【摘要】 Wavelet是基于MATLAB的一个重要应用软件包。但在利用Wavelet对于一些典型信号 ,如正弦信号、δ 信号进行连续小波变换 (CWT)时 ,却出现一些与常识不相符的“异常”图象。针对这个问题 ,利用Morlet小波基 ,从连续小波变换基本公式出发 ,通过数学上的严格推证 ,指出了这些特殊图象的形成原因 ,分析了小波变换所体现的“数学显微镜”的特点 ,并得到一个有趣的结论 :只有当小波Morlet小波基的振荡频率略微小于正弦信号的振荡频率时 ,才会达到小波变换的最大值更多还原

【Abstract】 Wavelet is an important software package based on MATLAB.However some “strange”images occur when such typical signals as sin (x) and δ(x) using continuous wavelet transform (CWT) are analyzed based on wavelet.Making use of Morlet wavelet basis and considering the continuous wavelet transform,a strict mathematical derivation is presented,an explanation to the formation of these “strange”images is given,and and the characteristics of wavelet transform are analyzed.Finally,an interesting fact is pointed out,i.e,only when the frequency of Morlet wavelet basis is slightly less than the frequency of sin(x),the maximum value of wavelet transform can be obtained.更多还原