The paper compares the accuracy of two different three points Interpolated Discrete Fourier Transform (M3IpDFT and C3IpDFT) algorithms in the presence of Gaussian white noise. The above two algorithms use the magnitude and the complex value of spectrum line for interpolation, respectively. The theoretical expressions of variances of frequency estimation due to noise are derived and then verified by simulations. From the theoretical and simulation results, the variances of frequency estimation are inversely proportional to the signal-to-noise ratio (SNR) and the length of DFT. Simulation shows that the C3IpDFT outperforms the M3IpDFT.

中文翻译：

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噪声对三点插值离散傅里叶变换频率估计的影响比较

论文比较了两种不同的三点插值离散傅里叶变换（M3IpDFT和C3IpDFT）算法在存在高斯白噪声的情况下的精度。以上两种算法分别使用谱线的幅值和复数值进行插值。推导了噪声引起的频率估计方差的理论表达式，并通过仿真进行了验证。从理论和仿真结果来看，频率估计的方差与信噪比 (SNR) 和 DFT 的长度成反比。仿真表明 C3IpDFT 优于 M3IpDFT。