Volume 37 Issue 10
Oct.  2011
Turn off MathJax
Article Contents
Guo Xujing, Wang Zulin. Fast transform and frequency estimation algorithm of finite Ramanujan Fourier transformation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(10): 1317-1320,1325. doi: CNKI:11-2625/V.20111020.1126.006(in Chinese)
Citation: Guo Xujing, Wang Zulin. Fast transform and frequency estimation algorithm of finite Ramanujan Fourier transformation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(10): 1317-1320,1325. doi: CNKI:11-2625/V.20111020.1126.006(in Chinese)

Fast transform and frequency estimation algorithm of finite Ramanujan Fourier transformation

doi: CNKI:11-2625/V.20111020.1126.006
  • Received Date: 08 Jun 2010
  • Publish Date: 30 Oct 2011
  • A new Ramanujan transformation (RFT) is an arithmetic transformation based on Ramanujan sums, well adapted to the analysis of signals with fractional frequency. First, spectrum characteristic for the finite Ramanujan transform and the distribution model of Ramanujan base vectors were presented. Second, the fast algorithm for RFT was derived and the multiplication computation amount of the Ramanujan transformation with that of the fast Fourier transformation was compared. Furthermore, a recursive frequency estimation algorithm for RFT and the frequency resolution analysis had been presented. Finally, over the non-Gaussian noise, the frequency estimation performance comparison of RFT and Fourier transformation has shown that the normalized mean square error (MSE) of RFT can reach at 10-3 for the non-Gaussian noise with the SNR equal to -20 dB.

     

  • loading
  • [1] Knockaert L.A generalized mobius transform,arithmetic Frouier transform and primitive roots[J].IEEE Trans on Signal Processing,1996,44(5):1307-1310 [2] 高静,刘华宁.广义Mobius变换和算术Fourier变换[J].应用数学学报,2004,27(3):531-535 Gao jing,Liu Huaning.Generalized mobius transform and arithmetic Fourier transform[J].Acta Mathematicae Applicatae Sinica,2004,27(3):531-535 (in Chinese) [3] Planat M,Rosu H,Perrine S.Ramanujan sums for signal processing of low-frequency noise[C]//Proceedings of 2002 IEEE International Frequency Control Symposium and PDA Exhibition.New Orleans:[s.n.],2002:715-720 [4] Ramanujan S.On certain trigonometric sums and their applications in the theory of numbers[J].Trans Camb Phil Soc,1918,22:259-276 [5] Samadi S,Ahmad M O,Swamy M.Ramanujan sums and discrete Fourier transforms[J].IEEE Signal Processing Letters,2005,12(4):293-296 [6] Pei Soo Chang,Chang Kuo Wei.Odd ramanujan sums of complex roots of unity[J].IEEE Signal Processing Letters,2007,14(1):20-23 [7] Geetha K S,Ananthashayana V K.Fast multiplierless recursive transforms using Ramanujan numbers[C]//Proceedings of IEEE Multimedia,Signal Processing and Communication Technologies.Aliqarh,India:[s.n.],2009 :116-119 [8] Mainardi L T,Bertinelli M,Sassi R.Analysis of T-wave alternans using the Ramanujan transform[J].Computer in Cardiology Bologna,2008,35:605-608 [9] Mohand Lagha,Messaoud Bensebti.Doppler spectrum estimation by Ramanujan-Fourier transform(RFT)[J].Digital Signal Processing,2009,19(5):843-851
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views(3615) PDF downloads(6) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return