中文摘要：

研究用FFT谱连续细化傅里叶变换分析法进行离散频谱校正时的参数估计误差。分析无噪声情况下频率、相位、幅值的估计误差随细化倍数的变化规律，估计精度随细化倍数的增大而提高，当细化倍数大于40时，最大估计误差几乎可忽略不计。在高斯白噪声的影响下，细化后频谱序列最大值找错的概率随细化倍数的增加而增加，综合考虑频率分辨率对频率估计精度的影响及频谱序列最大值找错的概率，提出用归一化频率估计综合误差和归一化频率估计最大可能误差两个指标评价此校正法对频率的估计精度，并基于此给出不同信噪比条件下的最优细化倍数。采用非线性最小二乘拟合法对噪声影响下的FFT谱连续细化傅里叶变换分析校正法进行改进，通过仿真模拟验证改进后该校正方法具备更高的校正精度和抗噪能力。

英文摘要：

The parameter estimation error of continuous zoom analysis Fourier transform is studied by applying FFT and FT to spectrum correction. The relation between estimation error of frequency, phase and amplitude and zoom multiples is revealed in the presence of noise-free signal. Parameter estimation accuracy can be improved by increasing zoom multiples, and the maximum error of each parameter is very little when zoom multiple is greater than 40. To the signal with Gaussian white noise, the probability of finding the wrong maximum spectrum line increases with the rise of zoom multiple. Considering the influence of frequency resolution on frequency estimation accuracy and the probability mentioned above, two evaluation indicators, called normalized frequency estimation comprehensive error （NFE） and normalized frequency estimation maximum error （NFEM） are given to provide the best zoom multiple under different signal to noise ratio. The FFT and FT spectrum correction method is modified and improved, and the simulation results indicate that the improved method has higher correction accuracy and anti-noise ability.