Research On Computational Problems Of Signal Initialization In Multiresolution Analysis

This article discusses the computational problems of signal initialization in MRA with Daubechies scaling function.We first obtain an equivalence relation between the stable sampling points and the frame.Then,in the numerical experiment,we not only find the reason that the condition number of the coefficient matrix is too large in the problem of correspondence calculation,especially the larger the support set of the selected Daubechies scaling function,the bigger the conditional number will be,but also give the corresponding improvement methods.At the same time,the relationship between the sampling interval and the condition number of coefficient matrix is analyzed.It is shown that the sampling point is not the denser the better.Finally,two concrete examples are given to illustrate the difference of approximation in different approximate spaces between stationary signal and high frequency signal.