对两个频率相近成分作频谱校正的非迭代形式研究

双频率模型(DFM)的频谱校正是否存在类似于单频率模型(CSM)的非迭代校正形式，以及相应的校正性能尚未见文献报道。作者分析了CSM存在简单校正公式的原因,给出了DFM加矩形窗的非迭代校正式,采用包含幅度相差10倍的DFM对校正式进行了仿真考核。研究结果表明:CSM存在简单校正式的原因在于窗谱函数可以分解为超越函数与有理分式的乘积,前者在相邻的离散谱线上绝对值相等;由这两个特性可建立DFM相对简单频谱校正关系,但是除了DFM加矩形窗的情形外,其它均涉及高于2次的多项式方程。仿真考核表明,给出的校正式对幅度强的成分的误差小于幅度弱者,并且当DFM频率间隔超过两个经典频率分别率时，最后采用CSM校正式。

Non-iterative spectrum correction for signals with closely spaced frequency components

For a complex sinusoid model (CSM), there exists a set of explicit expressions for spectrum correction. However, it is not clear whether there exist corresponding formulas for double-frequency model (DFM). To determine feasibility of the explicit expressions to the DFM, the innate of ratio correction for CSM was analyzed. The explicit correction formulas were present for the DFM without windowing, and were examined by a DFM signal with one strong component amplitude 10 times the weaker one. The study shows, firstly, the essence of existence of simple correction expression for the CSM is that the spectrum functions of common windows can be factorized as transcendental part multiplying a rational fraction, and absolutes of the former are equal on the neighbor lines of discrete spectrum. Secondly, with the above properties, the frequency equations for DFM, only containing the rational fraction, can be deduced. Only for the case of the DFM without windowing, can the frequency equations be simplified to a quadratic polynomial, and will be implicated with at least cubic polynomial for other cases, such as Hanning window. In conclusion, it is not worthy or impossible to find the explicit correction expressions except for the DFM without windowing. The simulation results show that, the precision of the given correction expression can be achieved for the strong component better than the weaker one. In the frequency scanning 0.5~2.0 resolutions of the fast Fourier transform. But the CSM based correction is preferred if the frequency difference of DFM is greater than 2 canonical resolutions of FFT.