基于FFT的正弦信号频率估算新方法

A New FFT Based Algorithm for Sinusoid Frequency Estimation

介绍一种新的基于FFT的正弦信号频率估计的插值方法。该方法利用了DFT最大值谱线及与其相邻两根谱线系数的实部(或虚部)进行插值得到频率估计值。与传统的算法不同,在本方法中不需要判断第二大峰值谱线的位置,避免了找该谱线时可能会出错,从而使频率估算值出错的问题。另外,插值时算法中先对几根谱线DFT系数的实部和虚部的大小进行比较,实部大于虚部时用利用实部进行插值,反过来则利用虚部进行插值,从而减少了噪声的影响并提高了估算精度。数值模拟结果表明利用该方法可以得到良好的插值效果,能取得很小的频率估算偏差。

A new interpolation algorithm for sinusoid frequency estimation based on FFF is developed in this paper. Real parts （or imaginary parts） of DFT coefficients of the maximum and its two neighboring spectral peaks are used for the interpolation in the algorithm to acquire the estimation frequency. Contrast to the traditional approaches, it does not need to know the position of the second largest spectral peak; therefore, the possibility of incorrect estimation because of missed location is avoided when the position is searched. In addition, the real parts and imaginary parts of the DFF coefficients are compared before the interpolation and real parts are chosen for the interpolation when they are larger than the imaginary parts, and vice versa. As a result, the affection of noise on estimation is reduced and thus the estimation accuracy is improved. The mathematic simulation result indicates that the algorithm holds a good interpolation effect with which a very small mean estimation error can be achieved.