中文摘要：

探讨将Vilenkin群上的小波理论运用到实际信号分析的算法,根据实际需要重新定义Vilenkin群的二元运算,引入经典的尺度函数和小波函数,在此基础上建立相应的多分辨分析,分析了定义在它上面的信号,运用多分辨分析的特性得到信号分解和重构的算法.进一步给出了康托尔二元群上信号分解和重构的具体算法,得到了Vilenkin群上信号的分解定理和重构定理.

英文摘要：

Aim to study the algorithm which apply the wavelet theory to the actual signal analysis.According to the actual needs,the dyadic operation on Vilenkin groups is redefined.Then by leading the scaling function and wavelet functions into the Vilenkin groups,the multiresolution analysis is built up.In the followings,the algorithm of decomposition and reconstruction for signals are put foward through analogy and analysis.What＇s more,the algorithm for signals on the Cantor group is demonstratively given.And the decomposition theorem and reconstruction theorem of the signal on the Vilenkin group are obtained.