频率分辨率的研究

Research on the frequency resolution

频率分辨率对信号的Fourier频谱分析有重要意义。对信号Fourier变换的频率分辨率进行了研究,将信号Fourier变换频率分辨率的估计问题建模为一个优化问题,并建立了相应的优化模型。为了求解该模型,研究了最小可分辨频率差问题,导出了最小可分辨频率差的下界。进一步,得到了该优化模型的解,从而给出了信号Fourier变换频率分辨率的精确估计。研究证明,如果信号的观测时间是T,那么信号Fourier变换频率分辨率为1.6355/T。仿真实验的结果证明了结论的正确性。

Frequency Resolution is very important for the Fourier frequency spectrum analysis.This paper studies the question of how to estimate the frequency resolution of the Fourier transform of the signal.We treat the question of the estimation of the frequency resolution of the Fourier transform of the signal as an optimization problem and establish the relevant model.To solve this optimization problem,we study the question of the estimation of the smallest resolvable frequency difference,and derive the lower bound of the resolvable frequency difference.Furthermore,by solving the optimization problem,we obtain the exact estimation of the frequency resolution of the Fourier transform of the signal.It is shown that,for the signal with duration T,the frequency resolution of the Fourier transform of the signal is equal to 1.6355/T.The simulation results confirm its effectiveness.