedule. Based on the interconnectedness, a new approach for calculating the inversed order sequence with length N is proposed and the corresponding procedure flow is shown. The algorithm is simulated and the correctness of the algorithm is verified. The algorithm not only can be realized simply, but also has high efficiency. Compared with the traditional method, the new algorithm can improve the computing efficiency by three orders of magnitude.
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  • 收稿日期:  2017-06-21
  • 修回日期:  2017-11-28
  • 刊出日期:  2018-03-19

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