离散频谱的能量重心校正法

针对离散频谱三点卷积幅值校正方法只能校正幅值，不能校正频率和相位的问题，从理论上推导了常用离散窗谱函数的能量重心就是坐标原点，由此得到了能量重心法校正频率和相位的公式。误差分析和仿真计算表明：与其它校正方法相比，此方法能对多段平均功率谱直接进行校正，算法简单，计算速度快，负频率成分和间隔较近的多频率成分产生的干涉现象所带来的误差对精度的影响小，校正方法适用于各种对称窗函数，解决了三点卷积幅值校正法不能校正信号频率和相位的缺点。在工程应用中，对噪声小的信号，推荐加Hanning窗n=1（三点卷积法）的方法进行校正，频率间隔大于等于4个频率分辨率的信号校正后的幅值误差小于1％，频率误差小于0.01个频率分辨率，相位误差小于5度，这种方法不适用于频率过于密集的分析场合或连续谱。

Energy Centrobaric Correction Method for Discrete Spectrum

In order to solve the problem that Three point Convolution Correction Method for discrete spectrum is unable to correct frequency and phase, this paper demonstrates that the energy centroid of discrete spectrum of frequently used windows is near the origin of coordinate, and deduces the correction formula of frequency and phase using Energy Centrobaric Correcting Method. The error analysis and simulation calculation demonstrate that Energy Centrobaric Correction Method has features as follows. Compared with other correcting methods, this method can correct multi zone mean power spectrum directly, and is simple and fast. The affection of interference caused by negative frequency and close multi frequency is small. This method does not depend on window functions, and solves the problem of Three point Convolution Correction Method that can not correct frequency and phase. In engineering application, we recommend to correct the spectrum involved low level noise with Hanning window and n=1. When the signal of which frequency intervals are no less than 4 resolutions is corrected, the error of amplitude, frequency and phase is under 1%, 0.011 resolution and 5 degrees respectively. But this method is not suitable to the dense or continuous spectrum.