复合FFT插值
Composite Interpolated Fast Fourier Transform

现有的插值FFT一般仅利用谱峰附近最高/次高谱线对。为了降低估计方差, 首先,利用谱峰附近4条谱线给出３个估计式;然后,对其加权平均。 给出了使方差最小的优化权系数, 以及优化后的方差。理论分析表明:新方法的方差小于Quinn方法;在整周期采样的情形下, 新方法方差只有Quinn方法的4/9。采用仿真算例对新方法进行了考核，结果表明:在高信噪比(SNR,50　dB)且非整周期采样条件下, 模拟方差与理论解一致;就所模拟的范围(SNR低至0　dB),模拟方差超过理论解最大仅有25%。
In most existing cases of interpolated fast Fourier (IpFFT), only the first and second highest spectral lines around the spectral peak are used. To decrease estimation variance, the composite IpFFT on four consecutive spectral lines around the peak is studied. Four consecutive lines render three estimators. The optimal coefficients at the minimum variance are deduced after the weighted average of the estimators. Theoretical analysis shows that the variance of the proposed composite correction is lower than that of the Quinn, and the greatest improvement is achieved under the coherent samplingcondition, with the variance deduction down to 4/9 of the Quinn′s. This theoretical analysis is validated through numerical simulation. It is shown that the empirical variance fits the theoretical expression when the signal-noise ratio (SNR) is high (50 dB) and the sampling is non-coherent. When the SNR is down to 0 dB, the empirical variance deviates from the theoretical expression no more than 25%.