消除信号趋势项时小波基优选方法研究

在消除信号趋势项时引入小波基函数对信号进行分解和重构.小波基函数的选择会影响消除信号趋势项后的结果.提出了消趋误差指数的概念及其计算公式,并使用该公式计算了34种常用小波基的消趋误差指数,优选出sym10等6种消趋误差指数较小的小波基.使用sym10小波基及另外两种非优选小波基对实测的汽车车身振动加速度信号进行消除趋势项处理.结果表明,使用sym10小波基提取的信号趋势项比其它非优选小波基更为准确,验证了提出的消趋误差指数计算公式的有效性. 

Optimal Selection of Wavelet Base Functions for Eliminating Signal Trend Based on Wavelet Analysis

To eliminate the signal trend terms, wavelet base functions are introduced for signal decomposition and reconstruction. The selection of wavelet bases may affect the result of eliminating signal trend. The concept of error index of signal trend elimination was proposed and the formula for calculating the index was presented. Using this formula, the error indexes of signal trend elimination of 34 types of wavelet bases were calculated. It was found that the wavelet bases of sym10 and other 5 types could be selected as preferred ones with less error indexes of signal trend elimination. Further, the sym10 and other two non-preferred wavelet bases were used to carry out the signal trend elimination of measured car body acceleration signal. The result shows that wavelet base of sym10 extracts the signal trend more precisely than other two non-preferred wavelet bases and the effectiveness of the presented formula for calculating the error index of signal trend elimination is validated.