北京航空航天大学学报 ›› 2011, Vol. 37 ›› Issue (10): 1317-1320,1325.doi: CNKI:11-2625/V.20111020.1126.006

• 论文 • 上一篇    下一篇

有限长Ramanujan-Fourier快速变换及频率估计

郭旭静, 王祖林   

  1. 北京航空航天大学 电子信息工程学院, 北京 100191
  • 收稿日期:2010-06-08 出版日期:2011-10-30 发布日期:2011-11-03
  • 作者简介:郭旭静(1975-),女,山西长治人,讲师,guoxujing@126.com.
  • 基金资助:

    中央高校基本科研业务费专项资金资助项目; 国家自然科学基金资助项目(61071070)

Fast transform and frequency estimation algorithm of finite Ramanujan Fourier transformation

Guo Xujing, Wang Zulin   

  1. School of Electronics and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2010-06-08 Online:2011-10-30 Published:2011-11-03

摘要: 近来出现的Ramnujan-Fourier变换(RFT,Ramanujan Fourier Transformation)是以"Ramanujan和"为基向量的算术变换,该变换可提供分数频率分辨力.首先分析了有限长Ramanujan频谱特点,给出了基向量分布情况,推导了该变换的快速算法,比较了有限长RFT与快速傅里叶变换的乘法计算量;其次,给出了利用RFT的递归峰值检测频率估计算法,并分析了RFT的频率分辨率和适用特点,在非高斯噪声条件下,仿真比较了RFT与傅里叶变换对信号进行频率估计的性能,得到在信噪比为-20 dB的非高斯噪声情况下,频率估计的归一化均方误差可以达到 10-3.

Abstract: 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.

中图分类号: 


版权所有 © 《北京航空航天大学学报》编辑部
通讯地址:北京市海淀区学院路37号 北京航空航天大学学报编辑部 邮编:100191 E-mail:jbuaa@buaa.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发