线性时变系统参数辨识的小波基函数展开

Expansion of Wavelet Basis Functions for Parameters Identification of Linear Time Varying System

运用信号的基函数展开方法,以时变参数的AR模型为研究对象,采用具有时频局部特性的小波分解和重构滤波器作为基函数,获得对模型时变参数的辨识算法.利用周期延拓对信号边缘进行处理.忽略部分高频小波系数以克服小波重构层数对线性方程组求解的制约问题,获得模型阶数与最小重构层数的关系.研究发现,方法对时变参数的变化趋势及频率特征辨识有效,提高采样率可以改善被忽略的高频成分的影响,有助于辨识快变及瞬变参数的高频特征.

By applying basis-functions expansion that uses wavelet decomposition and reconstruction filters and is rich in local time-frequency features, we introduce a novel algorithm identifying time varying parameters in TV-AR model. A periodical extension method for processing two terminals of signals is implemented. Some high frequency coefficients in the wavelet decomposition are neglected to overcome the restriction in solving linear equations by layer number of wavelet reconstruction and the relationship between the model order and the minimal layer nmnber of wavelet reconstruction. Research shows that the algorithm is effective in identifying the trend and frequency features of time-varying parameters. Increasing the sampling rate can reduce the effect of the neglected high frequency component, which is helpful to the identification the high frequency features of fast and instantaneous change signal.