关键词: 白噪声, 参数估计, 傅里叶变换, 频谱校正

Abstract: 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.

Key words: Fourier transform, Parameter estimation, Spectrum correction, White noise