小波变换的局部谱特征

小波变换因其固有的多分辨能力而受到人们的青睐，但其变换结果却缺乏直观的物理意义。笔者经过一系列的推导，揭示出实信号的实小波变换结果缺乏直观性的根源。进而指出，以复解析小波为母小波的尺度图具有直观的物理意义，它反映的就是信号的局部频谱信息。据此，就几种典型信号给出了以实小波及复解析小波为母小波时的尺度图比较。结果表明，由复解析小波交换所得尺度图也更有利于信号瞬变时刻的准确定位。

Local Spectral Characteristics of Wavelet Transform

Wavelt transform enjoys multi-resolution property that endears it to the signal processing community. However, the result obtained lacks intuitive physical meaning. This paper unveils the reason why the results (referred to as R-scalogram) produced by real wavelet transform of a real signal is not intuitive. Then it points out that the scalogram (referred to as C-scalogram) provided by analytic one has intuitive physical meaning. It characterizes the local spectrum of signal under analysis. Finally, comparison between the C-scalograms and R-scalograms of several typical signals is performed. It shows that C-scalogram is also more appropriate for detection and localization of transient phenomena than R-scalogram.