基于FFT的正弦信号幅值估计研究

Research on Amplitude Estimation of Sinusoid Signal Based on FFT

为了实现基于FFT求取正弦信号频率的同时得到信号的幅值,推导了利用Matlab中FFT计算得到的幅值系数与信号真正幅值之间的关系,研究了在仿真中准确估计信号幅值的两个影响因素,即频率分辨率和信噪比。针对信号长度小于FFT计算点数时出现的估计误差,提出了先对信号进行周期延拓再进行FFT计算的方法,并对频率分辨率进行了重新定义,使其适用范围更广。针对信噪比在幅值估计中的影响进行了定量分析,确定了基于FFT估计信号幅值方法的适用范围以及不同信噪比下的估计精度。

In order to obtain the frequency and amplitude of sinusoid signal based on FFT simultaneously, and the relationship between true signal amplitude and amplitude coefficient in FFT calculation based on Matlab was derived and then the two factors（ frequency resolution and SNR ） which influenced signal amplitude estimation accurately in simulation were discussed. Aiming at the estimation error resulted from that signal length is not equal to the calculation points in FFT,a method based on period extension before FFT calculation was presented,and frequency resolution which is widely used was redefined. Lastly,the SNR influence to amplitude estimation was analyzed quantitatively. Application scope and estimation accuracy for different SNR of this presented method were confirmed.