基于直接算法的虚拟式小波变换信号分析仪

A Virtual Wavelet Transform Analyzer for the Signal Analysis Based on the Direct Algorithm

介绍了作者研制开发的一台基于直接算法的虚拟式小波变换信号分析仪 ,从而实现了用直接算法对信号进行离散小波变换和连续小波变换的功能。介绍了小波变换的直接算法公式 ,即由小波变换的原始公式通过直接数值化方法获得的数值算法公式。作者通过研究获得了直接算法中的一些结论 ,如离散小波变换直接算法中对小波的采样原理和技术、小波尺度范围的限定 ,边缘现象的解决措施 ,以及连续小波变换直接算法中的一些结论。基于这些研究 ,结合虚拟仪器技术开发出的基于直接算法的虚拟式小波变换信号分析仪能用任何母小波对信号进行离散小波变换和连续小波变换。它即可用于对母小波的研究和对小波理论的学习 ,也可用于一些工程信号分析。给出了分析仪应用的几个典型例子 ,表明本文的分析仪在许多情况下可以获得应用。

A virtual wavelet transform analyzer for the signal analysis based on the direct algorithm is introduced so that the discrete wavelet transform and continuous wavelet transform is maken to signal in the direct algorithm. The authors first introduce the direct algorithm of the WT, which is numerical algorithm obtained from the original formula of the wavelet transform by directly numericalizing. Then some conclusions are drawn on the direct algorithm. The examples are the sampling principle and technology for the wavelets, the limitation of the scale range of the wavelets and the measures to solve the edge phenomenal in the direct algorithm of the discrete wavelet transform, and some conclusions in the direct algorithm of the continuous wavelet transform. The virtual wavelet transform analyzer for the signal analysis based on the direct algorithm explored based on these studies and combined with virtual instrument technique can make the discrete wavelet transform and continuous wavelet transform to signal with any basic wavelet. It can be applied in studying the property of any basic wavelet and learning the theory on the wavelet transform, and also in making some engineering signal analysis. In the end, the authors give some typical examples for the application of the virtual analyzer. These examples show that the analyzer can be applied in many situations.