Realization of decomposition and reconstructionalgorithms for discrete orthogonal wavelets
离散空间中正交小波分解重构算法的实现

In view of the complex process of the current algorithms, this paper mainly studied the realization of decomposition and reconstruction algorithms for periodic and nonperiodic wavelets in discrete spaces. Firstly, one proved that the multilevel algorithms could be realized by pyramid frame as Mallat algorithms, which connected the wavelet theory of the discrete sequence spaces to that of the function spaces. Then, it took an example to show that the decomposition and reconstruction algorithms in discrete spaces were more flexible than Mallat algorithms in function spaces. Finally, numerical experiments show better effects of discrete wavelets in some applications of signal processing .