伯格谱估计算法的一种改进

An Improved Algorithm for Estimating Power Spectrum

在实数据情况下 ,由伯格算法得到的谱有时会出现谱分裂和谱峰偏移。已有文献对这种现象产生的原因作了各种分析和猜测。其中之一认为由于一阶反射系数的计算存在误差 ,导致预测误差滤波器 ( PEF)其余系数计算的误差。根据这种分析 ,本文提出了一种改进算法。该算法不是直接利用伯格算法计算一阶反射系数 ,而是按二阶 PEF输出总功率最小的原则 ,求解二阶 PEF系数 ,再求得一阶反射系数。在获得二阶 PEF系数之后 ,仍用伯格递推算法求其他高阶系数。结果 ,在几乎不增加计算量的情况下 ,使谱估计的性能得到明显改善。对信号长度为 1 / 4信号周期的奇数倍且初相为π/ 4时的最坏情况 ,在计算机上进行了计算。结果表明 ,谱峰偏移大为减小。

In the case of real data, the spectral estimate obtained by Burg algorithm sometimes has line splitting and peak shifting. The different analyses and guess for this phenomenon have been done. An error is existed in calculating the first reflecting coefficient, which results in the errors of the higher prediction-error-filter (PEF) coefficients. Based on this analysis, an improved algorithm is proposed. In this algorithm, the first reflecting coefficient is not directly obtained by Burg algorithm but by solving the coefficients of second order PEF coefficients according to making the total output power minimize. After obtaining the coefficients of the second order PEF, the other higher order coefficients of PEF are calculated by using Burg recursive algorithm. The performance of the resulting spectral estimate is obviously improved without increasing computation cost. For the worst situation where the length of signal is the odd multiple number of signal period and the original phase is π/4, some calculation has been done on computer. Results indicate that the peak shifting of the spectrum is reduced.