基于小波变换的采样问题研究

Study on Sampling Problem Based on Wavelet Transform

香农曾提出时域采样定理,满足一定条件下对原始模拟信号进行采样,再用离散点的取值和插值公式的线性组合可以重建出原信号,此后香农等人又提出非均匀采样定理。文章用小波变换这种新型研究信号处理的工具来研究采样问题,并以最典型的Harr小波为例进行分析,论证说明小波采样升维分析降低了对香农采样定理中要求是带限连续信号要求,而只要求信号为一平方可积函数即可。

Shannon has proposed the time domain sampling theorem. The original signal can be rebuilt bysampling the original analog signals under certain conditions, and using the values of discrete points and thelinear combination of the interpolation formula. After that, Shannon et al. proposed a nonuniform samplingtheorem. In this paper, a new signal processing tool is used to study the sampling problem by using thewavelet transform. The analysis of the most typical Harr wavelets is taken as an example. It is demonstratedthat the wavelet sampling and ascending dimension analysis reduces the requirement of the Shannon samplingtheorem, which only requires the signal to bea square integrable function.