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算術(shù)傅里葉變換的實(shí)際實(shí)現(xiàn)方法

張憲超,  徐云,  陳國(guó)良

張憲超, 徐云, 陳國(guó)良. 算術(shù)傅里葉變換的實(shí)際實(shí)現(xiàn)方法[J]. 電子與信息學(xué)報(bào), 2004, 26(6): 935-939.
引用本文: 張憲超, 徐云, 陳國(guó)良. 算術(shù)傅里葉變換的實(shí)際實(shí)現(xiàn)方法[J]. 電子與信息學(xué)報(bào), 2004, 26(6): 935-939.
Zhang Xian-chao, XU Yun, Chen Guo-liang. Practical Implementation of the Arithmetic Fourier Transform[J]. Journal of Electronics & Information Technology, 2004, 26(6): 935-939.
Citation: Zhang Xian-chao, XU Yun, Chen Guo-liang. Practical Implementation of the Arithmetic Fourier Transform[J]. Journal of Electronics & Information Technology, 2004, 26(6): 935-939.

算術(shù)傅里葉變換的實(shí)際實(shí)現(xiàn)方法

Practical Implementation of the Arithmetic Fourier Transform

  • 摘要: 算術(shù)傅里葉變換(AFT)結(jié)構(gòu)簡(jiǎn)單，乘法量少，具有廣闊的應(yīng)用。但在AFT在具體實(shí)現(xiàn)中往往需要過(guò)采樣來(lái)滿足實(shí)際應(yīng)用中的精度要求。過(guò)采樣問(wèn)題是AFT的一個(gè)重要缺陷且限制了它的應(yīng)用范圍。該文利用AFT的線性插值實(shí)現(xiàn)技術(shù)精度很高的特點(diǎn)，在線性插值實(shí)現(xiàn)技術(shù)和過(guò)采樣技術(shù)的基礎(chǔ)上提出了一個(gè)新的實(shí)現(xiàn)策略，可以達(dá)到接近過(guò)采樣的精度。從而解決了AFT的過(guò)采樣問(wèn)題。
    Abstract: The Arithmetic Fourier Transform (AFT) is widely used because of its simple computational structure and little multiplications. But over-sampling is often needed for the implementation of AFT to meet the accuracy requirements in real applications and this is one of the main drawbacks of AFT and limits its application. In this paper, with the fact that linear interpolation implementation can gain very high accuracy, a new implementation is presented based on linear interpolation and over-sampling. This implementation can get accuracy close to that by over-sampling, thus the over-sampling problem of AFT is overcome.
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  • Bruns H.Grundlinien des Wissenschaftlichnen Rechnens[M].Leipzig,Personal Publication,1903.[2]Tufts D W,Sadasiv G.The arithmetic Fourier transform[J].IEEE ASSP Mag,1988,5(1):13-17.[3]Reed I S,Tufts D W,Xiao Yu,et al..Fourier analysis and signal processing by use of Mobius inversion formular[J].IEEE Trans.on Acoust,Speech,Signal Processing.1990,38(3):458-470[4]Reed I S,Shih M T,Troung T K,et al..A VLSI architecture for simplified arithmetic Fourier transform algorithms[J].IEEE Trans.on Acoust,Speech,Signal Processing,1993,40(5):1122-1132.[5]Lovine F P,Tantaratanas S.Some alternate realizations of the arithmetic Fourier transform.[C].Proceedings of the Twenty-Seventh Annual Asilomar Conference on Signals,Systems,and Computers,Pacific Grove,California,1993:310-314.[6]Ge Xi-Jin,Chen Nan-Xian,Chen Zhao-Dou.Efficient algorithm for 2-D arithmetic Fourier transform[J].IEEE Trans.on Signal Processing.1997,45(8):2136-2140[7]張憲超,武繼剛,蔣增榮,陳國(guó)良.離散傅里葉變換的算術(shù)傅里葉變換算法[J].電子學(xué)報(bào),2000,28(5):105-107.[8]張憲超,李寧,陳國(guó)良.離散余弦變換的改進(jìn)的箅術(shù)傅里葉變換算法[J].電子學(xué)報(bào),2000,28(9):88-90.[9]張憲超,陳國(guó)良,李寧.改進(jìn)的算術(shù)傅里葉變換算法[J].電子學(xué)報(bào),2001,29(3):329-331.[10]Wigley N Jullien.A sampling reduction for the arithmetic Fourier transform[C].Proc,32nd Midwest Symposium on Circuits and Systems,Champaign,IL,1990:841-844.[11]Knckaert L.A generalized Mobius transform,arithmetic Fourier transform,and primitive roots[J].IEEE Trans.on Signal Processing.1996,44(5):1307-1310[12]Schiff J,Walker W.The arithmetic Fourier transform.Analysis,geometry and groups:A Riemann legacy volume,Hadronic Press Collect.Orig.Artic.,Palm Harbor,FL,Hadronic Press,1993:613-625.[13]Walker W.The arithmetic Fourier transform and real neural networks:summability by primes[J].J.Math.Anal.Appl.1995,190:211-219.[14]Walker W.A summability method for the arithmetic Fourier transform[J].BIT.1994,34(2):304-309[15]Tufts D W,Chen H.Iterative realization of the arithmetic Fouier transform[J].IEEE Trans.Signal Processing.1993,41(1):152-161
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出版歷程
  • 收稿日期:  2003-01-07
  • 修回日期:  2003-05-27
  • 刊出日期:  2004-06-19

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