Research on the selection of wavelet bases for wavelet-based signal trend elimination

The accuracy and effectiveness of wavelet analysis for signal trend elimination could be associated with the selection of wavelet bases. A new concept named detrending error exponent (DEE) is presented and the formula for calculating the DEE is proposed. The DEE that includes global error item and part error item reflects the capability of the wavelet bases function on signal trend elimination. For different wavelet bases adopted to detrend based wavelet, the values of DEE are also different and the wavelet bases with less DEE means more suitable to eliminate signal trend. Based on a simulated signal with defined trend, the DEE values of 34 general wavelet bases are calculated by using proposed formulas with same weights of global error and part error, and top 8 wavelet bases with the least integrated DEE are selected as preferred wavelet bases. For validating the result of selection, one preferred wavelet bases 'sym10' and two non-preferred wavelet bases are applied to detrend an acceleration data measured from a car body and then compared with each other. For further analysis, the integrated DEE values of 8 preferred wavelet bases are recalculated with different weights of global error and part error. The comparison of calculating result shows that the different weights of global error and part error cause the DEE values of 8 preferred wavelet bases changed, but their rank place remain unchanged. Considering the change on the components of simulated signal trend, namely the proportion of linear trend, sine trend and nonlinear trend, the DEE values of 8 preferred wavelet bases are recalculated and compared again. The result shows that the rank of 8 preferred wavelet bases is unchanged when sine trend is adjusted but changed obviously when nonlinear trends is adjusted.