利用三条谱线计算频率紧邻的两个成分的参数

对频率间隔小于2个FFT分辨率的两个成分，直接使用比值校正法精度较差。就双频率模型(DFM)而言，利用谱峰附近三点的频谱可建立一个非线性复约束的DFM方程，它表现为一个复行列式等于零。给出了牛顿法求解该约束的具体格式，讨论了迭代的相关细节。研究结果表明：这种方法对初值要求比较苛刻；通过设置容许区间和随机重置初值等措施，可减弱对初值的要求；除了一些奇异点外，若初值选择合适。经过大约10次迭代，两个频率可收敛到准确值；当两个频率计算准确之后，幅值和相位可由另外一组线性关系解出。

Computing Parameters of Two Closely Spaced Components from Three Spectrum Lines

If the frequency difference between two closely spaced components is less than two fast Fourier transform(FFT) resolutions, it is impossible to retrieve parameters precisely by applying ratio-rectifying algorithm directly. As for the double frequency model(DFM), a complex constraint is deduced out between the two frequencies of DFM and the discrete spectrums of three lines nearby the spectrum peaks, which canonically takes on a determinant equal to 0. The iteration based on Newton method is present, and some details are discussed. It is shown that this method needs very strict initial values. By setting allowable zone(AZ), this requirement can be related by randomly resetting initial values in AZ after the iteration values move beyond AZ. Except for a few singular points, as long as the initial values are appropriate, the two frequencies can converge to the accured values after about 10 iteration rounds. After two frequencies are estimated accurately, the other parameters, amplitudes and phases can be obtained from another set of linear equations.