连续子波变换数值实现中尺度采样间隔的确定

Determination of Scale Sample Step for Getting Numerical Result of the Continuous Wavelet Transform

为了确定连续小波变换数值实现中各种母波相应尺度采样间隔的最佳值,按照数字信号序列的最高数字频率等于或小于π的两种情况,论证了均匀点格采样时连续子波变换数值实现中Morelet母波以及偶对称或奇对称的各阶高斯函数导数解析母波的尺度采样间隔的最佳取值,奇对称母波数值实现中同时所需的时间平移量,偶对称或奇对称的各阶高斯函数导数解析母波的相应数字滤波器的波动情况。本结果应用于信号小波分析的工程实现和理论研究,试验结果与理论结论完全符合。

In order to determine the best corresponding scale-sampling step among the mother waves, the paper discusses, in light of the two cases when the biggest angle frequency of digital signal series is equal to or smaller than π, the best result of analytical mother wave of differential coefficient of all phases Gauss function of Morlet and even or odd symmetrical mother wave in continuous wavelet transforming when equality dot-grid sampling is adopted, and the time parallel moving required by getting numerical result of odd symmetrical mother wave, and the waving conditions of corresponding digital filter of analytical mother wave of Gauss function's differential coefficient of even or odd symmetric mother wave. The conclusion has been put in use in the field of engineering and research work of signal wavelet analyses, and the feedback result is confirmed with theoretically deduced result.