Fast transform and frequency estimation algorithm of finite Ramanujan Fourier transformation
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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.
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关键词:
- Ramanujan Fourier变换 /
- Ramanujan和 /
- 傅里叶变换 /
- 频率估计
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. -
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