To cope with the differences of seismic and logging data in terms of time,phase,frequency and amplitude,we discussed resample of well data and multi-resolution decomposition of synthetic seismogram and seismic traces nearby borehole by using Mallat's algorithm.

The principle of wavelet transform s algorithm of Mallat is discussed in this paper,and then the realization of fast algorithm of wavelet transform is introduced.

Based on the MALLAT arithmetic,which is important part of wavelet theory,we put an quick realization method and use it in yawp active control.

Border extension in the implementation of Mallat Algorithm;

Initialization of Mallat algorithm;

Optical implementation of Mallat algorithm;

Secondly,we use Mallat method to reconstruct the signal by a few value of given signal.

In this paper,firstly,we use one dimensional parameter orthogonal wavelet filters to approach a double orthogonal wavelet filters,secondly,we use Mallat method to reconstruct the signal by a few value of given signal,finally,we use an example to show our algorithm.

In the paper,the low-frequency information which reflects the trend of stock price change is extracted using wavelet MRA and the Mallat method,and the time of stockjobbing is analyzed.