Burg算法在基于AR模型多普勒血流信号时频分析中的应用

Application of Burg Algorithm in Time-frequency Analysis of Doppler Blood Flow Signal Based on AR Modeling

多普勒超声血流信号是一个非平稳的高斯随机过程,其时频分布与血流的速度及其变化有密切的关系。由于假设信号在一定时间间隔内是平稳的,实际上难以获得同时具有较好的时间、频率分辨率的超声多普勒时频分布。一种估计多普勒超声血流信号时频分布的方法是基于Levinson-Durbin算法的自回归(AR)模型法。但用该算法估计出的参数的误差随时间间隔的缩短而增大。Burg提出一种递推算法,不需要计算自相关,而是用使前向与后向预测误差能量之和最小的方法求出模型的参数。我们将用两种算法估计出的多普勒时频分布及理论的时频分布进行比较,发现用Burg算法估计出的多普勒时频分布比用Levinson-Durbin递推算法估计出的多普勒时频分布更接近理论的时频分布,尤其是频率带宽性能得到了明显的改善。

The Doppler blood flow signal is inherently a nonstationary Gaussian random process whose time-frequency representation associates with the time-varying velocity of blood flow and its variations. With the assumption that the signal being analyzed is stationary during a short time interval, we can not get Doppler time-frequency representations with satisfactory time and frequency resolution. AR modeling based on Levinson-Durbin algorithm has been used to generate time-frequency representations of Doppler blood flow signals. But the errors of the parameters computed by the algorithm will be aggrandized by the shortening of the time interval. Burg has advanced an algorithm, which computes the parameters by making the sum of forward and backward forecasting errors minimum. In the paper, time-frequency representations computed by Burg and Levinson-Durbin algorithm were compared with the theoretical representation. We found that the time-frequency representations computed by Burg algorithm are more similar to the theoretical representation, especially in frequency band.